Nothing
R/TrapezoidalFuzzyNumberList.R
In FuzzyStatTraEOO: Package 'FuzzyStatTra' in Encapsulated Object Oriented Programming
#' @title 'TrapezoidalFuzzyNumberList' is a child class of 'StatList'.
#'
#' @description
#' 'TrapezoidalFuzzyNumberList' must contain valid 'TrapezoidalFuzzyNumbers'.
#' This class implements a version of the empty 'StatList' methods.
#'
#' @note In case you find (almost surely existing) bugs or have recommendations
#' for improving the method, comments are welcome to the above mentioned mail addresses.
#'
#' @author(s) Andrea Garcia Cernuda <uo270115@uniovi.es>, Asun Lubiano <lubiano@uniovi.es>,
#' Sara de la Rosa de Saa
#'
#' @references
#' [1] De la Rosa de Saa, S.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano M.A.: Fuzzy
#' rating scale-based questionnaires and their statistical analysis, IEEE Transactions on
#' Fuzzy Systems 23(1), 111-126 (2015)
#'
#' [2] De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: Robust scale
#' estimators for fuzzy data, Advances in Data Analysis and Classification 11(4), 731-758 (2017)
#'
#' [3] De la Rosa de Sáa, S.; Lubiano, M.A.; Sinova, B.; Filzmoser, P.; Gil, M.Á.: Location-free
#' robust scale estimates for fuzzy data, IEEE Transactions on Fuzzy Systems 29(6), 1682-1694 (2021)
#'
#' [4] Lubiano, M.A.; Gil, M.A.: f-Inequality indices for fuzzy random variables, in Statistical
#' Modeling, Analysis and Management of Fuzzy Data (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.),
#' Physica-Verlag, 43-63 (2002)
#'
#' [5] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis
#' testing for means in connection with fuzzy rating scale-based data: algorithms and
#' applications, European Journal of Operational Research 251, 918-929 (2016)
#'
#' [6] Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy
#' numbers for an approach to central tendency of fuzzy data, Information Sciences 242,
#' 22-34 (2013)
#'
#' [7] Sinova, B.; De la Rosa de Saa, S.; Lubiano, M.A.; Gil, M.A.: An overview on the statistical
#' central tendency for fuzzy datasets, International Journal of Uncertainty, Fuzziness and
#' Knowledge-Based Systems 23 (Suppl. 1), 105-132 (2015)
#'
#' [8] Sinova, B.; Gil, M.A.; Colubi, A.; Van Aelst, S.: The median of a random fuzzy number. The
#' 1-norm distance approach, Fuzzy Sets and Systems 200, 99-115 (2012)
#'
#' [9] Sinova, B.; Gil, M.A.; Lopez, M.T.; Van Aelst, S.: A parameterized L2 metric between fuzzy
#' numbers and its parameter interpretation, Fuzzy Sets and Systems 245, 101-115 (2014)
#'
#' [10] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central
#' tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)
#'
#' @import R6
#'
#' @export TrapezoidalFuzzyNumberList
TrapezoidalFuzzyNumberList <- R6::R6Class(
classname = "TrapezoidalFuzzyNumberList",
inherit = StatList,
private = list (
# numbers is a collection of trapezoidal fuzzy numbers.
numbers = NULL,
# auxiliary method used in the dthetaphi public method
# x is a vector, a and b are the parameters of the dthetaphi public method
integrand = function(x = NA,
a = NA,
b = NA) {
return (x * dbeta(x, a, b))
},
# auxiliary method used in the dthetaphi public method
# x is a vector, a and b are the parameters of the dthetaphi public method
integrandsq = function(x = NA,
a = NA,
b = NA) {
return (x ^ 2 * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
inf = function(x = NA,
i = NA,
list = NA) {
return (
list$getDimension(i)$getInf0() + x * (
list$getDimension(i)$getInf1() - list$getDimension(i)$getInf0()
)
)
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
sup = function(x = NA,
i = NA,
list = NA) {
return (
list$getDimension(i)$getSup0() + x * (
list$getDimension(i)$getSup1() - list$getDimension(i)$getSup0()
)
)
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
mid = function(x = NA,
i = NA,
list = NA) {
return ((private$inf(x, i, list) + private$sup(x, i, list)) / 2)
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i is an integer and list is a TrapezoidalFuzzyNumberList
integrandWabl = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$mid(x, i, list) * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public function
# a and b are the parameters of the dwablphi public function
# i is an integer and list is a TrapezoidalFuzzyNumberList
wabl = function(i = NA,
list = NA,
a = NA,
b = NA) {
return (integrate(
private$integrandWabl,
0,
1,
i = i,
list = list,
a =
a,
b = b
)$val)
},
# auxiliary method used in the dwablphi public function
# x is a vector, i is an integer, a and b are the parameters of the dwablphi public function
# list is a TrapezoidalFuzzyNumberList
ldev = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$wabl(i, list, a, b) - private$inf(x, i, list))
},
# auxiliary method used in the dwablphi public function
# x is a vector, i is an integer, a and b are the parameters of the dwablphi public function
# list is a TrapezoidalFuzzyNumberList
rdev = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$sup(x, i, list) - private$wabl(i, list, a, b))
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i and j are integers, list1 and list2 are TrapezoidalFuzzyNumberLists
integrand1 = function(x = NA,
i = NA,
j = NA,
list1 = NA,
list2 = NA,
a = NA,
b = NA) {
return (abs(
private$ldev(x, i, list = list1, a, b) - private$ldev(x, i = j, list =
list2, a, b)
) * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i and j are integers, list1 and list2 are TrapezoidalFuzzyNumberLists
integrand2 = function(x = NA,
i = NA,
j = NA,
list1 = NA,
list2 = NA,
a = NA,
b = NA) {
return (abs(
private$rdev(x, i, list = list1, a, b) - private$rdev(x, i = j, list =
list2, a, b)
) * dbeta(x, a, b))
},
# auxiliary method used in the mEstimator public function
# x is a vector and f is the name of the loss function
weight = function(x = NA,
f = NA) {
rho <- 0
rhod <- 0
w <- 0
if (f == "Huber") {
# Huber M-estimator
rho <- min(x ^ 2, 1)
rhod <- 2
} else if (f == "Tukey") {
# Tukey M-estimator
rho <- min(3 * x ^ 2 - 3 * x ^ 4 + x ^ 6, 1)
rhod <- 6
} else if (f == "Cauchy") {
# Cauchy M-estimator
rho <- x ^ 2 / (x ^ 2 + 1)
rhod <- 2
}
if (x == 0) {
w <- rhod
} else {
w <- rho / x ^ 2
}
return(w)
},
# auxiliary method used in the gsi, hyperI, mean, medianWabl, transfTra and
# wablphi public functions
extractMatrix = function() {
F <- matrix(ncol = 4)
for (i in 1:private$dimensions) {
F <-
rbind(
F,
c(
private$numbers[[i]]$getInf0(),
private$numbers[[i]]$getInf1(),
private$numbers[[i]]$getSup1(),
private$numbers[[i]]$getSup0()
)
)
}
return (F)
}
),
public = list(
#' @description
#' This method creates a 'TrapezoidalFuzzyNumberList' object with all the attributes
#' set if the 'TrapezoidalFuzzyNumbers' are valid.
#'
#' @param numbers is a list which contains n TrapezoidalFuzzyNumbers.
#'
#' @details See examples.
#'
#' @return The TrapezoidalFuzzyNumberList object created with all attributes
#' set if the 'TrapezoidalFuzzyNumbers' are valid.
#'
#' @examples
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1, 2, 3, 4),
#' TrapezoidalFuzzyNumber$new(-8, -6, -4, -2),
#' TrapezoidalFuzzyNumber$new(-1, -1, 2, 3),
#' TrapezoidalFuzzyNumber$new(1, 2, 3, 3)))
initialize = function(numbers = NA) {
stopifnot(is.list(numbers))
for (val in 1:length(numbers)) {
stopifnot(class(numbers[[val]])[1] == "TrapezoidalFuzzyNumber")
}
private$rows <- 1
private$columns <- 4
private$dimensions <- length(numbers)
private$numbers <- numbers
},
#' @description
#' This method calculates the scale measure Average Distance Deviation (ADD)
#' of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList'
#' or with respect to a 'FuzzyNumberList' containing a unique valid fuzzy number.
#' The employed metric in the calculation can be the 1-norm distance, the mid/spr
#' distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2017) [2].
#'
#' @param s is a TrapezoidalFuzzyNumberList containing a unique valid TrapezoidalFuzzyNumber
#' or it is a FuzzyNumberList containing a unique valid FuzzyNumber.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure ADD, which is a real number. If the body's method
#' inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' S=F$mean()
#' F$add(S,1L)
#'
#' # Example 5:
#' F=Simulation$new()$simulCase1(100L)
#' S=F$median1Norm()
#' F$add(S,2L,2,1,1)
#'
#' # Example 6:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(1L)
#' F$add(U,2L)
#'
#' # Example 7:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$transfTra()
#' F$add(U,2L)
#'
#' # Example 8:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(2L)
#' F$add(U,2L)
add = function(s = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[2] == "StatList")
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
if (s$getLength() == 1) {
u <- NULL
if (class(s)[1] == "FuzzyNumberList") {
u <-
self$transfTra(as.integer(nrow(
s$getDimension(1L)$getAlphaLevels()
)))
} else{
# class(s)[1] == "TrapezoidalFuzzyNumberList"
u <- self
}
add <- 0
if (type == 1) {
add <- mean(s$rho1(u))
} else if (type == 2) {
add <- mean(s$dthetaphi(u, a, b, theta))
} else{
# type == 3
add <- mean(s$dwablphi(u, a, b, theta))
}
return (add)
}
return (NA)
},
#' @description
#' This method calculates the mid/spr distance between the 'TrapezoidalFuzzyNumbers'
#' contained in the current object and the one passed as parameter.
#' See Lubiano et al. (2016) [5].
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance.
#'
#' @details See examples.
#'
#' @return a matrix containing the mid/spr distances between the two previous
#' mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
#' TrapezoidalFuzzyNumberList$new( c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),1,1,1)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(6L)
#' S=Simulation$new()$simulCase1(8L)
#' F$dthetaphi(S,1,5,1)
dthetaphi = function(s = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
super$dthetaphi(s, a, b, theta)
r <- private$dimensions
p <- s$getLength()
c <- matrix(nrow = r, ncol = p)
d <- matrix(nrow = r, ncol = p)
e <- matrix(nrow = r, ncol = p)
f <- matrix(nrow = r, ncol = p)
dthetaphicua <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
c[i, j] <-
((
private$numbers[[i]]$getInf0() + private$numbers[[i]]$getSup0()
) -
(
s$getDimension(j)$getInf0() + s$getDimension(j)$getSup0()
)
) / 2
d[i, j] <-
((
private$numbers[[i]]$getSup0() - private$numbers[[i]]$getInf0()
) -
(
s$getDimension(j)$getSup0() - s$getDimension(j)$getInf0()
)
) / 2
e[i, j] <-
((
private$numbers[[i]]$getInf1() + private$numbers[[i]]$getSup1()
) -
(
s$getDimension(j)$getInf1() + s$getDimension(j)$getSup1()
)
) / 2 - c[i, j]
f[i, j] <-
((
private$numbers[[i]]$getSup1() - private$numbers[[i]]$getInf1()
) -
(
s$getDimension(j)$getSup1() - s$getDimension(j)$getInf1()
)
) / 2 - d[i, j]
dthetaphicua[i, j] <-
c[i, j] ^ 2 + theta * d[i, j] ^ 2 +
(e[i, j] ^ 2 + theta * f[i, j] ^ 2) * integrate(private$integrandsq, 0, 1, a =
a, b = b)$val +
2 * (c[i, j] * e[i, j] + theta * d[i, j] * f[i, j]) * integrate(private$integrand, 0, 1, a =
a, b = b)$val
}
}
dthetaphi <- sqrt(dthetaphicua)
return(dthetaphi)
},
#' @description
#' This method calculates the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance
#' between the 'TrapezoidalFuzzyNumbers' contained in two 'TrapezoidalFuzzyNumberLists'.
#' See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' ldev and rdev in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return a matrix containing the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distances
#' between the two previous mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),5,1,1)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(10L)
#' S=Simulation$new()$simulCase1(20L)
#' F$dwablphi(S)
dwablphi = function(s = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
super$dwablphi(s, a, b, theta)
r <- private$dimensions
p <- s$getLength()
wablR <- vector()
wablS <- vector()
dwablphi <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
int1 <-
integrate(
private$integrand1,
0,
1,
i = i,
j = j,
list1 = self,
list2 = s,
a = a,
b = b
)$val
int2 <-
integrate(
private$integrand2,
0,
1,
i = i,
j = j,
list1 = self,
list2 = s,
a = a,
b = b
)$val
dwablphi[i, j] <-
abs(private$wabl(i, list = self, a, b) - private$wabl(i =
j, list = s, a, b)) + (theta /
2) * int1 + (theta / 2) * int2
}
}
return (dwablphi)
},
#' @description
#' This method calculates the Gini-Simpson diversity index for a sample of
#' 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'.
#' See De la Rosa de Saa et al. (2015) [1].
#'
#' @details See examples.
#'
#' @return the Gini-Simpson diversity index, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$gsi()
#'
#' # Example 2:
#' F=Simulation$new()$simulCase1(50L)
#' F$gsi()
gsi = function() {
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
U <-
unique(F) # deletes the equal rows (equal fuzzy numbers)
u <-
nrow(U) # number of different fuzzy numbers in the matrix F
fr = vector(length = u) # relative frequency of each fuzzy number of the matrix U
for (i in 1:u) {
cont <- 0
for (j in 1:n) {
if (sum(U[i,] == F[j,]) == ncol(F))
cont <- cont + 1
}
fr[i] <- cont / n
}
gini <- 1 - sum(fr ^ 2)
return(gini)
},
#' @description
#' This method calculates the hyperbolic inequality index for a sample of
#' 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'.
#' The method checks if all 'TrapezoidalFuzzyNumbers' are positive.
#' See De la Rosa de Saa et al. (2015) [1] and Lubiano and Gil (2002) [4].
#'
#' @param c number in [0,0.5]. The c*100% trimmed mean will be used in the calculation
#' of the hyperbolic inequality index.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return the hyperbolic inequality index, which is a real number. If the body's
#' method inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI(0.5)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,4,6,8)))$hyperI()
#'
#' # Example 4:
#' F=Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)
#' F$hyperI()
#'
#' # Example 5:
#' F=Simulation$new()$simulCase2(10L)
#' F$hyperI(0.5)
hyperI = function(c = 0, verbose = TRUE) {
stopifnot(is.double(c) && c >= 0 && c <= 0.5)
for (i in 1:private$dimensions) {
if (!private$numbers[[i]]$is_positive()) {
if (verbose) {
print("all the fuzzy numbers should be positive")
}
return (NA)
}
}
F <- private$extractMatrix()
n <- nrow(F)
l <- vector()
fmean <-
apply(F[2:n,], 2, mean, trim = c) # mean of the trapezoidal fuzzy numbers
a1 = fmean[3] - fmean[4]
b1 = fmean[4]
a2 = fmean[2] - fmean[1]
b2 = fmean[1]
for (i in 2:n) {
c1 = F[i, 2] - F[i, 1]
d1 = F[i, 1]
c2 = F[i, 3] - F[i, 4]
d2 = F[i, 4]
if ((abs(c1) <= .Machine$double.eps) &
(abs(c2) <= .Machine$double.eps))
l[i] = (1 / d1) * (a1 / 2 + b1) + (1 / d2) * (a2 / 2 + b2)
else if ((abs(c1) <= .Machine$double.eps) &
(abs(c2) > .Machine$double.eps))
l[i] = (1 / d1) * (a1 / 2 + b1) + a2 / c2 + (b2 - ((a2 * d2) /
c2)) * (1 / c2) * (log(abs(c2 + d2)) - log(abs(d2)))
else if ((abs(c1) > .Machine$double.eps) &
(abs(c2) <= .Machine$double.eps))
l[i] = a1 / c1 + (b1 - ((a1 * d1) / c1)) * (1 / c1) * (log(abs(c1 +
d1)) - log(abs(d1))) + (1 / d2) * (a2 / 2 + b2)
else if ((abs(c1) > .Machine$double.eps) &
(abs(c2) > .Machine$double.eps))
l[i] = a1 / c1 + (b1 - ((a1 * d1) / c1)) * (1 / c1) * (log(abs(c1 +
d1)) - log(abs(d1))) + a2 / c2 + (b2 - ((a2 * d2) / c2)) * (1 / c2) * (log(abs(c2 +
d2)) - log(abs(d2)))
}
hyper = (1 / 2) * mean(l[2:length(l)], trim = c) - 1
return(hyper)
},
#' @description
#' This method calculates the M-estimator of scale with loss method given
#' in a 'TrapezoidalFuzzyNumberList' containing 'TrapezoidalFuzzyNumbers'.
#' For computing the M-estimator, a method called “iterative reweighting” is
#' used. The employed metric in the M-equation can be the 1-norm distance, the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @param f is the name of the loss function. It can be "Huber", "Tukey" or "Cauchy".
#' @param estInitial real number > 0.
#' @param delta real number in (0,1). It is present in the f-equation.
#' @param epsilon real number > 0. It is the tolerance allowed in the algorithm.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the value of the M-estimator of scale, which is a real number.
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Huber",0.321,0.5,10^(-5),
#' 1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Tukey",0.123,0.5,10^(-5),
#' 2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Cauchy",0.123,0.5,10^(-5),
#' 3L,0.75,0.5,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(100L)
#' U=F$median1Norm()
#' estInitial=F$mdd(U,1L)
#' delta=0.5
#' epsilon=10^(-5)
#' F$mEstimator("Huber",estInitial,delta,epsilon,1L)
mEstimator = function(f = NA,
estInitial = NA,
delta = NA,
epsilon = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(f) == "character" &&
(f == "Huber" || f == "Tukey" || f == "Cauchy"))
stopifnot(typeof(estInitial) == "double" && estInitial > 0)
stopifnot(typeof(delta) == "double" && delta > 0 && delta < 1)
stopifnot(typeof(epsilon) == "double" && epsilon > 0)
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(estInitial) ||
is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
x <-
matrix() # distances between the numbers of F and the number 0
t <-
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0, 0, 0, 0)))
if (type == 1) {
# metric Rho1
x <- self$rho1(t)
}
else if (type == 2) {
# metric Dthetaphi
x <- self$dthetaphi(t, a, b, theta)
}
else if (type == 3) {
# metric Dwablphi
x <- self$dwablphi(t, a, b, theta)
}
# Iterative algorithm:
n <- private$dimensions
k <- 1
sigma <- vector()
sigma[k] <- estInitial
omega <- vector(length = n)
repeat {
for (j in 1:n) {
omega[j] <- private$weight((x[j] / sigma[k]), f)
}
k <- k + 1
sigma[k] <- sqrt((1 / (n * delta)) * sum(omega * x ^ 2))
if ((abs(sigma[k] / sigma[k - 1] - 1) < epsilon) |
(sigma[k] < 10 ^ (-10))) {
break
}
}
return (sigma[length(sigma)]) # last sigma
},
#' @description
#' This method calculates the scale measure Median Distance Deviation (MDD)
#' of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList'
#' or with respect to a 'FuzzyNumberList' with a unique valid fuzzy number.
#' The employed metric in the calculation can be the 1-norm distance, the mid/spr
#' distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2015) [2] and De la Rosa de Saa et al. (2021) [3].
#'
#' @param s is a TrapezoidalFuzzyNumberList containing a unique TrapezoidalFuzzyNumber
#' or it is a FuzzyNumberList containing a unique FuzzyNumber.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure MDD, which is a real number.If the body's
#' method inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase3(10L)
#' U=F$mean()
#' F$mdd(U,3L,1,2,1)
#'
#' # Example 5:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$median1Norm()
#' F$mdd(U,2L)
#'
#' # Example 6:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(1L)
#' F$mdd(U,2L)
#'
#' # Example 7:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$transfTra()
#' F$mdd(U,2L)
#'
#' # Example 8:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(2L)
#' F$mdd(U,2L)
mdd = function(s = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[2] == "StatList")
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
if (s$getLength() == 1) {
u <- NULL
if (class(s)[1] == "FuzzyNumberList") {
u <-
self$transfTra(as.integer(nrow(
s$getDimension(1L)$getAlphaLevels()
)))
} else{
# class(s)[1] == "TrapezoidalFuzzyNumberList"
u <- self
}
mdd <- 0
if (type == 1) {
mdd <- median(s$rho1(u))
} else if (type == 2) {
mdd <- median(s$dthetaphi(u, a, b, theta))
} else{
# type == 3
mdd <- median(s$dwablphi(u, a, b, theta))
}
return (mdd)
}
return (NA)
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the Aumann-type mean of these numbers (which is a
#' 'TrapezoidalFuzzyNumber' too).
#' See Sinova et al. (2015) [7].
#'
#' @details See examples.
#'
#' @return the Aumann-type mean, given as a TrapezoidalFuzzyNumber contained in
#' a TrapezoidalFuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mean()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(
#' c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$mean()
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(100L)
#' F$mean()
mean = function() {
F <- private$extractMatrix()
m <-
t(as.matrix(apply(F[2:nrow(F),], 2, mean)))
return(TrapezoidalFuzzyNumberList$new(c(
TrapezoidalFuzzyNumber$new(m[1, 1], m[1, 2], m[1, 3], m[1, 4])
)))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the 1-norm median of these numbers, characterized
#' by means of nl equidistant \eqn{\alpha}-levels (by default nl=101), including
#' always the 0 and 1 levels, with their infimum and supremum values.
#' See Sinova et al. (2012) [8].
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the 1-norm median.
#'
#' @details See examples.
#'
#' @return the 1-norm median, given in form of a FuzzyNumber contained in a
#' FuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm(200L)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(10L)
#' F$median1Norm(200L)
median1Norm = function(nl = 101L) {
stopifnot(is.integer(nl) && nl >= 2)
# transforms the current TrapezoidalFuzzyNumberList into a FuzzyNumberList
fuzzyArray <- self$transfTra(nl)
alpha <- seq(0, 1, len = nl) # alpha-levels
result <- array(dim = c(nl, 3, 1))
l <- fuzzyArray$getLength()
F <- array(dim = c(nl, 3, l))
for (i in 1:l) {
F[, 2, i] <- fuzzyArray$getDimension(i)$getInfimums()
F[, 3, i] <- fuzzyArray$getDimension(i)$getSupremums()
}
result[, 1, 1] = alpha
result[, 2, 1] = apply(F[, 2,], 1, median) # second column: medians of the infimum
# values of each alpha-level
result[, 3, 1] = apply(F[, 3,], 1, median) # third column: medians of the supremum
# values of each alpha-level
return(FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(result[, 1, 1], result[, 2, 1], result[, 3, 1]), dim = c(length(result[, 1, 1]), 3)
)))))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the \eqn{\phi}-wabl/ldev/rdev median of these numbers,
#' characterized by means of nl equidistant \eqn{\alpha}-levels (by default nl=101),
#' including always the 0 and 1 levels, with their infimum and supremum values.
#' See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the \eqn{\phi}-wabl/ldev/rdev
#' median.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#'
#' @details See examples.
#'
#' @return the \eqn{\phi}-wabl/ldev/rdev median in form of a FuzzyNUmber given
#' in a FuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L,2.2,2.8)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$medianWabl(3L)
medianWabl = function(nl = 101L,
a = 1,
b = 1) {
stopifnot(is.integer(nl) && nl >= 2)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
if (is.infinite(a) || is.infinite(b)) {
stop("The parameters cannot be Inf neither -Inf.")
}
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
wablF <- vector()
medianldev <- vector()
medianrdev <- vector()
for (i in 1:n) {
wablF[i] <- private$wabl(i, list = self, a, b)
}
medianwabl <- median(wablF)
alpha <- seq(0, 1, len = nl) # alpha-levels
median <- array(dim = c(nl, 3, 1))
median[, 1, 1] <- alpha # first column: alpha-levels
for (j in 1:nl) {
ldevF <- wablF - (F[, 1] + alpha[j] * (F[, 2] - F[, 1]))
medianldev[j] <- median(ldevF)
rdevF <- F[, 4] + alpha[j] * (F[, 3] - F[, 4]) - wablF
medianrdev[j] <- median(rdevF)
}
median[, 2, 1] <- medianwabl - medianldev # second column
median[, 3, 1] <- medianwabl + medianrdev # third column
return(FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(median[, 1, 1], median[, 2, 1], median[, 3, 1]), dim = c(length(median[, 1, 1]), 3)
)))))
},
#' @description
#' This method calculates scale measure Qn for a matrix of 'TrapezoidalFuzzyNumbers'
#'contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Qn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(2L,5,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$qn(3L,1,1,1)
qn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
distMitad <- 0
if (type == 1) {
rho1 <- self$rho1(self)
distMitad <-
rho1[lower.tri(rho1)] # upper triangle of the matrix rho1
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
distMitad <-
dthetaphi[lower.tri(dthetaphi)] # upper triangle of the matrix dthetaphi
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
distMitad <-
dwablphi[lower.tri(dwablphi)] # upper triangle of the matrix dwablphi
}
return (sort(distMitad)[choose(floor(n / 2) + 1, 2)])
},
#' @description
#' This method calculates the 1-norm distance between the 'TrapezoidalFuzzyNumbers'
#' contained in two 'TrapezoidalFuzzyNumberLists'.
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#'
#' @details See examples.
#'
#' @return a matrix containing the 1-norm distances between the two previous
#' mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$rho1(TrapezoidalFuzzyNumberList$new(
#' c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' F=Simulation$new()$simulCase1(4L)
#' S=Simulation$new()$simulCase1(5L)
#' F$rho1(S)
#' S$rho1(F)
rho1 = function(s = NA) {
stopifnot(class(s)[2] == "StatList")
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
r <- private$dimensions
p <- s$getLength()
c <- matrix(nrow = r, ncol = p)
d <- matrix(nrow = r, ncol = p)
e <- matrix(nrow = r, ncol = p)
f <- matrix(nrow = r, ncol = p)
rho <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
c[i, j] <-
private$numbers[[i]]$getInf0() - s$getDimension(j)$getInf0()
d[i, j] <-
private$numbers[[i]]$getInf1() - s$getDimension(j)$getInf1()
e[i, j] <-
private$numbers[[i]]$getSup1() - s$getDimension(j)$getSup1()
f[i, j] <-
private$numbers[[i]]$getSup0() - s$getDimension(j)$getSup0()
if ((abs(d[i, j] - c[i, j]) > .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) > .Machine$double.eps))
rho[i, j] = (1 / 2) * ((d[i, j] * abs(d[i, j]) - c[i, j] *
abs(c[i, j])) / (2 * (d[i, j] - c[i, j])) +
(e[i, j] * abs(e[i, j]) - f[i, j] * abs(f[i, j])) /
(2 * (e[i, j] - f[i, j])))
if ((abs(d[i, j] - c[i, j]) <= .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) > .Machine$double.eps))
rho[i, j] = (1 / 2) * (abs(c[i, j]) +
(e[i, j] * abs(e[i, j]) - f[i, j] * abs(f[i, j])) /
(2 * (e[i, j] - f[i, j])))
if ((abs(d[i, j] - c[i, j]) > .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) <= .Machine$double.eps))
rho[i, j] = (1 / 2) * ((d[i, j] * abs(d[i, j]) - c[i, j] *
abs(c[i, j])) / (2 * (d[i, j] - c[i, j])) +
abs(f[i, j]))
if ((abs(d[i, j] - c[i, j]) <= .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) <= .Machine$double.eps))
rho[i, j] = (1 / 2) * (abs(c[i, j]) + abs(f[i, j]))
}
}
return(rho)
},
#' @description
#' This method calculates scale measure Sn for a matrix of 'TrapezoidalFuzzyNumbers'
#'contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Sn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(3L,5,1,0.5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$sn(2L,5,1,0.5)
sn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
if (type == 1) {
rho1 <- self$rho1(self)
# this vector contains the n high medians calculated on each row of the matrix rho1
medRho1Filas <- vector(length = n)
for (i in 1:n) {
medRho1Filas[i] <- sort(rho1[i, ])[floor(n / 2) + 1] # high median
}
return (mean(sort(medRho1Filas)[floor((n + 1) / 2)])) # low median
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dthetaphi
medDthetaphiFilas <- vector(length = n)
for (i in 1:n) {
medDthetaphiFilas[i] <-
sort(dthetaphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDthetaphiFilas)[floor((n + 1) / 2)])) # low median
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dwablphi
medDwablphiFilas <- vector(length = n)
for (i in 1:n) {
medDwablphiFilas[i] <-
sort(dwablphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDwablphiFilas)[floor((n + 1) / 2)])) # low median
}
},
#' @description
#' This method calculates scale measure Tn for a matrix of 'TrapezoidalFuzzyNumbers'
#' contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Tn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(3L,5,1,0.5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$tn(1L)
tn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
if (type == 1) {
rho1 <- self$rho1(self)
# this vector contains the n high medians calculated on each row of the matrix rho1
medRho1Filas <- vector(length = n)
for (i in 1:n) {
medRho1Filas[i] <- sort(rho1[i, ])[floor(n / 2) + 1] # high median
}
return (mean(sort(medRho1Filas)[1:(floor(n / 2) + 1)]))
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dthetaphi
medDthetaphiFilas <- vector(length = n)
for (i in 1:n) {
medDthetaphiFilas[i] <-
sort(dthetaphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDthetaphiFilas)[1:(floor(n / 2) + 1)]))
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dwablphi
medDwablphiFilas <- vector(length = n)
for (i in 1:n) {
medDwablphiFilas[i] <-
sort(dwablphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDwablphiFilas)[1:(floor(n / 2) + 1)]))
}
},
#' @description
#' This method transforms a 'TrapezoidalFuzzyNumberList' containing valid
#' 'TrapezoidalFuzzyNumbers' characterized by their four values inf0, inf1,
#' sup1, sup0 into a 'FuzzyNumberList' containing these same amount of fuzzy
#' numbers, characterized by means of nl equidistant \eqn{\alpha}-levels each
#' (by default nl=101).
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the trapezoidal
#' fuzzy numbers.
#'
#' @details See examples.
#'
#' @return a FuzzyNumberList containing the transformed TrapezoidalFuzzyNumbers
#' into FuzzyNumbers.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(3L)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(10L)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase3(10L)
#' F$transfTra(200L)
transfTra = function(nl = 101L) {
stopifnot(typeof(nl) == "integer" && nl >= 2)
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
alpha <- seq(0, 1, len = nl) # alpha-levels
inf <- matrix(nrow = n, ncol = nl)
sup <- matrix(nrow = n, ncol = nl)
for (i in 1:n) {
for (j in 1:nl) {
inf[i, j] <-
(1 - alpha[j]) * F[i, 1] + alpha[j] * F[i, 2] # matrix n x nl
sup[i, j] <-
(1 - alpha[j]) * F[i, 4] + alpha[j] * F[i, 3] # matrix n x nl
}
}
# inf is a matrix n x nl, whose element (i,j) is the
# infimum of the alpha-level for the fuzzy number F(i), with
# alpha=alpha(j)
# sup is a matrix n x nl, whose element (i,j) is the
# supremum of the alpha-level for the fuzzy number F(i), with
# alpha=alpha(j)
result <-
FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(alpha, inf[1,], sup[1,]), dim = c(nl, 3)
))))
if (n > 1) {
for (i in 2:n) {
result$addFuzzyNumber(FuzzyNumber$new(array(c(
alpha, inf[i,], sup[i,]
), dim = c(nl, 3))))
}
}
return(result)
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the variance of these numbers with respect to the
#' mid/spr distance.
#' See De la Rosa de Saa et al. (2017) [2].
#'
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance.
#'
#' @details See examples.
#'
#' @return the variance of the sample with respect to the mid/spr distance,
#' which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1/3,1/3,1/5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$var(1,1,1)
var = function(a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
return (mean(self$dthetaphi(self$mean(), a, b, theta) ^ 2))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the \eqn{\phi}-wabl value for each of these numbers.
#' See Sinova et al. (2014) [9].
#'
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#'
#' @details See examples.
#'
#' @return a vector giving the \eqn{\phi}-wabl values of each TrapezoidalFuzzyNumber.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2.2,1.1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase4(60L)
#' F$wablphi(2,1)
wablphi = function(a = 1, b = 1) {
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
if (is.infinite(a) || is.infinite(b)) {
stop("The parameters cannot be Inf neither -Inf.")
}
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
wablF <- vector()
for (i in 1:n) {
wablF[i] <- private$wabl(i, list = self, a, b)
}
return (wablF)
},
#' @description
#' This method adds a 'TrapezoidalFuzzyNumber' to the current collection inside
#' the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field
#' is increased in a unit.
#'
#' @param n is the TrapezoidalFuzzyNumber to be added to the current collection
#' inside the current TrapezoidalFuzzyNumberList.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return nothing.
#'
#' @examples
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$addTrapezoidalFuzzyNumber(TrapezoidalFuzzyNumber$new(3,4,5,6))
addTrapezoidalFuzzyNumber = function(n = NA, verbose = TRUE) {
stopifnot(class(n)[1] == "TrapezoidalFuzzyNumber")
private$dimensions <- private$dimensions + 1
private$numbers <- append(private$numbers, n)
if (verbose) {
cat("numbers updated, current dimension is", private$dimensions)
}
},
#' @description
#' This method removes a 'TrapezoidalFuzzyNumber' to the current collection inside
#' the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field
#' is decreased in a unit.
#'
#' @param i is the position of the TrapezoidalFuzzyNumber to be removed in the
#' current collection inside the current TrapezoidalFuzzyNumberList.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return nothing.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(2L)
removeTrapezoidalFuzzyNumber = function(i = NA, verbose = TRUE) {
stopifnot(typeof(i) == "integer" &&
i > 0 && i <= private$dimensions)
private$dimensions <- private$dimensions - 1
private$numbers <- private$numbers[-i]
if (verbose) {
cat("numbers updated, current dimension is", private$dimensions)
}
},
#' @description
#' This method gives the number contained in the dimension passed as parameter
#' when the dimension is greater than 0 and not greater than the dimensions
#' of the TrapezoidalFuzzyNumberList's numbers array.
#'
#' @param i is the dimension of the TrapezoidalFuzzyNumber wanted to be retrieved.
#'
#' @details See examples.
#'
#' @return The TrapezoidalFuzzyNumber contained in the dimension passed as parameter
#' or an error if the dimension is not valid.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(2L)
getDimension = function(i = NA) {
stopifnot(typeof(i) == "integer" &&
i > 0 && i <= private$dimensions)
return(private$numbers[[i]])
},
#' @description
#' This method shows in a graph the values of the attribute numbers of the
#' corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @param color is the color of the lines representing the numbers to be shown
#' in the graph. The default value is grey, other colors can be specified, the
#' option palette() too.
#'
#' @details See examples.
#'
#' @return a graph with the values of the attribute numbers of the corresponding
#' 'TrapezoidalFuzzyNumberList'.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,5)))$plot()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4)))$plot()
#'
#' # Example 3:
#' Simulation$new()$simulCase1(8L)$plot(palette())
#'
#' # Example 4:
#' Simulation$new()$simulCase1(5L)$plot(palette()[2:6])
plot = function(color = "grey") {
dims <- private$dimensions
p <- (length(color) > 1 && dims > 1)
x <- c()
minimo <- c()
maximo <- c()
for (i in 1:dims) {
number <- private$numbers[[i]]
x <-
append(x,
c(
number$getInf0(),
number$getInf1(),
number$getSup1(),
number$getSup0()
))
minimo <- append(minimo, number$getInf0())
maximo <- append(maximo, number$getSup0())
}
plot(
c(),
c(),
type = "l",
col = color,
lty = 1,
lwd = 3,
xlim = c(min(minimo) - 0.25, max(maximo) + 0.25),
ylim = c(0, 1),
xlab = "",
ylab = "",
main = "TrapezoidalFuzzyNumberList"
)
if (p) {
for (i in seq(1, length(x), by = 4)) {
points(x[i:(i + 3)], c(0, 1, 1, 0), type = "l", col = color[runif(1, min =
1, max = length(color))])
}
} else {
for (i in seq(1, length(x), by = 4)) {
points(x[i:(i + 3)], c(0, 1, 1, 0), type = "l", col = color)
}
}
},
#' @description
#' This method returns the number of dimensions that are equivalent to the number
#' of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @details See examples.
#'
#' @return the number of dimensions that are equivalent to the number of
#' 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$getLength()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4)))$getLength()
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4),TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$getLength()
getLength = function() {
return(private$dimensions)
}
)
)
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#' @title 'TrapezoidalFuzzyNumberList' is a child class of 'StatList'.
#'
#' @description
#' 'TrapezoidalFuzzyNumberList' must contain valid 'TrapezoidalFuzzyNumbers'.
#' This class implements a version of the empty 'StatList' methods.
#'
#' @note In case you find (almost surely existing) bugs or have recommendations
#' for improving the method, comments are welcome to the above mentioned mail addresses.
#'
#' @author(s) Andrea Garcia Cernuda <uo270115@uniovi.es>, Asun Lubiano <lubiano@uniovi.es>,
#' Sara de la Rosa de Saa
#'
#' @references
#' [1] De la Rosa de Saa, S.; Gil, M.A.; Gonzalez-Rodriguez, G.; Lopez, M.T.; Lubiano M.A.: Fuzzy
#' rating scale-based questionnaires and their statistical analysis, IEEE Transactions on
#' Fuzzy Systems 23(1), 111-126 (2015)
#'
#' [2] De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: Robust scale
#' estimators for fuzzy data, Advances in Data Analysis and Classification 11(4), 731-758 (2017)
#'
#' [3] De la Rosa de Sáa, S.; Lubiano, M.A.; Sinova, B.; Filzmoser, P.; Gil, M.Á.: Location-free
#' robust scale estimates for fuzzy data, IEEE Transactions on Fuzzy Systems 29(6), 1682-1694 (2021)
#'
#' [4] Lubiano, M.A.; Gil, M.A.: f-Inequality indices for fuzzy random variables, in Statistical
#' Modeling, Analysis and Management of Fuzzy Data (Bertoluzza, C., Gil, M.A., Ralescu, D.A., Eds.),
#' Physica-Verlag, 43-63 (2002)
#'
#' [5] Lubiano, M.A.; Montenegro, M.; Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: Hypothesis
#' testing for means in connection with fuzzy rating scale-based data: algorithms and
#' applications, European Journal of Operational Research 251, 918-929 (2016)
#'
#' [6] Sinova, B.; De la Rosa de Saa, S.; Gil, M.A.: A generalized L1-type metric between fuzzy
#' numbers for an approach to central tendency of fuzzy data, Information Sciences 242,
#' 22-34 (2013)
#'
#' [7] Sinova, B.; De la Rosa de Saa, S.; Lubiano, M.A.; Gil, M.A.: An overview on the statistical
#' central tendency for fuzzy datasets, International Journal of Uncertainty, Fuzziness and
#' Knowledge-Based Systems 23 (Suppl. 1), 105-132 (2015)
#'
#' [8] Sinova, B.; Gil, M.A.; Colubi, A.; Van Aelst, S.: The median of a random fuzzy number. The
#' 1-norm distance approach, Fuzzy Sets and Systems 200, 99-115 (2012)
#'
#' [9] Sinova, B.; Gil, M.A.; Lopez, M.T.; Van Aelst, S.: A parameterized L2 metric between fuzzy
#' numbers and its parameter interpretation, Fuzzy Sets and Systems 245, 101-115 (2014)
#'
#' [10] Sinova, B.; Gil, M.A.; Van Aelst, S.: M-estimates of location for the robust central
#' tendency of fuzzy data, IEEE Transactions on Fuzzy Systems 24(4), 945-956 (2016)
#'
#' @import R6
#'
#' @export TrapezoidalFuzzyNumberList
TrapezoidalFuzzyNumberList <- R6::R6Class(
classname = "TrapezoidalFuzzyNumberList",
inherit = StatList,
private = list (
# numbers is a collection of trapezoidal fuzzy numbers.
numbers = NULL,
# auxiliary method used in the dthetaphi public method
# x is a vector, a and b are the parameters of the dthetaphi public method
integrand = function(x = NA,
a = NA,
b = NA) {
return (x * dbeta(x, a, b))
},
# auxiliary method used in the dthetaphi public method
# x is a vector, a and b are the parameters of the dthetaphi public method
integrandsq = function(x = NA,
a = NA,
b = NA) {
return (x ^ 2 * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
inf = function(x = NA,
i = NA,
list = NA) {
return (
list$getDimension(i)$getInf0() + x * (
list$getDimension(i)$getInf1() - list$getDimension(i)$getInf0()
)
)
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
sup = function(x = NA,
i = NA,
list = NA) {
return (
list$getDimension(i)$getSup0() + x * (
list$getDimension(i)$getSup1() - list$getDimension(i)$getSup0()
)
)
},
# auxiliary method used in the dwablphi public method
# x is a vector,i is an integer and list is a TrapezoidalFuzzyNumberList
mid = function(x = NA,
i = NA,
list = NA) {
return ((private$inf(x, i, list) + private$sup(x, i, list)) / 2)
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i is an integer and list is a TrapezoidalFuzzyNumberList
integrandWabl = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$mid(x, i, list) * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public function
# a and b are the parameters of the dwablphi public function
# i is an integer and list is a TrapezoidalFuzzyNumberList
wabl = function(i = NA,
list = NA,
a = NA,
b = NA) {
return (integrate(
private$integrandWabl,
0,
1,
i = i,
list = list,
a =
a,
b = b
)$val)
},
# auxiliary method used in the dwablphi public function
# x is a vector, i is an integer, a and b are the parameters of the dwablphi public function
# list is a TrapezoidalFuzzyNumberList
ldev = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$wabl(i, list, a, b) - private$inf(x, i, list))
},
# auxiliary method used in the dwablphi public function
# x is a vector, i is an integer, a and b are the parameters of the dwablphi public function
# list is a TrapezoidalFuzzyNumberList
rdev = function(x = NA,
i = NA,
list = NA,
a = NA,
b = NA) {
return (private$sup(x, i, list) - private$wabl(i, list, a, b))
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i and j are integers, list1 and list2 are TrapezoidalFuzzyNumberLists
integrand1 = function(x = NA,
i = NA,
j = NA,
list1 = NA,
list2 = NA,
a = NA,
b = NA) {
return (abs(
private$ldev(x, i, list = list1, a, b) - private$ldev(x, i = j, list =
list2, a, b)
) * dbeta(x, a, b))
},
# auxiliary method used in the dwablphi public function
# x is a vector, a and b are the parameters of the dwablphi public function
# i and j are integers, list1 and list2 are TrapezoidalFuzzyNumberLists
integrand2 = function(x = NA,
i = NA,
j = NA,
list1 = NA,
list2 = NA,
a = NA,
b = NA) {
return (abs(
private$rdev(x, i, list = list1, a, b) - private$rdev(x, i = j, list =
list2, a, b)
) * dbeta(x, a, b))
},
# auxiliary method used in the mEstimator public function
# x is a vector and f is the name of the loss function
weight = function(x = NA,
f = NA) {
rho <- 0
rhod <- 0
w <- 0
if (f == "Huber") {
# Huber M-estimator
rho <- min(x ^ 2, 1)
rhod <- 2
} else if (f == "Tukey") {
# Tukey M-estimator
rho <- min(3 * x ^ 2 - 3 * x ^ 4 + x ^ 6, 1)
rhod <- 6
} else if (f == "Cauchy") {
# Cauchy M-estimator
rho <- x ^ 2 / (x ^ 2 + 1)
rhod <- 2
}
if (x == 0) {
w <- rhod
} else {
w <- rho / x ^ 2
}
return(w)
},
# auxiliary method used in the gsi, hyperI, mean, medianWabl, transfTra and
# wablphi public functions
extractMatrix = function() {
F <- matrix(ncol = 4)
for (i in 1:private$dimensions) {
F <-
rbind(
F,
c(
private$numbers[[i]]$getInf0(),
private$numbers[[i]]$getInf1(),
private$numbers[[i]]$getSup1(),
private$numbers[[i]]$getSup0()
)
)
}
return (F)
}
),
public = list(
#' @description
#' This method creates a 'TrapezoidalFuzzyNumberList' object with all the attributes
#' set if the 'TrapezoidalFuzzyNumbers' are valid.
#'
#' @param numbers is a list which contains n TrapezoidalFuzzyNumbers.
#'
#' @details See examples.
#'
#' @return The TrapezoidalFuzzyNumberList object created with all attributes
#' set if the 'TrapezoidalFuzzyNumbers' are valid.
#'
#' @examples
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1, 2, 3, 4),
#' TrapezoidalFuzzyNumber$new(-8, -6, -4, -2),
#' TrapezoidalFuzzyNumber$new(-1, -1, 2, 3),
#' TrapezoidalFuzzyNumber$new(1, 2, 3, 3)))
initialize = function(numbers = NA) {
stopifnot(is.list(numbers))
for (val in 1:length(numbers)) {
stopifnot(class(numbers[[val]])[1] == "TrapezoidalFuzzyNumber")
}
private$rows <- 1
private$columns <- 4
private$dimensions <- length(numbers)
private$numbers <- numbers
},
#' @description
#' This method calculates the scale measure Average Distance Deviation (ADD)
#' of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList'
#' or with respect to a 'FuzzyNumberList' containing a unique valid fuzzy number.
#' The employed metric in the calculation can be the 1-norm distance, the mid/spr
#' distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2017) [2].
#'
#' @param s is a TrapezoidalFuzzyNumberList containing a unique valid TrapezoidalFuzzyNumber
#' or it is a FuzzyNumberList containing a unique valid FuzzyNumber.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure ADD, which is a real number. If the body's method
#' inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$add(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' S=F$mean()
#' F$add(S,1L)
#'
#' # Example 5:
#' F=Simulation$new()$simulCase1(100L)
#' S=F$median1Norm()
#' F$add(S,2L,2,1,1)
#'
#' # Example 6:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(1L)
#' F$add(U,2L)
#'
#' # Example 7:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$transfTra()
#' F$add(U,2L)
#'
#' # Example 8:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(2L)
#' F$add(U,2L)
add = function(s = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[2] == "StatList")
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
if (s$getLength() == 1) {
u <- NULL
if (class(s)[1] == "FuzzyNumberList") {
u <-
self$transfTra(as.integer(nrow(
s$getDimension(1L)$getAlphaLevels()
)))
} else{
# class(s)[1] == "TrapezoidalFuzzyNumberList"
u <- self
}
add <- 0
if (type == 1) {
add <- mean(s$rho1(u))
} else if (type == 2) {
add <- mean(s$dthetaphi(u, a, b, theta))
} else{
# type == 3
add <- mean(s$dwablphi(u, a, b, theta))
}
return (add)
}
return (NA)
},
#' @description
#' This method calculates the mid/spr distance between the 'TrapezoidalFuzzyNumbers'
#' contained in the current object and the one passed as parameter.
#' See Lubiano et al. (2016) [5].
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance.
#'
#' @details See examples.
#'
#' @return a matrix containing the mid/spr distances between the two previous
#' mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dthetaphi(
#' TrapezoidalFuzzyNumberList$new( c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),1,1,1)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(6L)
#' S=Simulation$new()$simulCase1(8L)
#' F$dthetaphi(S,1,5,1)
dthetaphi = function(s = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
super$dthetaphi(s, a, b, theta)
r <- private$dimensions
p <- s$getLength()
c <- matrix(nrow = r, ncol = p)
d <- matrix(nrow = r, ncol = p)
e <- matrix(nrow = r, ncol = p)
f <- matrix(nrow = r, ncol = p)
dthetaphicua <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
c[i, j] <-
((
private$numbers[[i]]$getInf0() + private$numbers[[i]]$getSup0()
) -
(
s$getDimension(j)$getInf0() + s$getDimension(j)$getSup0()
)
) / 2
d[i, j] <-
((
private$numbers[[i]]$getSup0() - private$numbers[[i]]$getInf0()
) -
(
s$getDimension(j)$getSup0() - s$getDimension(j)$getInf0()
)
) / 2
e[i, j] <-
((
private$numbers[[i]]$getInf1() + private$numbers[[i]]$getSup1()
) -
(
s$getDimension(j)$getInf1() + s$getDimension(j)$getSup1()
)
) / 2 - c[i, j]
f[i, j] <-
((
private$numbers[[i]]$getSup1() - private$numbers[[i]]$getInf1()
) -
(
s$getDimension(j)$getSup1() - s$getDimension(j)$getInf1()
)
) / 2 - d[i, j]
dthetaphicua[i, j] <-
c[i, j] ^ 2 + theta * d[i, j] ^ 2 +
(e[i, j] ^ 2 + theta * f[i, j] ^ 2) * integrate(private$integrandsq, 0, 1, a =
a, b = b)$val +
2 * (c[i, j] * e[i, j] + theta * d[i, j] * f[i, j]) * integrate(private$integrand, 0, 1, a =
a, b = b)$val
}
}
dthetaphi <- sqrt(dthetaphicua)
return(dthetaphi)
},
#' @description
#' This method calculates the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance
#' between the 'TrapezoidalFuzzyNumbers' contained in two 'TrapezoidalFuzzyNumberLists'.
#' See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' ldev and rdev in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return a matrix containing the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distances
#' between the two previous mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$dwablphi(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))),5,1,1)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(10L)
#' S=Simulation$new()$simulCase1(20L)
#' F$dwablphi(S)
dwablphi = function(s = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
super$dwablphi(s, a, b, theta)
r <- private$dimensions
p <- s$getLength()
wablR <- vector()
wablS <- vector()
dwablphi <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
int1 <-
integrate(
private$integrand1,
0,
1,
i = i,
j = j,
list1 = self,
list2 = s,
a = a,
b = b
)$val
int2 <-
integrate(
private$integrand2,
0,
1,
i = i,
j = j,
list1 = self,
list2 = s,
a = a,
b = b
)$val
dwablphi[i, j] <-
abs(private$wabl(i, list = self, a, b) - private$wabl(i =
j, list = s, a, b)) + (theta /
2) * int1 + (theta / 2) * int2
}
}
return (dwablphi)
},
#' @description
#' This method calculates the Gini-Simpson diversity index for a sample of
#' 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'.
#' See De la Rosa de Saa et al. (2015) [1].
#'
#' @details See examples.
#'
#' @return the Gini-Simpson diversity index, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$gsi()
#'
#' # Example 2:
#' F=Simulation$new()$simulCase1(50L)
#' F$gsi()
gsi = function() {
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
U <-
unique(F) # deletes the equal rows (equal fuzzy numbers)
u <-
nrow(U) # number of different fuzzy numbers in the matrix F
fr = vector(length = u) # relative frequency of each fuzzy number of the matrix U
for (i in 1:u) {
cont <- 0
for (j in 1:n) {
if (sum(U[i,] == F[j,]) == ncol(F))
cont <- cont + 1
}
fr[i] <- cont / n
}
gini <- 1 - sum(fr ^ 2)
return(gini)
},
#' @description
#' This method calculates the hyperbolic inequality index for a sample of
#' 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList'.
#' The method checks if all 'TrapezoidalFuzzyNumbers' are positive.
#' See De la Rosa de Saa et al. (2015) [1] and Lubiano and Gil (2002) [4].
#'
#' @param c number in [0,0.5]. The c*100% trimmed mean will be used in the calculation
#' of the hyperbolic inequality index.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return the hyperbolic inequality index, which is a real number. If the body's
#' method inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$hyperI(0.5)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,4,6,8)))$hyperI()
#'
#' # Example 4:
#' F=Simulation$new()$simulFRSTra(100L,0.05,0.35,0.6,2,1)
#' F$hyperI()
#'
#' # Example 5:
#' F=Simulation$new()$simulCase2(10L)
#' F$hyperI(0.5)
hyperI = function(c = 0, verbose = TRUE) {
stopifnot(is.double(c) && c >= 0 && c <= 0.5)
for (i in 1:private$dimensions) {
if (!private$numbers[[i]]$is_positive()) {
if (verbose) {
print("all the fuzzy numbers should be positive")
}
return (NA)
}
}
F <- private$extractMatrix()
n <- nrow(F)
l <- vector()
fmean <-
apply(F[2:n,], 2, mean, trim = c) # mean of the trapezoidal fuzzy numbers
a1 = fmean[3] - fmean[4]
b1 = fmean[4]
a2 = fmean[2] - fmean[1]
b2 = fmean[1]
for (i in 2:n) {
c1 = F[i, 2] - F[i, 1]
d1 = F[i, 1]
c2 = F[i, 3] - F[i, 4]
d2 = F[i, 4]
if ((abs(c1) <= .Machine$double.eps) &
(abs(c2) <= .Machine$double.eps))
l[i] = (1 / d1) * (a1 / 2 + b1) + (1 / d2) * (a2 / 2 + b2)
else if ((abs(c1) <= .Machine$double.eps) &
(abs(c2) > .Machine$double.eps))
l[i] = (1 / d1) * (a1 / 2 + b1) + a2 / c2 + (b2 - ((a2 * d2) /
c2)) * (1 / c2) * (log(abs(c2 + d2)) - log(abs(d2)))
else if ((abs(c1) > .Machine$double.eps) &
(abs(c2) <= .Machine$double.eps))
l[i] = a1 / c1 + (b1 - ((a1 * d1) / c1)) * (1 / c1) * (log(abs(c1 +
d1)) - log(abs(d1))) + (1 / d2) * (a2 / 2 + b2)
else if ((abs(c1) > .Machine$double.eps) &
(abs(c2) > .Machine$double.eps))
l[i] = a1 / c1 + (b1 - ((a1 * d1) / c1)) * (1 / c1) * (log(abs(c1 +
d1)) - log(abs(d1))) + a2 / c2 + (b2 - ((a2 * d2) / c2)) * (1 / c2) * (log(abs(c2 +
d2)) - log(abs(d2)))
}
hyper = (1 / 2) * mean(l[2:length(l)], trim = c) - 1
return(hyper)
},
#' @description
#' This method calculates the M-estimator of scale with loss method given
#' in a 'TrapezoidalFuzzyNumberList' containing 'TrapezoidalFuzzyNumbers'.
#' For computing the M-estimator, a method called “iterative reweighting” is
#' used. The employed metric in the M-equation can be the 1-norm distance, the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @param f is the name of the loss function. It can be "Huber", "Tukey" or "Cauchy".
#' @param estInitial real number > 0.
#' @param delta real number in (0,1). It is present in the f-equation.
#' @param epsilon real number > 0. It is the tolerance allowed in the algorithm.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the value of the M-estimator of scale, which is a real number.
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Huber",0.321,0.5,10^(-5),
#' 1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Tukey",0.123,0.5,10^(-5),
#' 2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mEstimator("Cauchy",0.123,0.5,10^(-5),
#' 3L,0.75,0.5,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(100L)
#' U=F$median1Norm()
#' estInitial=F$mdd(U,1L)
#' delta=0.5
#' epsilon=10^(-5)
#' F$mEstimator("Huber",estInitial,delta,epsilon,1L)
mEstimator = function(f = NA,
estInitial = NA,
delta = NA,
epsilon = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(f) == "character" &&
(f == "Huber" || f == "Tukey" || f == "Cauchy"))
stopifnot(typeof(estInitial) == "double" && estInitial > 0)
stopifnot(typeof(delta) == "double" && delta > 0 && delta < 1)
stopifnot(typeof(epsilon) == "double" && epsilon > 0)
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(estInitial) ||
is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
x <-
matrix() # distances between the numbers of F and the number 0
t <-
TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0, 0, 0, 0)))
if (type == 1) {
# metric Rho1
x <- self$rho1(t)
}
else if (type == 2) {
# metric Dthetaphi
x <- self$dthetaphi(t, a, b, theta)
}
else if (type == 3) {
# metric Dwablphi
x <- self$dwablphi(t, a, b, theta)
}
# Iterative algorithm:
n <- private$dimensions
k <- 1
sigma <- vector()
sigma[k] <- estInitial
omega <- vector(length = n)
repeat {
for (j in 1:n) {
omega[j] <- private$weight((x[j] / sigma[k]), f)
}
k <- k + 1
sigma[k] <- sqrt((1 / (n * delta)) * sum(omega * x ^ 2))
if ((abs(sigma[k] / sigma[k - 1] - 1) < epsilon) |
(sigma[k] < 10 ^ (-10))) {
break
}
}
return (sigma[length(sigma)]) # last sigma
},
#' @description
#' This method calculates the scale measure Median Distance Deviation (MDD)
#' of a 'TrapezoidalFuzzyNumberList' with respect to a 'TrapezoidalFuzzyNumberList'
#' or with respect to a 'FuzzyNumberList' with a unique valid fuzzy number.
#' The employed metric in the calculation can be the 1-norm distance, the mid/spr
#' distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2015) [2] and De la Rosa de Saa et al. (2021) [3].
#'
#' @param s is a TrapezoidalFuzzyNumberList containing a unique TrapezoidalFuzzyNumber
#' or it is a FuzzyNumberList containing a unique FuzzyNumber.
#' @param type positive integer 1, 2 or 3: if type==1, the 1-norm distance will
#' be considered in the calculation of the measure ADD. If type==2, the mid/spr
#' distance will be considered. By contrast, if type==3, the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev
#' distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or in the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure MDD, which is a real number.If the body's
#' method inner conditions are not met, NA will be returned.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' FuzzyNumberList$new(c(FuzzyNumber$new(array(c(0.0, 0.5, 1.0,-1.5,-1.25,-1.0,
#' 3.0, 2.0, 1.0), dim = c(3, 3))))),2L,2,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(0,0.1,0.2,0.3),
#' TrapezoidalFuzzyNumber$new(1,2,3,4),TrapezoidalFuzzyNumber$new(2,3,4,5)))$mdd(
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(5,6,7,8))),3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase3(10L)
#' U=F$mean()
#' F$mdd(U,3L,1,2,1)
#'
#' # Example 5:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$median1Norm()
#' F$mdd(U,2L)
#'
#' # Example 6:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(1L)
#' F$mdd(U,2L)
#'
#' # Example 7:
#' F=Simulation$new()$simulCase2(10L)
#' U=F$transfTra()
#' F$mdd(U,2L)
#'
#' # Example 8:
#' F=Simulation$new()$simulCase2(10L)
#' U=Simulation$new()$simulCase2(2L)
#' F$mdd(U,2L)
mdd = function(s = NA,
type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(class(s)[2] == "StatList")
stopifnot(typeof(type) == "integer" &&
type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
if (s$getLength() == 1) {
u <- NULL
if (class(s)[1] == "FuzzyNumberList") {
u <-
self$transfTra(as.integer(nrow(
s$getDimension(1L)$getAlphaLevels()
)))
} else{
# class(s)[1] == "TrapezoidalFuzzyNumberList"
u <- self
}
mdd <- 0
if (type == 1) {
mdd <- median(s$rho1(u))
} else if (type == 2) {
mdd <- median(s$dthetaphi(u, a, b, theta))
} else{
# type == 3
mdd <- median(s$dwablphi(u, a, b, theta))
}
return (mdd)
}
return (NA)
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the Aumann-type mean of these numbers (which is a
#' 'TrapezoidalFuzzyNumber' too).
#' See Sinova et al. (2015) [7].
#'
#' @details See examples.
#'
#' @return the Aumann-type mean, given as a TrapezoidalFuzzyNumber contained in
#' a TrapezoidalFuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$mean()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(
#' c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$mean()
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(100L)
#' F$mean()
mean = function() {
F <- private$extractMatrix()
m <-
t(as.matrix(apply(F[2:nrow(F),], 2, mean)))
return(TrapezoidalFuzzyNumberList$new(c(
TrapezoidalFuzzyNumber$new(m[1, 1], m[1, 2], m[1, 3], m[1, 4])
)))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the 1-norm median of these numbers, characterized
#' by means of nl equidistant \eqn{\alpha}-levels (by default nl=101), including
#' always the 0 and 1 levels, with their infimum and supremum values.
#' See Sinova et al. (2012) [8].
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the 1-norm median.
#'
#' @details See examples.
#'
#' @return the 1-norm median, given in form of a FuzzyNumber contained in a
#' FuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$median1Norm(200L)
#'
#' # Example 3:
#' F=Simulation$new()$simulCase1(10L)
#' F$median1Norm(200L)
median1Norm = function(nl = 101L) {
stopifnot(is.integer(nl) && nl >= 2)
# transforms the current TrapezoidalFuzzyNumberList into a FuzzyNumberList
fuzzyArray <- self$transfTra(nl)
alpha <- seq(0, 1, len = nl) # alpha-levels
result <- array(dim = c(nl, 3, 1))
l <- fuzzyArray$getLength()
F <- array(dim = c(nl, 3, l))
for (i in 1:l) {
F[, 2, i] <- fuzzyArray$getDimension(i)$getInfimums()
F[, 3, i] <- fuzzyArray$getDimension(i)$getSupremums()
}
result[, 1, 1] = alpha
result[, 2, 1] = apply(F[, 2,], 1, median) # second column: medians of the infimum
# values of each alpha-level
result[, 3, 1] = apply(F[, 3,], 1, median) # third column: medians of the supremum
# values of each alpha-level
return(FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(result[, 1, 1], result[, 2, 1], result[, 3, 1]), dim = c(length(result[, 1, 1]), 3)
)))))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the \eqn{\phi}-wabl/ldev/rdev median of these numbers,
#' characterized by means of nl equidistant \eqn{\alpha}-levels (by default nl=101),
#' including always the 0 and 1 levels, with their infimum and supremum values.
#' See Sinova et al. (2013) [6] and Sinova et al. (2016) [10].
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the \eqn{\phi}-wabl/ldev/rdev
#' median.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#'
#' @details See examples.
#'
#' @return the \eqn{\phi}-wabl/ldev/rdev median in form of a FuzzyNUmber given
#' in a FuzzyNumberList.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$medianWabl(3L,2.2,2.8)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$medianWabl(3L)
medianWabl = function(nl = 101L,
a = 1,
b = 1) {
stopifnot(is.integer(nl) && nl >= 2)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
if (is.infinite(a) || is.infinite(b)) {
stop("The parameters cannot be Inf neither -Inf.")
}
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
wablF <- vector()
medianldev <- vector()
medianrdev <- vector()
for (i in 1:n) {
wablF[i] <- private$wabl(i, list = self, a, b)
}
medianwabl <- median(wablF)
alpha <- seq(0, 1, len = nl) # alpha-levels
median <- array(dim = c(nl, 3, 1))
median[, 1, 1] <- alpha # first column: alpha-levels
for (j in 1:nl) {
ldevF <- wablF - (F[, 1] + alpha[j] * (F[, 2] - F[, 1]))
medianldev[j] <- median(ldevF)
rdevF <- F[, 4] + alpha[j] * (F[, 3] - F[, 4]) - wablF
medianrdev[j] <- median(rdevF)
}
median[, 2, 1] <- medianwabl - medianldev # second column
median[, 3, 1] <- medianwabl + medianrdev # third column
return(FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(median[, 1, 1], median[, 2, 1], median[, 3, 1]), dim = c(length(median[, 1, 1]), 3)
)))))
},
#' @description
#' This method calculates scale measure Qn for a matrix of 'TrapezoidalFuzzyNumbers'
#'contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Qn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(2L,5,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$qn(3L,1,1,1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$qn(3L,1,1,1)
qn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
distMitad <- 0
if (type == 1) {
rho1 <- self$rho1(self)
distMitad <-
rho1[lower.tri(rho1)] # upper triangle of the matrix rho1
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
distMitad <-
dthetaphi[lower.tri(dthetaphi)] # upper triangle of the matrix dthetaphi
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
distMitad <-
dwablphi[lower.tri(dwablphi)] # upper triangle of the matrix dwablphi
}
return (sort(distMitad)[choose(floor(n / 2) + 1, 2)])
},
#' @description
#' This method calculates the 1-norm distance between the 'TrapezoidalFuzzyNumbers'
#' contained in two 'TrapezoidalFuzzyNumberLists'.
#'
#' @param s TrapezoidalFuzzyNumberList containing valid TrapezoidalFuzzyNumbers
#' characterized by their four values inf0, inf1, sup1, sup0.
#'
#' @details See examples.
#'
#' @return a matrix containing the 1-norm distances between the two previous
#' mentioned TrapezoidalFuzzyNumberLists.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1)))$rho1(TrapezoidalFuzzyNumberList$new(
#' c(TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58))))
#'
#' # Example 2:
#' F=Simulation$new()$simulCase1(4L)
#' S=Simulation$new()$simulCase1(5L)
#' F$rho1(S)
#' S$rho1(F)
rho1 = function(s = NA) {
stopifnot(class(s)[2] == "StatList")
stopifnot(class(s)[1] == "TrapezoidalFuzzyNumberList")
r <- private$dimensions
p <- s$getLength()
c <- matrix(nrow = r, ncol = p)
d <- matrix(nrow = r, ncol = p)
e <- matrix(nrow = r, ncol = p)
f <- matrix(nrow = r, ncol = p)
rho <- matrix(nrow = r, ncol = p)
for (i in 1:r) {
for (j in 1:p) {
c[i, j] <-
private$numbers[[i]]$getInf0() - s$getDimension(j)$getInf0()
d[i, j] <-
private$numbers[[i]]$getInf1() - s$getDimension(j)$getInf1()
e[i, j] <-
private$numbers[[i]]$getSup1() - s$getDimension(j)$getSup1()
f[i, j] <-
private$numbers[[i]]$getSup0() - s$getDimension(j)$getSup0()
if ((abs(d[i, j] - c[i, j]) > .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) > .Machine$double.eps))
rho[i, j] = (1 / 2) * ((d[i, j] * abs(d[i, j]) - c[i, j] *
abs(c[i, j])) / (2 * (d[i, j] - c[i, j])) +
(e[i, j] * abs(e[i, j]) - f[i, j] * abs(f[i, j])) /
(2 * (e[i, j] - f[i, j])))
if ((abs(d[i, j] - c[i, j]) <= .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) > .Machine$double.eps))
rho[i, j] = (1 / 2) * (abs(c[i, j]) +
(e[i, j] * abs(e[i, j]) - f[i, j] * abs(f[i, j])) /
(2 * (e[i, j] - f[i, j])))
if ((abs(d[i, j] - c[i, j]) > .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) <= .Machine$double.eps))
rho[i, j] = (1 / 2) * ((d[i, j] * abs(d[i, j]) - c[i, j] *
abs(c[i, j])) / (2 * (d[i, j] - c[i, j])) +
abs(f[i, j]))
if ((abs(d[i, j] - c[i, j]) <= .Machine$double.eps) &
(abs(e[i, j] - f[i, j]) <= .Machine$double.eps))
rho[i, j] = (1 / 2) * (abs(c[i, j]) + abs(f[i, j]))
}
}
return(rho)
},
#' @description
#' This method calculates scale measure Sn for a matrix of 'TrapezoidalFuzzyNumbers'
#'contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Sn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$sn(3L,5,1,0.5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$sn(2L,5,1,0.5)
sn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
if (type == 1) {
rho1 <- self$rho1(self)
# this vector contains the n high medians calculated on each row of the matrix rho1
medRho1Filas <- vector(length = n)
for (i in 1:n) {
medRho1Filas[i] <- sort(rho1[i, ])[floor(n / 2) + 1] # high median
}
return (mean(sort(medRho1Filas)[floor((n + 1) / 2)])) # low median
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dthetaphi
medDthetaphiFilas <- vector(length = n)
for (i in 1:n) {
medDthetaphiFilas[i] <-
sort(dthetaphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDthetaphiFilas)[floor((n + 1) / 2)])) # low median
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dwablphi
medDwablphiFilas <- vector(length = n)
for (i in 1:n) {
medDwablphiFilas[i] <-
sort(dwablphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDwablphiFilas)[floor((n + 1) / 2)])) # low median
}
},
#' @description
#' This method calculates scale measure Tn for a matrix of 'TrapezoidalFuzzyNumbers'
#' contained in the current 'TrapezoidalFuzzyNumber'. The employed metric
#' in the calculation can be the 1-norm distance, the mid/spr distance or the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' See De la Rosa de Saa et al. (2021) [3].
#'
#' @param type integer number that can be 1, 2 or 3: if type==1, the 1-norm
#' distance will be considered in the calculation of the measure ADD. If type==2,
#' the mid/spr distance will be considered. By contrast, if type==3, the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance will be used.
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1] in the
#' mid/spr distance or the (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance and the weight of the ldev and rdev in the
#' (\eqn{\phi},\eqn{\theta})-wabl/ldev/rdev distance.
#'
#' @details See examples.
#'
#' @return the scale measure Tn, which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(2L,1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$tn(3L,5,1,0.5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$tn(1L)
tn = function(type = NA,
a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(type) == "integer" && type >= 1L && type <= 3L)
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
n <- private$dimensions
if (type == 1) {
rho1 <- self$rho1(self)
# this vector contains the n high medians calculated on each row of the matrix rho1
medRho1Filas <- vector(length = n)
for (i in 1:n) {
medRho1Filas[i] <- sort(rho1[i, ])[floor(n / 2) + 1] # high median
}
return (mean(sort(medRho1Filas)[1:(floor(n / 2) + 1)]))
} else if (type == 2) {
dthetaphi <- self$dthetaphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dthetaphi
medDthetaphiFilas <- vector(length = n)
for (i in 1:n) {
medDthetaphiFilas[i] <-
sort(dthetaphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDthetaphiFilas)[1:(floor(n / 2) + 1)]))
} else {
# type == 3
dwablphi <- self$dwablphi(self, a, b, theta)
# this vector contains the n high medians calculated on each row of the matrix dwablphi
medDwablphiFilas <- vector(length = n)
for (i in 1:n) {
medDwablphiFilas[i] <-
sort(dwablphi[i,])[floor(n / 2) + 1] # high median
}
return (mean(sort(medDwablphiFilas)[1:(floor(n / 2) + 1)]))
}
},
#' @description
#' This method transforms a 'TrapezoidalFuzzyNumberList' containing valid
#' 'TrapezoidalFuzzyNumbers' characterized by their four values inf0, inf1,
#' sup1, sup0 into a 'FuzzyNumberList' containing these same amount of fuzzy
#' numbers, characterized by means of nl equidistant \eqn{\alpha}-levels each
#' (by default nl=101).
#'
#' @param nl integer greater or equal to 2, by default nl=101. It indicates the
#' number of desired \eqn{\alpha}-levels for characterizing the trapezoidal
#' fuzzy numbers.
#'
#' @details See examples.
#'
#' @return a FuzzyNumberList containing the transformed TrapezoidalFuzzyNumbers
#' into FuzzyNumbers.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(3L)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$transfTra(10L)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase3(10L)
#' F$transfTra(200L)
transfTra = function(nl = 101L) {
stopifnot(typeof(nl) == "integer" && nl >= 2)
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
alpha <- seq(0, 1, len = nl) # alpha-levels
inf <- matrix(nrow = n, ncol = nl)
sup <- matrix(nrow = n, ncol = nl)
for (i in 1:n) {
for (j in 1:nl) {
inf[i, j] <-
(1 - alpha[j]) * F[i, 1] + alpha[j] * F[i, 2] # matrix n x nl
sup[i, j] <-
(1 - alpha[j]) * F[i, 4] + alpha[j] * F[i, 3] # matrix n x nl
}
}
# inf is a matrix n x nl, whose element (i,j) is the
# infimum of the alpha-level for the fuzzy number F(i), with
# alpha=alpha(j)
# sup is a matrix n x nl, whose element (i,j) is the
# supremum of the alpha-level for the fuzzy number F(i), with
# alpha=alpha(j)
result <-
FuzzyNumberList$new(c(FuzzyNumber$new(array(
c(alpha, inf[1,], sup[1,]), dim = c(nl, 3)
))))
if (n > 1) {
for (i in 2:n) {
result$addFuzzyNumber(FuzzyNumber$new(array(c(
alpha, inf[i,], sup[i,]
), dim = c(nl, 3))))
}
}
return(result)
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the variance of these numbers with respect to the
#' mid/spr distance.
#' See De la Rosa de Saa et al. (2017) [2].
#'
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param theta real number > 0, by default theta=1. It is the weight of the
#' spread in the mid/spr distance.
#'
#' @details See examples.
#'
#' @return the variance of the sample with respect to the mid/spr distance,
#' which is a real number.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1,1,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$var(1/3,1/3,1/5)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase1(10L)
#' F$var(1,1,1)
var = function(a = 1,
b = 1,
theta = 1) {
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
stopifnot(typeof(theta) == "double" && theta > 0)
if (is.infinite(a) || is.infinite(b) || is.infinite(theta)) {
stop("The parameters cannot be Inf neither -Inf.")
}
return (mean(self$dthetaphi(self$mean(), a, b, theta) ^ 2))
},
#' @description
#' Given a sample of 'TrapezoidalFuzzyNumbers' contained in a 'TrapezoidalFuzzyNumberList',
#' the method calculates the \eqn{\phi}-wabl value for each of these numbers.
#' See Sinova et al. (2014) [9].
#'
#' @param a real number > 0, by default a=1. It is the first parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#' @param b real number > 0, by default b=1. It is the second parameter of a
#' beta distribution which corresponds to a weighting measure on [0,1].
#'
#' @details See examples.
#'
#' @return a vector giving the \eqn{\phi}-wabl values of each TrapezoidalFuzzyNumber.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2,1)
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),TrapezoidalFuzzyNumber$new(1.5,2,3.75,4),
#' TrapezoidalFuzzyNumber$new(-4.2,-3.6,-2,-1.58)))$wablphi(2.2,1.1)
#'
#' # Example 4:
#' F=Simulation$new()$simulCase4(60L)
#' F$wablphi(2,1)
wablphi = function(a = 1, b = 1) {
stopifnot(typeof(a) == "double" && a > 0)
stopifnot(typeof(b) == "double" && b > 0)
if (is.infinite(a) || is.infinite(b)) {
stop("The parameters cannot be Inf neither -Inf.")
}
F <- matrix(private$extractMatrix()[-1, ], ncol = 4)
n <- nrow(F)
wablF <- vector()
for (i in 1:n) {
wablF[i] <- private$wabl(i, list = self, a, b)
}
return (wablF)
},
#' @description
#' This method adds a 'TrapezoidalFuzzyNumber' to the current collection inside
#' the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field
#' is increased in a unit.
#'
#' @param n is the TrapezoidalFuzzyNumber to be added to the current collection
#' inside the current TrapezoidalFuzzyNumberList.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return nothing.
#'
#' @examples
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$addTrapezoidalFuzzyNumber(TrapezoidalFuzzyNumber$new(3,4,5,6))
addTrapezoidalFuzzyNumber = function(n = NA, verbose = TRUE) {
stopifnot(class(n)[1] == "TrapezoidalFuzzyNumber")
private$dimensions <- private$dimensions + 1
private$numbers <- append(private$numbers, n)
if (verbose) {
cat("numbers updated, current dimension is", private$dimensions)
}
},
#' @description
#' This method removes a 'TrapezoidalFuzzyNumber' to the current collection inside
#' the current 'TrapezoidalFuzzyNumberList'. Therefore, the dimensions' field
#' is decreased in a unit.
#'
#' @param i is the position of the TrapezoidalFuzzyNumber to be removed in the
#' current collection inside the current TrapezoidalFuzzyNumberList.
#' @param verbose if TRUE the messages are written to the console unless the
#' user actively decides to set verbose=FALSE.
#'
#' @details See examples.
#'
#' @return nothing.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$removeTrapezoidalFuzzyNumber(2L)
removeTrapezoidalFuzzyNumber = function(i = NA, verbose = TRUE) {
stopifnot(typeof(i) == "integer" &&
i > 0 && i <= private$dimensions)
private$dimensions <- private$dimensions - 1
private$numbers <- private$numbers[-i]
if (verbose) {
cat("numbers updated, current dimension is", private$dimensions)
}
},
#' @description
#' This method gives the number contained in the dimension passed as parameter
#' when the dimension is greater than 0 and not greater than the dimensions
#' of the TrapezoidalFuzzyNumberList's numbers array.
#'
#' @param i is the dimension of the TrapezoidalFuzzyNumber wanted to be retrieved.
#'
#' @details See examples.
#'
#' @return The TrapezoidalFuzzyNumber contained in the dimension passed as parameter
#' or an error if the dimension is not valid.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(1L)
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,4)))$getDimension(2L)
getDimension = function(i = NA) {
stopifnot(typeof(i) == "integer" &&
i > 0 && i <= private$dimensions)
return(private$numbers[[i]])
},
#' @description
#' This method shows in a graph the values of the attribute numbers of the
#' corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @param color is the color of the lines representing the numbers to be shown
#' in the graph. The default value is grey, other colors can be specified, the
#' option palette() too.
#'
#' @details See examples.
#'
#' @return a graph with the values of the attribute numbers of the corresponding
#' 'TrapezoidalFuzzyNumberList'.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4),
#' TrapezoidalFuzzyNumber$new(2,3,4,5)))$plot()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4)))$plot()
#'
#' # Example 3:
#' Simulation$new()$simulCase1(8L)$plot(palette())
#'
#' # Example 4:
#' Simulation$new()$simulCase1(5L)$plot(palette()[2:6])
plot = function(color = "grey") {
dims <- private$dimensions
p <- (length(color) > 1 && dims > 1)
x <- c()
minimo <- c()
maximo <- c()
for (i in 1:dims) {
number <- private$numbers[[i]]
x <-
append(x,
c(
number$getInf0(),
number$getInf1(),
number$getSup1(),
number$getSup0()
))
minimo <- append(minimo, number$getInf0())
maximo <- append(maximo, number$getSup0())
}
plot(
c(),
c(),
type = "l",
col = color,
lty = 1,
lwd = 3,
xlim = c(min(minimo) - 0.25, max(maximo) + 0.25),
ylim = c(0, 1),
xlab = "",
ylab = "",
main = "TrapezoidalFuzzyNumberList"
)
if (p) {
for (i in seq(1, length(x), by = 4)) {
points(x[i:(i + 3)], c(0, 1, 1, 0), type = "l", col = color[runif(1, min =
1, max = length(color))])
}
} else {
for (i in seq(1, length(x), by = 4)) {
points(x[i:(i + 3)], c(0, 1, 1, 0), type = "l", col = color)
}
}
},
#' @description
#' This method returns the number of dimensions that are equivalent to the number
#' of 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @details See examples.
#'
#' @return the number of dimensions that are equivalent to the number of
#' 'TrapezoidalFuzzyNumbers' in the corresponding 'TrapezoidalFuzzyNumberList'.
#'
#' @examples
#' # Example 1:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$getLength()
#'
#' # Example 2:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4)))$getLength()
#'
#' # Example 3:
#' TrapezoidalFuzzyNumberList$new(c(TrapezoidalFuzzyNumber$new(-4,-3,-2,-1),
#' TrapezoidalFuzzyNumber$new(-6,0,1,4),TrapezoidalFuzzyNumber$new(1,2,3,4))
#' )$getLength()
getLength = function() {
return(private$dimensions)
}
)
)
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