Calculator.LR.FNs
Calculator for LR Fuzzy Numbers

Package index
Search the Calculator.LR.FNs package
Vignettes
Functions
14
Source code
12
Man pages
13
Home
/
CRAN
/
Calculator.LR.FNs
/
m: Product of two LR fuzzy numbers

m: Product of two LR fuzzy numbers
In Calculator.LR.FNs: Calculator for LR Fuzzy Numbers

Description Usage Arguments Value Author(s) References Examples

Description

This function calculates the multiplication (product) of two LR fuzzy numbers. Although on the basis of Zadeh extension principle, the class of LR fuzzy numbers is not closed under the operations multiplication and division, but we consider the following approximation for the product of two LR fuzzy numbers M=(m, α, β)_{LR} and N=(n, γ, δ)_{LR} in this package to work easy in the class of LR fuzzy numbers:

M \otimes N \simeq ≤ft\{ \begin{array}{lcc} (mn, m γ + n α, m δ + n β)_{LR} &\ \ if & \ \ M \succ 0 \ and \ N \succ 0 \\ (mn, m γ - n β, m δ - n α)_{RL} &\ \ if & \ \ M \succ 0 \ and \ N \prec 0 \\ (mn, -n β - m δ , -n α -m γ)_{RL} &\ \ if & \ \ M \prec 0 \ and \ N \prec 0 \end{array} \right.

Usage

1
m(M, N)

Arguments

M

The first LR (or RL or L) fuzzy number

N

The second LR (or RL or L) fuzzy number

Value

A LR (or RL or L) fuzzy number

Author(s)

Abbas Parchami

References

Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications. Academic Press (1980).

Dubois, D., Prade, H., Operations on fuzzy numbers. International Journal of Systems Science 9 (1978), 613-626.

Dubois, D., Prade, H., Fuzzy numbers: An overview. In In: Analysis of Fuzzy Information. Mathematical Logic, Vol. I. CRC Press (1987), 3-39.

Dubois, D., Prade, H., The mean value of a fuzzy number. Fuzzy Sets and Systems 24 (1987), 279-300.

Kaufmann, A., Gupta, M.M., Introduction to Fuzzy Arithmetic. van Nostrand Reinhold Company, New York (1985).

Taheri, S.M, Mashinchi, M., Introduction to Fuzzy Probability and Statistics. Shahid Bahonar University of Kerman Publications, In Persian (2009).

Viertl, R., Statistical Methods for Fuzzy Data. John Wiley & Sons, Chichester (2011).

Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences 8 (1975), 199-249.

Examples

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
# Example 1:
Left.fun  = function(x)  { (1-x)*(x>=0)}
Right.fun = function(x)  { (1/(1+(2*abs(x))))*(x>=0)}
A = LR(1, 0.6, 0.2)
B = LR(-3, 0.5, 1)
m(A, B)
m(B, A)
xlim = c(-5,4)
LRFN.plot( A, xlim=xlim, lwd=2, lty=2, col=2) 
LRFN.plot( B, lwd=2, lty=2, col=3, add=TRUE)
legend( "topright", c("A = LR(1, 0.6, 0.2)", "B = LR(-3, 0.5, 1)"), col = c(2, 3)
     , text.col = 1, lwd = c(2,2), lty = c(2, 2) )


# Example 2:
Left.fun  = function(x)  { (1-x)*(x>=0)}
Right.fun = function(x)  { (exp(-x))*(x>=0)}
A = LR(1.5, 1, 2)
B = LR(3, 2, 1)
LRFN.plot( A, xlim=c(-3,20), ylim=c(0,1), lwd=2, lty=2, col=2) 
LRFN.plot( B, lwd=2, lty=2, col=3, add=TRUE)
LRFN.plot( m(A,B), lwd=2, lty=3, col=1, add=TRUE)
legend( "topright", c("A = LR(1.5, 1, 2)", "B = LR(3, 2, 1)", "A * B = LR(4.5, 6, 7.5)")
     , col = c(2, 3, 1), text.col = 1, lwd = c(2,2,2), lty = c(2, 2, 3) )


# Example 3:
M = LR(1.2, 0.6, 0.2)
N = LR(3, 0.5, 1)

m(M,N)
m( LR(1.2, 0.6, 0.2) , LR(3, 0.5, 1) )

m(N,m(M,M))
m(m(N,M),M)

LRFN.plot( M, xlim=c(-2,10), ylim=c(0,1.4), lwd=2, lty=2, col=2) 
LRFN.plot( N, lwd=2, lty=2, col=3, add=TRUE)
LRFN.plot( m(M,N), lwd=2, lty=3, col=4, add=TRUE)
LRFN.plot( m(M,M), lwd=2, lty=4, col=5, add=TRUE)
LRFN.plot( m(m(N,M),M), lwd=2, lty=5, col=1, add=TRUE)
legend( "topright", c("M = LR(1.2, 0.6, 0.2)", "N = LR(3, 0.5, 1)", "M * N = LR(3.6, 2.4, 1.8)"
     , "M * M = LR(3.6, 2.4, 1.8)", "(N * M) * M = LR(4.32, 5.04, 2.88)"), col = c(2, 3, 4, 5, 1),
     text.col = 1, lwd = c(2,2,2,2,2), lty = c(2, 2, 3, 4, 5) )


## The function is currently defined as
function (M, N) 
{
    options(warn = -1)
    if (messages(M) != 1) {
        return(messages(M))
    }
    if (messages(N) != 1) {
        return(messages(N))
    }
    if (M[4] != N[4]) {
        return(noquote(paste0("Production has NOT a closed form of a LR fuzzy number")))
    }
    else if ((sign(M) == "Positive") & (sign(N) == "Positive")) {
        a1 = M[1] * N[1]
        a2 = (M[1] * N[2]) + (N[1] * M[2])
        a3 = (M[1] * N[3]) + (N[1] * M[3])
        a4 = (M[4] + N[4])/2
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Negative") & (sign(N) == "Negative")) {
        a1 = M[1] * N[1]
        a2 = -(M[1] * N[2]) - (N[1] * M[2])
        a3 = -(M[1] * N[3]) - (N[1] * M[3])
        a4 = abs(M[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Positive") & (sign(N) == "Negative")) {
        a1 = M[1] * N[1]
        a2 = (M[1] * N[2]) - (N[1] * M[3])
        a3 = (M[1] * N[3]) - (N[1] * M[2])
        a4 = abs(M[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Negative") & (sign(N) == "Positive")) {
        a1 = M[1] * N[1]
        a2 = (N[1] * M[2]) - (M[1] * N[3])
        a3 = (N[1] * M[3]) - (M[1] * N[2])
        a4 = abs(N[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else {
        return(noquote(paste0(
"A regular approxi. is not defined for multiplication since at least one of FNs is non + and non -"
              )))
    }
  }

Example output

Attaching package: 'Calculator.LR.FNs'

The following object is masked from 'package:base':

    sign

[1] A regular approximation is not defined for multiplication since at least one of LR fuzzy numbers is non-positive and non-negative fuzzy number
[1] A regular approximation is not defined for multiplication since at least one of LR fuzzy numbers is non-positive and non-negative fuzzy number
[1] the result of multiplication is approximately  (core = 4.5, left spread = 6, right spread = 7.5) LR
[1] the result of multiplication is approximately  (core = 3.6, left spread = 2.4, right spread = 1.8) LR
[1] the result of multiplication is approximately  (core = 3.6, left spread = 2.4, right spread = 1.8) LR
[1] the result of multiplication is approximately  (core = 1.44, left spread = 1.44, right spread = 0.48) LR
[1] the result of multiplication is approximately  (core = 4.32, left spread = 5.04, right spread = 2.88) LR
[1] the result of multiplication is approximately  (core = 3.6, left spread = 2.4, right spread = 1.8) LR
[1] the result of multiplication is approximately  (core = 4.32, left spread = 5.04, right spread = 2.88) LR
[1] the result of multiplication is approximately  (core = 3.6, left spread = 2.4, right spread = 1.8) LR
[1] the result of multiplication is approximately  (core = 1.44, left spread = 1.44, right spread = 0.48) LR
[1] the result of multiplication is approximately  (core = 3.6, left spread = 2.4, right spread = 1.8) LR
[1] the result of multiplication is approximately  (core = 4.32, left spread = 5.04, right spread = 2.88) LR
function (M, N) 
{
    options(warn = -1)
    if (messages(M) != 1) {
        return(messages(M))
    }
    if (messages(N) != 1) {
        return(messages(N))
    }
    if (M[4] != N[4]) {
        return(noquote(paste0("Production has NOT a closed form of a LR fuzzy number")))
    }
    else if ((sign(M) == "Positive") & (sign(N) == "Positive")) {
        a1 = M[1] * N[1]
        a2 = (M[1] * N[2]) + (N[1] * M[2])
        a3 = (M[1] * N[3]) + (N[1] * M[3])
        a4 = (M[4] + N[4])/2
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Negative") & (sign(N) == "Negative")) {
        a1 = M[1] * N[1]
        a2 = -(M[1] * N[2]) - (N[1] * M[2])
        a3 = -(M[1] * N[3]) - (N[1] * M[3])
        a4 = abs(M[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Positive") & (sign(N) == "Negative")) {
        a1 = M[1] * N[1]
        a2 = (M[1] * N[2]) - (N[1] * M[3])
        a3 = (M[1] * N[3]) - (N[1] * M[2])
        a4 = abs(M[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else if ((sign(M) == "Negative") & (sign(N) == "Positive")) {
        a1 = M[1] * N[1]
        a2 = (N[1] * M[2]) - (M[1] * N[3])
        a3 = (N[1] * M[3]) - (M[1] * N[2])
        a4 = abs(N[4] - 1)
        print(noquote(paste0("the result of multiplication is approximately  (core = ", 
            a1, ", left spread = ", a2, ", right spread = ", 
            a3, ")", if (a4 == 0) {
                paste0(" LR")
            }
            else if (a4 == 1) {
                paste0(" RL")
            }
            else {
                paste0(" L")
            })))
        return(invisible(c(a1, a2, a3, a4)))
    }
    else {
        return(noquote(paste0("A regular approxi. is not defined for multiplication since at least one of FNs is non + and non -")))
    }
}

Calculator.LR.FNs documentation built on May 2, 2019, 8:25 a.m.

Related to m in Calculator.LR.FNs...

Calculator.LR.FNs index
Package overview

R Package Documentation

rdrr.io home R language documentation Run R code online

Browse R Packages

CRAN packages Bioconductor packages R-Forge packages GitHub packages

We want your feedback!

Note that we can't provide technical support on individual packages. You should contact the package authors for that.
GitHub issue tracker
ian@mutexlabs.com
Personal blog

 
Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.

Close