R/WMethod.R

In FuzzyResampling: Resampling Methods for Triangular and Trapezoidal Fuzzy Numbers

#' w method for resampling triangular and trapezoidal fuzzy numbers
#'
#' @description
#' `WMethod` returns the secondary (bootstrapped) sample and uses the resampling
#' scheme based on the special \emph{w density} which is related to the left ends of the cores and increments
#'  (i.e. length of the core,
#'  left and right increment of the support) of the fuzzy variables from
#'  the initial sample (the d method, see (Romaniuk and Hryniewicz, 2019)).
#'
#'
#' @details
#' The initial sample should consist of triangular or trapezoidal fuzzy numbers, given as a single vector or a whole matrix.
#' In each row, there should be a single fuzzy number in one of the forms:
#' \enumerate{
#'  \item left end of the support, left end of the core, right end of the core, right end of the support, or
#'  \item left increment of the support, left end of the core, right end of the core, right increment of the support.
#' }
#' In this second case, the parameter \code{increases=TRUE} has to be used.
#'
#' The resampling procedure produces \code{b} fuzzy values.
#' During the first step, the four values are randomly generated using the special \emph{w density}:
#' left end of the core, length of the core, left and right increment of the support.
#' This \emph{w density} is calculated based on the whole fuzzy sample.
#' Then the new fuzzy variable, which preserves the above-mentioned characteristics, is created.
#' If the parameter \code{b} is not specified, it is equal to the length of the initial sample.
#' The output is given in the same form as the initial sample.
#'
#'
#' @param initialSample Initial sample of triangular or trapezoidal fuzzy numbers.
#'
#' @param b The number of fuzzy values in the resampled (secondary) sample.
#' If this parameter is not specified, the number of values in the initial sample is used.
#' The parameter should be integer value more than 0.
#'
#'
#' @param increases If \code{TRUE} is used, then the initial sample should consist of the fuzzy numbers in the form:
#'  left increment of the support, left end of the core, right end of the core,
#' right increment of the support. Otherwise, the default value \code{FALSE} is used and the fuzzy numbers should be given in the form:
#' left end of the support, left end of the core, right end of the core,
#' right end of the support.
#'
#' @return This function returns matrix with \code{b} rows of double values.
#' In each row, there is a single resampled fuzzy number.
#' These fuzzy numbers have the same form as the values from the initial sample depending on the provided parameter \code{increases}.
#'
#'
#' @family resampling functions
#'
#' @seealso \code{\link{ClassicalBootstrap}},
#' \code{\link{EWMethod}} for the EW method, \code{\link{VAFMethod}} for the VAF method,
#' \code{\link{VAAMethod}} for the VAA method
#'
#' @importFrom stats runif
#'
#' @examples
#'
#' # prepare some fuzzy numbers (first type of the initial sample)
#'
#' fuzzyValues <- matrix(c(0.25,0.5,1,1.25,0.75,1,1.5,2.2,-1,0,0,2),
#' ncol = 4,byrow = TRUE)
#'
#' # generate the secondary sample using the w method
#'
#' set.seed(12345)
#'
#' WMethod(fuzzyValues)
#'
#' WMethod(fuzzyValues,b=4)
#'
#' # prepare some fuzzy numbers (second type of the initial sample)
#'
#' fuzzyValuesInc <- matrix(c(0.25,0.5,1,0.25,0.25,1,1.5,0.7,1,0,0,2),
#' ncol = 4,byrow = TRUE)
#'
#' # generate the secondary sample using the w method
#'
#' WMethod(fuzzyValuesInc,increases = TRUE)
#'
#' WMethod(fuzzyValuesInc,b=4,increases = TRUE)
#'
#' @references
#'
#' Romaniuk, M., Hryniewicz, O. (2019)
#' Interval-based, nonparametric approach for resampling of fuzzy numbers
#' Soft Computing, 23 (14), pp. 5883-5903
#'
#' @export
#'



# w resampling method

WMethod <- function(initialSample, b = n, increases = FALSE)
{
  # changing possible vector to matrix

  if(is.vector(initialSample))
  {
    initialSample <- matrix(initialSample,nrow=1)
  }

  ParameterCheckForInitialSample(initialSample)

  # setting n

  n <- nrow(initialSample)

  # checking b parameter

  if(!IfInteger(b) | b <= 0)
  {
    stop("Parameter b should be integer value and > 0")
  }

  # checking the validity of increases

  if(!is.logical(increases))
  {
    stop("Parameter increases should have logical value")
  }


  # check form of the initial sample

  if(increases)
  {
    initialSample <- TransformFromIncreases(initialSample)
  }

  # checking consistency of fuzzy numbers

  if(!all(apply(initialSample, 1, IsFuzzy)))
  {
    stop("Some values in  initial sample are not correct fuzzy numbers")
  }

  # calculate and sort ends and increaments

  spreads <- TransformToAllSpreads(initialSample)

  # cat("spreads:\n")
  # print(spreads)

  spreads <- apply(spreads, 2, sort)

  # cat("Sorted spreads: \n")
  # print(as.matrix(spreads))

  # sample new cores and supports

  newLeftEndCore <- replicate(b,WFunction(spreads[,2]))

  # cat("newLeftEndCore: ", newLeftEndCore, "\n")

  newIncreaseCore <- replicate(b,WFunction(spreads[,3]))

  # cat("newIncreaseCore: ", newIncreaseCore, "\n")

  newLeftIncreaseSpread <- replicate(b,WFunction(spreads[,1]))

  # cat("newLeftIncreaseSpread: ", newLeftIncreaseSpread, "\n")

  newRightIncreaseSpread <- replicate(b,WFunction(spreads[,4]))

  # cat("newRightIncreaseSpread: ", newRightIncreaseSpread, "\n")

  # generate the output

  outputSample <- matrix(c(newLeftEndCore-newLeftIncreaseSpread,
                           newLeftEndCore,
                           newLeftEndCore+newIncreaseCore,
                           newLeftEndCore+newIncreaseCore+newRightIncreaseSpread),
                         ncol = 4)


  # change form of the output sample

  if(increases)
  {
    outputSample <- TransformToIncreases(outputSample)
  }

  return(outputSample)

}