ApplyZFunction: Function to apply the Zadeh's principle

In ZEP: Procedures Related to the Zadeh's Extension Principle for Fuzzy Data

Function to apply the Zadeh's principle

Description

ApplyZFunction applies the selected function to a fuzzy number using the Zadeh's principle.

Usage

ApplyZFunction(
  value,
  FUN,
  knots = 10,
  approximation = FALSE,
  method = "NearestEuclidean",
  ...
)

Arguments

value	Input fuzzy number.
FUN	Function used for the input fuzzy number with the help of the Zadeh's principle.
knots	Number of the alpha-cuts used during calculation of the output.
approximation	If TRUE, the approximated output is calculated.
method	The selected approximation method.
...	Additional parameters passed to other functions.

Details

The function takes the input fuzzy number value (which should be described by one of the classes from FuzzyNumbers package) and applies the function FUN using the Zadeh's principle. The output is given by a fuzzy number or its approximation (when approximation is set to TRUE and the respective method is selected). To properly find the output, value of FUN is calculated for many alpha-cuts of value. The number of these alpha-cuts is equal to knots (plus 2 for the support and the core).

The input fuzzy number value should be given by fuzzy number described by classes from FuzzyNumbers package.

Value

The output is a fuzzy number described by classes from FuzzyNumbers package (piecewise linear fuzzy number without approximation, various types with the approximation applied).

Examples

library(FuzzyNumbers)

# prepare complex fuzzy number

A <- FuzzyNumber(-5, 3, 6, 20, left=function(x)
pbeta(x,0.4,3),
right=function(x) 1-x^(1/4),
lower=function(alpha) qbeta(alpha,0.4,3),
upper=function(alpha) (1-alpha)^4)

# find the output via the Zadeh's principle

ApplyZFunction(A,FUN=function(x)x^3+2*x^2-1)

# find the approximated output via the Zadeh's principle

ApplyZFunction(A,FUN=function(x)x^3+2*x^2-1,approximation=TRUE)

ZEP documentation built on June 23, 2025, 9:07 a.m.