| Type: | Package |
| Title: | Procedures Related to the Zadeh's Extension Principle for Fuzzy Data |
| Version: | 0.1.5 |
| Description: | Procedures for calculation, plotting, and approximation of the outputs for fuzzy numbers (see A.I. Ban, L. Coroianu, P. Grzegorzewski "Fuzzy Numbers: Approximations, Ranking and Applications" (2015)) based on the Zadeh's Extension Principle (see de Barros, L.C., Bassanezi, R.C., Lodwick, W.A. (2017) <doi:10.1007/978-3-662-53324-6_2>). |
| License: | GPL-3 |
| NeedsCompilation: | no |
| Imports: | FuzzyNumbers, methods |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Depends: | R (≥ 3.5.0) |
| Suggests: | testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| Packaged: | 2025-06-23 03:34:12 UTC; mroman |
| Author: | Maciej Romaniuk 
[cre, aut] ((Systems Research Institute Polish Academy of Sciences,
Newelska 6, 01-447 Warszawa, Poland)),
Abbas Parchami
[aut] ((Mahani Math Center, Afzalipour Research Institute, Shahid
Bahonar University of Kerman, Kerman, Iran)),
Przemyslaw Grzegorzewski
[ctb]
((Faculty of Mathematics and Information Science, Warsaw University
of Technology, Koszykowa 75, 00-662 Warsaw, Poland)) |
| Maintainer: | Maciej Romaniuk <mroman@ibspan.waw.pl> |
| Repository: | CRAN |
| Date/Publication: | 2025-06-23 03:50:02 UTC |
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 |
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)
Function to calculate D(p,q) distance.
Description
DpqDistance calculates the generalized D(p,q) distance between two fuzzy numbers.
Usage
DpqDistance(value1, value2, p = 2, q = 1/2)
Arguments
value1 |
First fuzzy number. |
value2 |
Second fuzzy number. |
p |
Value of the power (and the the root) applied in the distance calculation. |
q |
Value of the weight for the second fuzzy number (for the first one this weight is calculated as |
Details
The function calculates the generalized D(p,q) distance between two fuzzy numbers value1 and value2,
where p is the value of the applied power, and q is the weight between these two fuzzy numbers.
All of the input values should be given by fuzzy numbers described by classes from FuzzyNumbers package.
Value
The output is a numerical value (the calculated distance).
Examples
library(FuzzyNumbers)
# prepare two fuzzy numbers
A <- TrapezoidalFuzzyNumber(0,1,2,3)
B <- TrapezoidalFuzzyNumber(1,3,4,6)
# calculate the distance
DpqDistance (A,B)
Function for approximation with the help of methods other than in FuzzyNumbers package
Description
FuzzyApproximation approximates the given fuzzy number.
Usage
FuzzyApproximation(value, method = "ExpectedValueCore", ...)
Arguments
value |
Fuzzy number to approximate. |
method |
The selected approximation method. |
... |
Additional parameters passed to other functions (like approximation method from the FuzzyNumbers package). |
Details
The function approximates the fuzzy number given by value with the method selected by
method. The following approximations are possible: ExpectedValueCore–preserving the
expected value and the core of value, TriangularSupportDist–constructs the
triangular fuzzy number based on minimization of DpqDistance, preserving the support of value,
and the approximation methods from the FuzzyNumbers package (namely: Naive, NearestEuclidean, ExpectedIntervalPreserving,
SupportCoreRestricted).
The input value should be given by a fuzzy number described by classes from FuzzyNumbers package.
Value
The output is a fuzzy number (triangular or trapezoidal one) described by
classes from FuzzyNumbers package.
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 approximation
FuzzyApproximation (A)
Plot input and output for the Zadeh's principle
Description
PlotZFunction applies the selected function to a fuzzy number using the Zadeh's principle, and plots
the input and output.
Usage
PlotZFunction(
value,
FUN,
knots = 10,
grid = TRUE,
alternate = FALSE,
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. |
grid |
If |
alternate |
If |
approximation |
If |
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 and output fuzzy numbers are plotted together with the applied function.
If the approximation is used, then also the approximated fuzzy number is shown (green line).
The input fuzzy number value should be given by fuzzy number described by classes from FuzzyNumbers package.
Value
Three (or four) figures are plotted: the input fuzzy number, the respective output (for the Zadeh's principle and the applied function), and the function. The output fuzzy number can be approximated with the selected method and also plotted.
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)
# plot the figures
PlotZFunction(A,FUN=function(x)x^3+2*x^2-1)
# find and plot the approximated output via the Zadeh's principle
PlotZFunction(A,FUN=function(x)x^3+2*x^2-1,approximation=TRUE)
A vector containing names of the built-in approximation methods.
Description
'approximationMehodsInside' is a vector containing names of the built-in approximation methods.
Usage
approximationMehodsInside
Format
An object of class character of length 2.
Value
This function returns a vector of strings.
Examples
# check the names
approximationMehodsInside