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Tools to Deal with Fuzzy Numbers in R

FuzzyNumbers is an open source (LGPL 3) package for R. It provides S4 classes and methods to deal with fuzzy numbers. The package may be used by researchers in FN theory, e.g., for preparing figures, generating numerical examples, or testing new algorithms.

Fuzzy set theory gives one of many ways (in particular, see Bayesian probabilities) to represent imprecise information. Fuzzy numbers form a particular subclass of fuzzy sets of the real line. The main idea behind this concept is motivated by the observation that people tend to describe their knowledge about objects through vague numbers, e.g., "I'm about 180 cm tall" or "The event happened between 2 and 3 p.m.".

The FuzzyNumbers package aims to provide the following functionality:

  • Representation of arbitrary fuzzy numbers (including FNs with discontinuous side functions and/or alpha-cuts), as well as their particular types, e.g., trapezoidal and piecewise linear fuzzy numbers,

  • Defuzzification and approximation of FNs by triangular and piecewise linear fuzzy numbers,

  • Visualization,

  • Basic arithmetic operations,

  • Ranking of fuzzy numbers (implemented operators <=, <, >, >= in forms of possibility and necessity functions - works only for PiecewiseLinearFuzzyNumbers for now),

  • and many more.

Package record on CRAN:

Tutorial: Gagolewski M., Caha J., A Guide to the FuzzyNumbers Package for R, 2019.

Author: Marek Gagolewski, with contributions from Jan Caha

To cite package FuzzyNumbers in publications please use:

"Gagolewski M., Caha J. (2021). FuzzyNumbers Package: Tools to deal with fuzzy numbers in R."

A BibTeX entry for LaTeX users is:

   title = {FuzzyNumbers Package: Tools to deal with fuzzy numbers in R},
   author = {Marek Gagolewski},
   year = {2021},
   url = {}