Tools to Deal with Fuzzy Numbers in R
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Tools to Deal with Fuzzy Numbers in R

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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 the practitioners as well as by the researchers in fuzzy numbers theory (e.g. for preparing figures, generating numerical examples, or testing new algorithms).

Fuzzy set theory lets us effectively and quite intuitively represent imprecise or vague information. Fuzzy numbers, which form a particular subclass of fuzzy sets of the real line, play a significant role in many important both theoretical and practical considerations. This is because we often describe our knowledge about objects through numbers, e.g. "I'm about 180 cm tall" or "The rocket was launched between 2 and 3 p.m.".

The 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 0.4-1 Package for R, 2015

On-line manual:

Author: Marek Gagolewski, with contributions from Jan Caha

To cite package FuzzyNumbers in publications please use:

"Gagolewski M., Caha J. (2015). 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 = {2015},
   url = {}