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 fuzzy numbers theory (e.g., for testing new algorithms, generating numerical examples, preparing figures).
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.".
For the formal definition of a fuzzy number
please refer to the '>FuzzyNumber man page.
Note that this package also deals with particular types
of fuzzy numbers like trapezoidal, piecewise linear, or ``parametric'' FNs
(see '>TrapezoidalFuzzyNumber
'>PiecewiseLinearFuzzyNumber,
'>PowerFuzzyNumber, and *EXPERIMENTAL*
'>DiscontinuousFuzzyNumber)
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 by triangular
and piecewise linear FNs (see e.g. expectedValue,
value, trapezoidalApproximation,
piecewiseLinearApproximation),
Visualization of FNs (see plot, as.character),
Basic operations on FNs (see e.g. fapply and Arithmetic),
etc.
For a complete list of classes and methods
call help(package="FuzzyNumbers").
Moreover, you will surely be interested in a step-by-step guide to the
package usage and features which is available at the project's webpage.
Keywords: Fuzzy Numbers, Fuzzy Sets, Shadowed Sets, Trapezoidal Approximation, Piecewise Linear Approximation, Approximate Reasoning, Imprecision, Vagueness, Randomness.
Acknowledgments: Many thanks to Jan Caha, Przemyslaw Grzegorzewski, Lucian Coroianu, and Pablo Villacorta Iglesias for stimulating discussion.
The development of the package in March-June 2013 was partially supported by the European Union from resources of the European Social Fund, Project PO KL ``Information technologies: Research and their interdisciplinary applications'', agreement UDA-POKL.04.01.01-00-051/10-00.
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