# FuzzyNumbers v0.4-6

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## Tools to Deal with Fuzzy Numbers

S4 classes and methods to deal with fuzzy numbers. They allow for computing any arithmetic operations (e.g., by using the Zadeh extension principle), performing approximation of arbitrary fuzzy numbers by trapezoidal and piecewise linear ones, preparing plots for publications, computing possibility and necessity values for comparisons, etc.

## Functions in FuzzyNumbers

 Name Description expectedInterval Calculate the Expected Interval of a Fuzzy Number PiecewiseLinearFuzzyNumber Creates a Piecewise Linear Fuzzy Number ^,PiecewiseLinearFuzzyNumber,numeric-method Integer power of fuzzy number PowerFuzzyNumber-class S4 class Representing a Fuzzy Number with Sides Given by Power Functions show Print Basic Information on a Fuzzy Number arctan2 Arc-tangent PowerFuzzyNumber Creates a Fuzzy Number with Sides Given by Power Functions as.FuzzyNumber Converts an Object to a Fuzzy Number TrapezoidalFuzzyNumber-class S4 class Representing a Trapezoidal Fuzzy Number core Calculate the Core of a Fuzzy Number distance Calculate the Distance Between Two Fuzzy Numbers expectedValue Calculate the Expected Value of a Fuzzy Number fapply Apply a Function on a Fuzzy Number necessityExceedance Necessity of exceedance necessityStrictExceedance Necessity of strict exceedance FuzzyNumber-class S4 class Representing a Fuzzy Number FuzzyNumber Creates a Fuzzy Number FuzzyNumbers-package Tools to Deal with Fuzzy Numbers PiecewiseLinearFuzzyNumber-class S4 Class Representing a Piecewise Linear Fuzzy Number TrapezoidalFuzzyNumber Creates a Trapezoidal Fuzzy Number Arithmetic Arithmetic Operations on Fuzzy Numbers supp Calculate the Support of a Fuzzy Number DiscontinuousFuzzyNumber-class **EXPERIMENTAL** S4 Class Representing a Fuzzy Number with Discontinuous Side Functions or Alpha-Cut Bounds trapezoidalApproximation Trapezoidal Approximation of a Fuzzy Number convertAlpha Convert a Given Upper/Lower Alpha-Cut Function to an Alpha-Cut Generating Function alphaInterval Compute the Alpha-Interval of a Fuzzy Number TriangularFuzzyNumber Creates a Triangular Fuzzy Number alphacut Compute Alpha-Cuts convertSide Convert a Given Side Function to Side Generating Function as.PiecewiseLinearFuzzyNumber Converts an Object to a Piecewise Linear Fuzzy Number integrateAlpha Numerically Integrate Alpha-Cut Bounds as.PowerFuzzyNumber Converts an Object to a Power Fuzzy Number as.TrapezoidalFuzzyNumber Converts an Object to a Trapezoidal Fuzzy Number as.character Get Basic Information on a Fuzzy Number in a String integrate_discont_val Integrate a Function with at Most Finite Number of Discontinuities *EXPERIMENTAL* piecewiseLinearApproximation Piecewise Linear Approximation of a Fuzzy Number maximum Maximum of fuzzy nubmers minimum Minimum of fuzzy nubmers plot Plot a Fuzzy Number necessityStrictUndervaluation Necessity of strict undervaluation necessityUndervaluation Necessity of undervaluation possibilityExceedance Possibility of exceedance value Calculate the Value of a Fuzzy Number possibilityStrictExceedance Possibility of strict exceedance possibilityStrictUndervaluation Possibility of strict undervaluation weightedExpectedValue Calculate the Weighted Expected Value of a Fuzzy Number possibilityUndervaluation Possibility of undervaluation width Calculate the Width of a Fuzzy Number DiscontinuousFuzzyNumber Creates a Fuzzy Number with Possibly Discontinuous Side Functions or Alpha-Cut Bounds Extract FuzzyNumber Slot Accessors approxInvert Approximate the Inverse of a Given Function ambiguity Calculate the Ambiguity of a Fuzzy Number evaluate Evaluate the Membership Function No Results!