S4 class Representing a Fuzzy Number with Sides Given by Power Functions

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Description

Bodjanova-type fuzzy numbers which sides are given by power functions are defined using four coefficients a1 <= a2 <= a3 <= a4, and parameters p.left, p.right>0, which determine exponents for the side functions.

Details

We have left(x)=x^p.left, and right(x)=(1-x)^p.right.

This class is a natural generalization of trapezoidal FNs. For other see PiecewiseLinearFuzzyNumber.

Slots

a1, a2, a3, a4, lower, upper, left, right:

Inherited from the FuzzyNumber class.

p.left:

single numeric value; 1.0 for a trapezoidal FN.

p.right:

single numeric value; 1.0 for a trapezoidal FN.

Extends

Class FuzzyNumber, directly.

References

Bodjanova S. (2005), Median value and median interval of a fuzzy number, Information Sciences 172, pp. 73-89.

See Also

PowerFuzzyNumber for a convenient constructor, as.PowerFuzzyNumber for conversion of objects to this class.

PowerFuzzyNumber for a convenient constructor

Other PowerFuzzyNumber-method: PowerFuzzyNumber; alphaInterval, alphaInterval,FuzzyNumber-method, alphaInterval,PiecewiseLinearFuzzyNumber-method, alphaInterval,PowerFuzzyNumber-method, alphaInterval,TrapezoidalFuzzyNumber-method; as.PowerFuzzyNumber, as.PowerFuzzyNumber,FuzzyNumber-method, as.PowerFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.PowerFuzzyNumber,PowerFuzzyNumber-method, as.PowerFuzzyNumber,TrapezoidalFuzzyNumber-method, as.PowerFuzzyNumber,numeric-method; as.TrapezoidalFuzzyNumber, as.TrapezoidalFuzzyNumber,FuzzyNumber-method, as.TrapezoidalFuzzyNumber,PiecewiseLinearFuzzyNumber-method, as.TrapezoidalFuzzyNumber,PowerFuzzyNumber-method, as.TrapezoidalFuzzyNumber,TrapezoidalFuzzyNumber-method, as.TrapezoidalFuzzyNumber,numeric-method; as.character, as.character,FuzzyNumber-method, as.character,PiecewiseLinearFuzzyNumber-method, as.character,PowerFuzzyNumber-method, as.character,TrapezoidalFuzzyNumber-method; expectedInterval, expectedInterval,FuzzyNumber-method, expectedInterval,PiecewiseLinearFuzzyNumber-method, expectedInterval,PowerFuzzyNumber-method, expectedInterval,TrapezoidalFuzzyNumber-method

Examples

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showClass("PowerFuzzyNumber")
showMethods(classes="PowerFuzzyNumber")

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