# PowerFuzzyNumber-class: S4 class Representing a Fuzzy Number with Sides Given by... In FuzzyNumbers: Tools to Deal with Fuzzy Numbers

## 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.

`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

 ```1 2``` ```showClass("PowerFuzzyNumber") showMethods(classes="PowerFuzzyNumber") ```

FuzzyNumbers documentation built on May 30, 2017, 3:47 a.m.