# 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: `Extract`, `PowerFuzzyNumber`, `alphaInterval()`, `as.PowerFuzzyNumber()`, `as.TrapezoidalFuzzyNumber()`, `as.character()`, `expectedInterval()`

## Examples

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

FuzzyNumbers documentation built on Nov. 15, 2021, 5:09 p.m.