PowerFuzzyNumber-class: S4 class Representing a Fuzzy Number with Sides Given by Power Functions
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.
Arguments
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.
Details
We have \(\mathtt{left}(x)=x^{\mathtt{p.left}}\),
and \(\mathtt{right}(x)=(1-x)^{\mathtt{p.right}}\).
This class is a natural generalization of trapezoidal FNs.
For other see '>PiecewiseLinearFuzzyNumber.
References
Bodjanova S. (2005), Median value and median interval of a fuzzy number,
Information Sciences 172, pp. 73-89.