Authors:
Pim van den Broek
1
and
Joost Noppen
2
Affiliations:
1
University of Twente, Netherlands
;
2
University of Lancaster, United Kingdom
Keyword(s):
Fuzzy weighted average, Membership functions.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Information Processing, Fusion, Text Mining
;
Fuzzy Systems
;
Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic
;
Soft Computing
Abstract:
An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact membership functions of the fuzzy weighted average. Up to now, only algorithms exist for the computation of the extremal values of the α-cuts for a fixed value of α. To illustrate the power of our algorithms, they are applied to several examples from the literature, providing exact membership functions in each case.