Towards a More Adequate Defuzzification of Interval-Valued Fuzzy Sets

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Van Nam Huynh
Yoshiteru Nakamori

Publication Date

6-2010

Comments

Technical Report: UTEP-CS-08-33a

To appear in the Proceedings of the 7th International Conference on Modeling Decisions for Artificial Intelligence MDAI'2010, Perpignan, French Catalonia, France, October 27-29, 2010

Abstract

It is known that interval-valued fuzzy sets [m(x)] provide a more adequate description of expert uncertainty than the more traditional "type-1" (number-valued) fuzzy techniques. Specifically, an interval-valued fuzzy set can be viewed as a class of possible fuzzy sets m(x) from [m(x)]. In this case, as a result of defuzzification, it is natural to return the range [u] of all possible values u(m) that can be obtained by defuzzifying membership functions m(x) from this class. In practice, it is reasonable to restrict ourselves only to fuzzy numbers m(x), i.e., to "unimodal" fuzzy sets. Under this restriction, in general, we get a narrower range [a] of possible values of u(m). In this paper, we describe a feasible algorithm for computing the new range [a].