Which Are the Correct Membership Functions? Correct "And"- and "Or"- Operations? Correct Defuzzification Procedure?

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Shahnaz Shahbazova, Azerbaijan Technical UniversityFollow

Publication Date

3-2020

Comments

Technical Report: UTEP-CS-20-22

Abstract

Even in the 1990s, when many successful examples of fuzzy control appeared all the time, many users were somewhat reluctant to use fuzzy control. One of the main reasons for this reluctance was the perceived subjective character of fuzzy techniques -- for the same natural-language rules, different experts may select somewhat different membership functions and thus get somewhat different control/recommendation strategies. In this paper, we promote the idea that this selection does not have to be subjective. We can always select the "correct" membership functions, i.e., functions for which, on previously tested case, we got the best possible control. Similarly, we can select the "correct" and- and or-operations, the correct defuzzification procedure, etc.