Operators and Membership Functions in Decision Models

Abstract

Many papers in the area of fuzzy sets start with statements such as “Given membership function µ _A (x) and assuming that the minimum operator is an appropriate model for the intersection of fuzzy sets.…” If fuzzy set theory is considered to be a purely formal theory, such statements are certainly acceptable, even though some kind of formal justification of these assumptions would be desirable. If, however, fuzzy set theory is used to model real phenomena and we assert these models to be true models of reality then some kind of empirical justification is absolutely necessary.