Fuzzy Relation Equations with Equality and Difference Composition Operators
In this Ch. we will introduce other composition operators which have a plausible logical interpretation. They will be called equality and difference operator, respectively. We first define a notion of equality and difference of any two grades of membership of a fuzzy set and of a fuzzy relation. In the sequel this concept will be utilized to form the respective composition operators and the related fuzzy equations. Afterwards, we provide a method of resolution of these equations, characterizing completely the set of the solutions. All the fuzzy sets involved are defined on finite sets and with membership values in [0,1].
KeywordsDifference Operator Composition Operator Maximal Element Great Element Fuzzy Relation
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