An Interpretation of Fuzzy Reasoning Based on Conjunction Functions in View of Uncertainty Generation Rules Using Necessity Measures

Abstract

In this paper, the conventional fuzzy reasoning methods, where the fuzzy relations are defined by using conjunctive functions, are interpreted in view of uncertainty generation rules using necessity measures. The variables in conclusion parts of uncertainty generation rules are regarded as conjunctive variables which represent the possible ranges of disjunctive variables. A disjunctive variable takes only one value in a specified range, whereas a conjunctive variable takes one or more values. Considering the difference between disjunctive and conjunctive variables, a fuzzy reasoning method based on the uncertainty generation rules using necessity measures is formulated. Since the formulated fuzzy reasoning method is resemble to the conventional fuzzy reasoning method using conjunctive function in form, the relationships are discussed. The class of the conventional fuzzy reasoning method interpreted as fuzzy reasoning method under uncertainty generation rules is obtained together with mapping from implication functions to conjunctive functions and the inverse. These obtained mappings represent the correspondence between an implication function used in the necessity measure and a conjunctive function used in fuzzy relation. The properties of the mappings are investigated.