Distance-type Fuzzy Reasoning algorithm for Generalization Fuzzy Rule

Abstract

In the previous paper, authors propose the distance type fuzzy reasoning method based on the distance between fuzzy sets. In this paper, the distance type fuzzy reasoning method for the fuzzy rule with the optional logic relation is proposed in order to expand use range of the distance type fuzzy reasoning method. The proposed new fuzzy reasoning method has the following advantages over the conventional method : (1) reasoning consequence also becomes, convex fuzzy sets if fuzzy sets are convex for the then part of the conditional proposition ; (2) modus ponens is strictly satisfied ; and (3) precise consequence can also be reasoned in the case that the antecedent is set of singleton type.