Bidirectional approximate reasoning based on interval-valued fuzzy sets

Abstract

This paper proposes a bidirectional approximate reasoning method based on interval-valued fuzzy sets, where fuzzy production rules are used for knowledge representation, and the fuzzy terms appearing in the fuzzy production rules of a rule-based system are represented by interval-valued fuzzy sets. The proposed method is more flexible than the one presented in the paper by Bien and Chun [IEEE Trans. Fuzzy Systems 2 (1994) 177] due to the fact that it allows the fuzzy terms appearing in the fuzzy production rules of a rule-based system to be represented by interval-valued fuzzy sets rather than general fuzzy sets. Furthermore, because the proposed method requires only simple arithmetic operations, and because it allows bidirectional approximate reasoning, it can be executed much faster and more flexible than the single-input-single-output approximate reasoning scheme presented in the paper by Gorzalczany [Fuzzy Sets and Systems 21 (1981) 10].