Robustness of fuzzy reasoning and δ-equalities of fuzzy sets

Abstract

Fuzzy reasoning methods (or approximate reasoning methods) are extensively used in intelligent systems and fuzzy control. In this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning, that is, he discusses the robustness of fuzzy reasoning. After reviewing his previous work (1996), he presents robustness results for various implication operators and inference rules. All the robustness results are formulated in terms of /spl delta/-equalities of fuzzy sets. Two fuzzy sets are said to be /spl delta/-equal if they are equal to an extent of /spl delta/.