Robustness of fuzzy reasoning and δ-equalities of fuzzy sets

Fuzzy reasoning methods or approximate reasoning methods are extensively used in intelligent systems and fuzzy control. In this paper we discuss how errors in premises affect conclusions in fuzzy reasoning, that is, we discuss robustness of fuzzy reasoning. After reviewing the previous work, we present robustness results for various implication operators and inference rules. All the robustness results are formulated in terms of δ-equalities of fuzzy sets. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ.