The representation of interaction among fuzzy rules

In this paper, we apply the interaction model established by M. Grabisch (Fuzzy Sets and System, Vol. 92, pp. 167-189, 1997) to the reasoning of fuzzy production rules. When fuzzy production rules are used in approximate reasoning, interaction exists among rules that have the same consequent but different antecedent. In order to deal with the interaction among fuzzy rules properly, we employ a kind of representation coming from cooperative game theory, named interaction index (e.g. Shapley value) and discuss how to determine the interaction index among fuzzy rules via the fuzzy measure which is defined on the set of fuzzy rules. This paper also roughly discusses how to examine the interaction about fuzzy rules coming from experience.