Some new qualitative insights into quality of fuzzy rule-based models

Rules in fuzzy rule-based models convey essential knowledge about the system under discussion. As such, they capture the essence of relationships occurring among input and output variables. While the quality of such fuzzy models is predominantly related with the accuracy and eventual interpretability of rules (although to a limited extent), the quality of rules being regarded as generic pieces of knowledge has not been studied so far. In this study, we formulate and investigate this problem by looking at the quality of rules, including aspects of (a) stability, (b) generalizability, and (c) conflict. We identify a concept of rule multiplicity, conflict, and study an emergence of rule generalization. A number of pertinent performance indices are developed, and their usage is presented through a series of experimental studies.