Interface optimality in fuzzy inference systems

In this paper we address the issue of designing optimal fuzzy interfaces, which are fundamental components of a fuzzy inference system. Due to the different roles of input and output interfaces, optimality conditions are analyzed separately for the two types of interface. We prove that input interfaces are optimal when based on a particular class of fuzzy sets called “bi-monotonic”, provided that mild conditions hold. The class of bi-monotonic fuzzy sets covers a broad range of fuzzy sets shapes, including convex fuzzy sets, so that the provided theoretical results can be applied to several fuzzy models. Such theoretical results are not applicable to output interfaces, for which a different optimality criterion is proposed. Such criterion leads to the definition of an optimality degree that measures the quality of a fuzzy output interface. Illustrative examples are presented to highlight the features of the proposed optimality degree in assessing the quality of output interfaces.