Interpretability Constraints and Criteria for Fuzzy Systems

Fuzzy systems are commonly considered suitable tools to express knowledge in a human comprehensible fashion. This kind of characterization makes them eligible for being applied in several contexts where interpretability is a major issue and humans may profit from a self-explanatory form of automatic computation. However, fuzzy systems are not interpretable per se and the simple adoption of a natural language representation does not guarantee full acceptance and plain confidence among human experts. A number of constraints and criteria have been proposed in literature to drive the design and the construction of fuzzy systems so that they can be deemed interpretable. The aim of this chapter is to provide a thorough exposition of constraints and criteria which have been variously adopted in the research community in this context of investigation. Due to their heterogeneity and multiplicity, we resorted to a particular arrangement of their presentation. By following a hierarchical organization, we start from the basic constituents of a fuzzy system (namely, the fuzzy sets) and we go through the other design levels where compound elements are involved: for each level, an exhaustive review of interpretability constraints and criteria is expounded supplying formal definitions, illustrative examples, and bibliographical references.