The authors correctly emphasize that taking “fuzzy logic” as referring to a particular control-engineering methodology is, although common, nevertheless a narrow and incomplete understanding of fuzzy logic research. At least two other AI-related topics can be found when scanning fuzzy set literature: multiple-valued logic and approximate reasoning.

After a short characterization of rule-based fuzzy control as a “simple device for interpolating between numerically valued conclusions of parallel rules,” they briefly present possibility theory as a formal framework for dealing with “uncertainty pervading available information in reasoning problems,” and with “preference among more or less acceptable values in a decision-oriented perspective.” Another important facet of fuzzy set theory is that it provides a natural interface between numerical and linguistic data, thereby allowing for capturing gradedness in reasoning devices.

Although fuzzy set theory proposes formalizations of some forms of, and has its root in, commonsense reasoning, it has not become part of mainstream AI research. The authors, however, believe that there is a realistic chance for full acceptance as part of AI based on the semantic, syntactic, and computational capabilities of fuzzy set methods.