Fuzzy concepts and formal methods: A sample specification for a fuzzy expert system

Abstract

A fuzzy logic toolkit has been developed for the formal specification language Z. It permits the incorporation of fuzzy concepts into the language while retaining the precision of any Z specification. The toolkit provides the necessary operators, measures and modifiers for the definition and manipulation of fuzzy sets and relations. This paper illustrates how the toolkit can be used to specify a simple fuzzy expert system. The focus is on the specification of the rule base and the operations necessary for fuzzy inferencing. In particular the example illustrates the use of the fuzzy cartesian product and fuzzy set truncation operators and offers a generic definition for a centroid defuzzification function.