Fuzzy Concepts and Formal Methods: A Fuzzy Logic Toolkit for Z

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the IS problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This paper suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. We provide a summary of a toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations. We also provide some examples of the laws which establishes an isomorphism between the extended notation presented here and conventional Z when applied to boolean sets and relations.

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