Fuzzy concepts and formal methods: some illustrative examples

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 information systems (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 identifies the problem types of interest and argues that they are characterised by uncertainty and imprecision. It suggests fuzzy set theory as a useful formalism for modelling aspects of this imprecision. The paper illustrates how a fuzzy logic toolkit for Z can be applied to such problem domains. Several examples are presented illustrating the representation of imprecise concepts as fuzzy sets and relations, and soft pre-conditions and system requirements as a series of linguistically quantified propositions.