Fuzzy concepts and formal methods: some illustrative examples

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Speci cation 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 di cult 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 working paper identi es 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 an extended notation for Z, incorporating fuzzy concepts, can be used across a variety of problem domains. Several examples are presented and these underpin the discussion. In particular the following issues are addressed: The representation of fuzzy concepts as invariant and/or multi-dimensional fuzzy sets. The limitation of a crisp approach when modelling such concepts. Operations that add or remove elements from fuzzy sets. Fuzzy relations. System requirements as a series of linguistically quanti ed propositions.