Fuzzy Concepts and Formal Methods

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 chapter 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 chapter provides a summary of a toolkit for Z that de nes the operators, measures and modi ers necessary for the manipulation of fuzzy sets and relations. It also illustrates, through a series of examples, how the toolkit could be applied. The chapter concludes with a re ection on some more general issues that arose during the formulation of the illustrative examples.