Fuzzy concepts and formal methods

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 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 thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.