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International Conference of B and Z Users

ZB 2000: ZB 2000: Formal Specification and Development in Z and B pp 491–510Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1878))

Abstract

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.

The authors would like to thank Dr. Roger Duke (Dept of Computer Science and Electrical Engineering, University of Queensland, Aus.) and Mr. Steve Dunne (School of Computing and Mathematics, University of Teesside, U.K.) for their constructive comments and suggestions made during the preparation of this paper.

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Authors and Affiliations

  1. Division of Information Technology, School of Management, Technology and Environment, La Trobe University, P.O. Box 199, Bendigo, 3552, Victoria, Australia

    Chris Matthews

  2. School of Management Information Sciences, Deakin University, Burwood, Victoria, Australia

    Paul A. Swatman

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  1. Chris Matthews
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  2. Paul A. Swatman
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Matthews, C., Swatman, P.A. (2000). Fuzzy Concepts and Formal Methods: A Fuzzy Logic Toolkit for Z. In: ZB 2000: Formal Specification and Development in Z and B. ZB 2000. Lecture Notes in Computer Science, vol 1878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44525-0_29

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  • DOI: https://doi.org/10.1007/3-540-44525-0_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67944-8

  • Online ISBN: 978-3-540-44525-8

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