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Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices

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Fuzzy Relation Equations and Their Applications to Knowledge Engineering

Part of the book series: Theory and Decision Library ((TDLD,volume 3))

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Abstract

In this Ch. we continue to study the max-min fuzzy relation equation (3.3) defined on finite sets and assuming L to be a linear lattice with universal bounds 0 and 1 but endowed with an additional structure L’ of a complete linear lattice with universal bounds 0’ and 1’, tied to the foregoing one by accurate and reasonable requirements. These are basic preliminaries in order to solve some important optimization problems in the set of solutions of a fuzzy equation. Strictly speaking, introducing a suitable functional which measures the “fuzziness content” of a fuzzy relation, we characterize all the solutions of a max-min composite fuzzy equation possessing the smallest and the greatest value of such fuzziness.

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Authors and Affiliations

  1. Facoltà di Architettura, Università di Napoli, Napoli, Italy

    Antonio di Nola & Salvatore Sessa

  2. Department of Electrical Engineering, Winnipeg, Canada

    Witold Pedrycz

  3. Faculté de Médecine, Université Aix-Marseille II, Marseille, France

    Elie Sanchez

Authors
  1. Antonio di Nola
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  2. Salvatore Sessa
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  3. Witold Pedrycz
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  4. Elie Sanchez
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© 1989 Springer Science+Business Media Dordrecht

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di Nola, A., Sessa, S., Pedrycz, W., Sanchez, E. (1989). Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices. In: Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Theory and Decision Library, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1650-5_4

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  • DOI: https://doi.org/10.1007/978-94-017-1650-5_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4050-3

  • Online ISBN: 978-94-017-1650-5

  • eBook Packages: Springer Book Archive

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