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α—Fuzzy Relation Equations and Decomposable Fuzzy Relations

  • Antonio di Nola
  • Salvatore Sessa
  • Witold Pedrycz
  • Elie Sanchez
Chapter
Part of the Theory and Decision Library book series (TDLD, volume 3)

Abstract

In this Ch., we investigate a new type of fuzzy relation equation defined on finite sets and with membership functions on a complete Brouwerian lattice. We characterize the entire set of the solutions when the fuzzy equation is assigned on a linear lattice. We also study when a fuzzy relation is pointwise decomposable in the intersection (resp. union) of two fuzzy sets and we show that such relations are max-min transitive (resp. compact). Finally, properties of convergence of powers of these fuzzy relations are established.

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Copyright information

© Springer Science+Business Media Dordrecht 1989

Authors and Affiliations

  • Antonio di Nola
    • 1
  • Salvatore Sessa
    • 1
  • Witold Pedrycz
    • 2
  • Elie Sanchez
    • 3
  1. 1.Facoltà di ArchitetturaUniversità di NapoliNapoliItaly
  2. 2.Department of Electrical EngineeringWinnipegCanada
  3. 3.Faculté de MédecineUniversité Aix-Marseille IIMarseilleFrance

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