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Max-Min Decomposition Problem of a Fuzzy Relation in Linear Lattices

  • 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 solve a decomposition problem, more complicated than the problem mentioned in Sec.6.5, and precisely, we present a numerical algorithm, illustrated by a flowchart, which assures the existence of a fuzzy relation Z∈F(X×X) such that Z⊙Z=R, where R∈F(X×X) is an assigned fuzzy relation defined on a referential set X and assuming values in a linear lattice L with universal bounds 0 and 1. Connections with results already existing in recent literature are also given.

Keywords

Fuzzy Relation Maximal Solution Decomposition Problem Algebraic Characterization Arbitrary Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. Di Nola, W. Pedrycz and S. Sessa, Decomposition problem of fuzzy relations, Internat. J. Gen. Syst. 10 (1985), 123 - 133.zbMATHCrossRefGoogle Scholar
  2. [2]
    A. Di Nola, W. Pedrycz, S. Sessa and M. Higashi, Minimal and maximal solutions of a decomposition problem of fuzzy relations, Internat. J. Gen. Syst. 11 (1985), 103 - 116.CrossRefGoogle Scholar

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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