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Fuzzy Relation Equations with Equality and Difference Composition Operators

  • 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 will introduce other composition operators which have a plausible logical interpretation. They will be called equality and difference operator, respectively. We first define a notion of equality and difference of any two grades of membership of a fuzzy set and of a fuzzy relation. In the sequel this concept will be utilized to form the respective composition operators and the related fuzzy equations. Afterwards, we provide a method of resolution of these equations, characterizing completely the set of the solutions. All the fuzzy sets involved are defined on finite sets and with membership values in [0,1].

Keywords

Difference Operator Composition Operator Maximal Element Great Element Fuzzy Relation 
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, Fuzzy relation equations with equality and difference composition operators, Fuzzy Sets and Systems 25 (1988), 205–215.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    A. Di Nola, W. Pedrycz and S. Sessa, Modus ponens for fuzzy data realized via equations with equality operators, Internat. J. Intelligent Systems,to appear.Google Scholar
  3. [3]
    A. Di Nola, W. Pedrycz and S.Sessa, On some finite fuzzy relation equations, Inform. Sciences,to appear.Google 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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