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Boolean Solutions of Max-Min Fuzzy Equations

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

Abstract

This Ch. is entirely dedicated to the study of the Boolean (i.e. non-fuzzy) solutions of a max-min fuzzy equation defined on a complete Brouwerian lattice L with universal bounds 0 and 1. In Sec.1, we give a simple necessary and sufficient condition for the existence of the greatest Boolean solution of S and in Sec.2, using some results of Ch.3, we determine the minimal Boolean elements of S if L is a linear lattice. In Sec.3, if Boolean solutions do not exist, an algorithm is presented to find the elements of S with maximum Boolean degree, i.e. with the maximum number of 0 and 1. The referential sets are assumed to be necessarily finite in Secs.2 and 3.

Keywords

Fundamental Theorem Minimal Element Fuzzy Relation Fuzzy Entropy Linear Lattice 
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 and A. Ventre, On Booleanity of relational equation in Brouwerian lattices, Boll. Un. Mat. Ital. (6) 3 - B (1984), 871 - 882.Google Scholar
  2. [2]
    S. Sessa, Characterizing the Boolean solutions of relational equations in Brouwerian lattices, Boll. Un. Mat. Ital. (6) 5 - B (1986), 39 - 49.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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