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Lower 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

The whole of this Ch. is devoted to the study of the lower solutions of max-min fuzzy equations. In all the Secs., except Secs. 5 and 6, we assume L to be a linear lattice with universal bounds 0 and 1 and the domains, on which fuzzy sets and fuzzy relations are defined, to be finite sets, we denote by |X| the cardinality of a finite set X. In Secs. 1 and 2, we deal with max-min fuzzy equations of type (2.5) and (2.6), respectively. Further lattice results in the set S are given in Sec.3 and interesting properties of a particular fuzzy relation of S are pointed out in Sec.4. Secs.5 and 6 are devoted to the study of lower solutions of max-min fuzzy equations defined on complete Brouwerian lattices and on complete completely distributive lattices, respectively.

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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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