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General Representation Theorems for Fuzzy Weak Orders

  • Ulrich Bodenhofer
  • Bernard De Baets
  • János Fodor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4342)

Abstract

The present paper gives a state-of-the-art overview of general representation results for fuzzy weak orders. We do not assume that the underlying domain of alternatives is finite. Instead, we concentrate on results that hold in the most general case that the underlying domain is possibly infinite. This paper presents three fundamental representation results: (i) score function-based representations, (ii) inclusion-based representations, (iii) representations by decomposition into crisp linear orders and fuzzy equivalence relations.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ulrich Bodenhofer
    • 1
  • Bernard De Baets
    • 2
  • János Fodor
    • 3
  1. 1.Institute of BioinformaticsJohannes Kepler UniversityLinzAustria
  2. 2.Dept. of Applied Mathematics, Biometrics, and Process ControlGhent UniversityGentBelgium
  3. 3.Institute of Intelligent Engineering SystemsBudapest TechBudapestHungary

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