A compendium of fuzzy weak orders: Representations and constructions

  • Authors:

  • Ulrich Bodenhofer;Bernard De Baets;János Fodor

  • Affiliations:

  • Institute of Bioinformatics, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, Austria;Department of Applied Mathematics, Biometrics, and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Institute of Intelligent Engineering Systems, Budapest Tech, H-1034 Budapest, Hungary

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2007

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Abstract

The present paper gives a state-of-the-art overview of representation and construction results for fuzzy weak orders. We do not assume that the underlying domain 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, each of which also provides a construction method: (i) score function-based representations, (ii) inclusion-based representations, (iii) representations by decomposition into crisp linear orders and fuzzy equivalence relations, which also facilitates a pseudo-metric-based construction.