A compendium of fuzzy weak orders: Representations and constructions

Ulrich Bodenhofer, Bernard De Baets, János Fodor

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)811-829
Number of pages19
JournalFuzzy Sets and Systems
Issue number8
Publication statusPublished - 16 Apr 2007
Externally publishedYes


  • Fuzzy preference modeling
  • Fuzzy relation
  • Fuzzy weak order


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