A compendium of fuzzy weak orders: Representations and constructions

Ulrich Bodenhofer, Bernard De Baets, János Fodor

Research output: Contribution to journalArticle

69 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)811-829
Number of pages19
JournalFuzzy Sets and Systems
Volume158
Issue number8
DOIs
Publication statusPublished - Apr 16 2007

Keywords

  • Fuzzy preference modeling
  • Fuzzy relation
  • Fuzzy weak order

ASJC Scopus subject areas

  • Logic
  • Artificial Intelligence

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