A compendium of fuzzy weak orders: Representations and constructions

U. Bodenhofer, B. De Baets, J. Fodor. A compendium of fuzzy weak orders: Representations and constructions. Fuzzy Sets and Systems, volume 158, number 8, pages 811-829, 2007.

Autoren
  • Ulrich Bodenhofer
  • Bernard De Baets
  • János Fodor
TypArtikel
JournalFuzzy Sets and Systems
Nummer8
Band158
Jahr2007
Seiten811-829
Abstract The present paper gives a state-of-the-art overview ofrepresentation 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.