General representation theorems for fuzzy weak orders

Autoren Ulrich Bodenhofer
Bernard De Baets
János Fodor
Editoren H.C.M. de Swart
E. Orlowska
M. Roubens. G. Schmidt
TitelGeneral representation theorems for fuzzy weak orders
BuchtitelTheory and Applications of Relationals Strucutes as Knowledge Instruments II
Typin Sammelband
VerlagSpringer
SerieLecture Notes in Computer Science
Band4342
AbteilungIDM
ISBN3-540-69223-1
Jahr2006
Seiten229-244
SCCH ID#606
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 functionbased representations, (ii) inclusion-based representations, (iii) representations by decomposition into crisp linear orders and fuzzy equivalence relations.