General representation theorems for fuzzy weak orders

Authors Ulrich Bodenhofer
Bernard De Baets
János Fodor
Editors H.C.M. de Swart
E. Orlowska
M. Roubens. G. Schmidt
Title General representation theorems for fuzzy weak orders
Booktitle Theory and Applications of Relationals Strucutes as Knowledge Instruments II
Type in collection
Publisher Springer
Series Lecture Notes in Computer Science
Volume 4342
Department IDM
ISBN 3-540-69223-1
Year 2006
Pages 229-244
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.