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
Titel General representation theorems for fuzzy weak orders
Buchtitel Theory and Applications of Relationals Strucutes as Knowledge Instruments II
Typ in Sammelband
Verlag Springer
Serie Lecture Notes in Computer Science
Band 4342
Abteilung IDM
ISBN 3-540-69223-1
Jahr 2006
Seiten 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.