General representation theorems for fuzzy weak orders
Bernard De Baets
H.C.M. de Swart
M. Roubens. G. Schmidt
|Title||General representation theorems for fuzzy weak orders|
|Booktitle||Theory and Applications of Relationals Strucutes as Knowledge Instruments II|
|Series||Lecture Notes in Computer Science|
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.