TY - JOUR
T1 - A compendium of fuzzy weak orders
T2 - Representations and constructions
AU - Bodenhofer, Ulrich
AU - De Baets, Bernard
AU - Fodor, János
N1 - Funding Information:
The authors gratefully acknowledge support by COST Action 274 “TARSKI”. When this paper was mainly written, Ulrich Bodenhofer was affiliated with Software Competence Center Hagenberg, A-4232 Hagenberg, Austria. Therefore, he thanks for support by the Austrian Government, the State of Upper Austria, and the Johannes Kepler University Linz in the framework of the Kplus Competence Center Program. János Fodor was partly supported by the Grant OTKA T046762.
PY - 2007/4/16
Y1 - 2007/4/16
N2 - The present paper gives a state-of-the-art overview of representation 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.
AB - The present paper gives a state-of-the-art overview of representation 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.
KW - Fuzzy preference modeling
KW - Fuzzy relation
KW - Fuzzy weak order
UR - http://www.scopus.com/inward/record.url?scp=33847258860&partnerID=8YFLogxK
U2 - 10.1016/j.fss.2006.10.005
DO - 10.1016/j.fss.2006.10.005
M3 - Article
AN - SCOPUS:33847258860
SN - 0165-0114
VL - 158
SP - 811
EP - 829
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
IS - 8
ER -