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A compendium of fuzzy weak orders: representations and constructions. (English) Zbl 1119.06001
Summary: 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.

MSC:
06A99 Ordered sets
03E72 Theory of fuzzy sets, etc.
91B08 Individual preferences
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