Representations and constructions of fuzzy weak orders

Abstract

In this memory,we have highlighted various representations of fuzzy weak orders.Score function-based representations and the decomposition of fuzzy weak orders into crisp linear orders and fuzzy equivalence relations also provided us with practically feasible construction methods.For the latter,we have exploited the correspondence between pseudo-mettrics and fuzzy equivalence relations that holds if we restrict to continuous Archmedes t-norms.Unlike most of the exsisting literature, we have not assumed that the underlying domain is finite.The exampelesin this memory demostrate that meaningful construction are possibel even for non-countable domains.