Continuity of utility functions representing fuzzy preferences |
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| Authors: | Louis Aimé Fono Maurice Salles |
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| Institution: | 1.Département de Mathématiques et Informatique, Faculté des Sciences,Université de Douala,Douala,Cameroun;2.CREM, Université de Caen,Caen cedex,France;3.Institute for SCW,Louvigny,France;4.CPNSS, London School of Economics,London,UK |
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| Abstract: | In a previous paper, we established necessary and sufficient conditions for a given binary fuzzy relation to be representable
by a utility function. In this article, we construct a crisp order topology associated to a given weakly complete fuzzy pre-order
and introduce the notion of “continuous fuzzy pre-order.” We show that this new condition and the conditions introduced in
the previous paper are together necessary and sufficient for a numerical representation of a given weakly complete fuzzy pre-order
by a continuous utility function. |
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