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Continuity of utility functions representing fuzzy preferences

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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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en

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http://eprints.lse.ac.uk/38289/

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