Intransitivity of uncertain preferential judgments and fuzzy utility modeling

The issues addressed here are systematic intransitivity of uncertain preferential judgments and their descriptive modeling by fuzzy utilities. Throughout this paper the ‘uncertainty’ of preferential judgments is associated with the degree of support for the judgments. First the degree of support for pairwise comparative judgments was understood as a membership grade in a fuzzy preference relation. Then three levels of fuzzy transitivities are introduced, and the paper hypothetically supposed the conditions under which empirically well-known typical stochastic intransitivities occur are same for the violation of such fuzzy transitivities. In this context some experiments were designed as paired comparisons between multiattribute alternatives. Their analyzed results suggested the occurrence of several types of intransitivities of fuzzy preferential judgments. Next, to comprehend the confirmed intransitivities, some properties on human judgmental processing were induced. Then, for representation of such properties the concepts of inter-activity and separability between fuzzy utilities were employed. This makes fuzzified additive utility difference structures effective to describe the intransitive preferential judgments. [In Japanese]