Admissibility of preferences and modeling capabilities of fuzzy integrals

In this paper, we formulate a novel framework for investigating the capabilities of modeling schemes for aggregated preferences and use this framework to examine the modeling capabilities of fuzzy integrals. We consider establishing a preference over a set of choices when each choice is assigned a set of preference scores, one score with respect to each of several attributes of the choices. First we examine the properties of rational preferences and define admissible and inadmissible preferences. Then we mathematically formulate two desirable properties of preference-modeling schemes. Using the new framework, we characterize the modeling capabilities of five forms of fuzzy integral-the Sugeno integral, the symmetric Sugeno integral, the cumulative-prospect-theory Sugeno integral, the bicapacity Sugeno integral, and Sugeno´s hierarchical integral. We examine whether these fuzzy integrals are capable of modeling all possible admissible preferences and whether they generate any inadmissible preferences.