Paper:

# Obtaining Admissible Preference Orders Using Hierarchical Bipolar Sugeno and Choquet Integrals

## Katsushige Fujimoto^{*} and Michio Sugeno^{**}

^{*}College of Symbiotic Systems Science, Fukushima University, 1 Kanayagawa, Fukushima 960-1296, Japan

^{**}European Centre for Soft Computing, Gonzalo Gutiérrez Quirós S/N, 33600 Mieres, Spain

In this paper, we demonstrate the modeling capabilities of certain types of fuzzy integrals such as hierarchical bipolar/cumulative-prospect-theory-type Sugeno and Choquet integrals. The notion of *admissible preference structures*, introduced by Nakama and Sugeno, is one of the weakest restrictions in rational preference structures. Nakama and Sugeno also proved that, under a certain condition, any admissible preference can be modeled by a hierarchical bipolar Sugeno integral. Here, we extend this result and show that if we use an extra dummy attribute, we can use the hierarchical Choquet integral to generate any admissible preference.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.17, No.4, pp. 493-503, 2013.

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