k-Additivity and C-decomposability of bi-capacities and its integral

Authors:
Katsushige Fujimoto;Toshiaki Murofushi;Michio Sugeno
Affiliations:
College of Symbiotic Systems Science, Fukushima University, 1 Kanayagawa, Fukushima 960-1296, Japan;Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan;Faculty of Culture and Information Science, Doshisha University, 1-3 Miyakodani Tatara, Kyotanabe-shi, Kyoto 610-0394, Japan
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

k-Additivity is a convenient way to have less complex (bi-)capacities. This paper gives a new characterization of k-additivity, introduced by Grabisch and Labreuche, of bi-capacities and contrasts between the existing characterization and the new one, that differs from the one of Saminger and Mesiar. Besides, in the same way for capacities, a concept of C-decomposability, distinct from the proposal of Saminger and Mesiar, but closely linked to k-additivity, is introduced for bi-capacities. Moreover, the concept of C-decomposability applies to the Choquet integral with respect to bi-capacities.