The Choquet integral with respect to a level dependent capacity

Authors:
Salvatore Greco;Benedetto Matarazzo;Silvio Giove
Affiliations:
Faculty of Economics, University of Catania, Corso Italia 55, Catania 95129, Italy;Faculty of Economics, University of Catania, Corso Italia 55, Catania 95129, Italy;Faculty of Economics, University of Venice, Dorsoduro 3825/E, Venezia 30123, Italy
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

We present a generalization of Choquet integral in which the capacity depends also on the value of the aggregated variables. We show that as particular cases of our generalization of Choquet integral there are the Sugeno integral, the Sipos integral and the Cumulative Prospect Theory functional. We also show that many concepts such as Mobius transform, importance index, interaction index, k-order capacities and OWA operators, introduced in the research about Choquet integral, can be generalized in the considered context.