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The Choquet integral with respect to a level dependent capacity. (English) Zbl 1218.28014
Summary: 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 Šipoš integral and the cumulative prospect theory functional. We also show that many concepts such as Möbius 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.

MSC:
28E10 Fuzzy measure theory
91B06 Decision theory
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