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Bipolar Fuzzy Integrals

In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last sixty years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral. Recently, the bipolar Choquet integral has been proposed for the case in which the underlying scale is bipolar. In this paper we propose the bipolar Shilkret integral and the bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all these three bipolar fuzzy integrals.