Bipolar Sugeno integrals, if–then rules and preference orderings

Abstract This paper elaborates on the symmetric Sugeno integral introduced by Michel Grabisch, and an asymmetric generalization of it devoted to handling bipolar qualitative information. We extend to this framework the representation results for Sugeno integrals in terms of if–then selection and elimination rules. We also study various preferences orderings induced by bipolar integrals, and relate them to a former approach to handing bipolar qualitative preference information in the setting of possibility theory. We finally propose a counterpart of Grabisch’s symmetric Sugeno integral in a qualitative bipolar scale where consecutive levels are assumed to be equidistant.