The bipolar universal integral

Abstract

The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the bipolar universal integral generalizing the Choquet, Shilkret and Sugeno bipolar integrals. To complete the generalization we also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. © 2012 Springer-Verlag Berlin Heidelberg.