On t-normed integrals with respect to possibility capacities on compacta

Abstract

Riesz Theorem establishes a correspondence between the set of σ-additive regular Borel measures and the set of linear positively defined functionals. We consider an idempotent analogue of this correspondence between possibility capacities and functionals preserving the maximum operation and t-norm operation using t-normed integrals. Additionally, we establish that this correspondence possesses a categorical sense, representing a morphism of monads. Furthermore, we delve into the investigation of the associated idempotent convexity.