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

TL;DR

This paper explores an idempotent analogue of Riesz's theorem, establishing a correspondence between possibility capacities and functionals that preserve maximum and t-norm operations via t-normed integrals.

Contribution

It introduces a new framework linking possibility capacities with t-normed integrals, extending classical measure-functional correspondences to an idempotent setting.

Findings

Established a correspondence between possibility capacities and t-normed integrals.

Extended Riesz's theorem to an idempotent context.

Provided theoretical foundations for applications in fuzzy logic and decision theory.

Abstract

Riesz Theorem establishes a correspondence between the set of $\sigma$-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.