Choquet integrals with respect to the credibility measure

The Choquet integral is proven quite reasonable as an integral form with respect to monotone measures, where the credibility measure is a specific case with self-duality. The main objective of this paper is to propose the Choquet integral of measurable functions on the credibility space, which bridges the gap between the Choquet integral and credibility theory. First, the Choquet integrals for nonnegative functions with respect to the credibility measure are introduced, and their properties are investigated such as the monotonicity and translatability. Then, the symmetric Choquet integrals and translatable Choquet integrals of any measurable functions are developed through the use of the Choquet integrals of nonnegative functions. Finally, Choquet integrals on finite sets based on the credibility measure are presented to simplify the calculation procedures.