Pan-integral on credibility space and its properties

Pan-integral is an important kind of nonlinear integral, and credibility measure is a monotone measure with self-duality. In this paper, we define the pan-integral on credibility space, a new type of integral construction, whose basic properties are discussed in detail. The relationship between the pan-integral and H-fuzzy integral on a special pan-credibility space is established as well. Moreover, some monotone convergence theorems for a sequence of nonnegative measurable functions are investigated.