Convergence theorems for Choquet integrals with generalized autocontinuity

We propose the concepts of generalized null-additivity and of generalized autocontinuity from below (resp. from above) relating to a pair of fuzzy measures, and discuss the rela-tionship among these new concepts, and null-additivity and autocontinuity (concerning a single fuzzy measure). By means of these structure characteristics of fuzzy measures we establish the generalized dominated convergence theorem and the generalized Vitali convergence theorem for Choquet integral in the framework involving an ordered pair of fuzzy measures. The previous related versions of dominated convergence theorem and of Vitali-like convergence theorem of Choquet integral are recovered by these generalized versions, respectively. In such a framework, the standard-type and pseudo-type of domi-nated convergence theorems (resp. Vitali-like convergence theorem) of Choquet integral are unified.(c) 2022 Elsevier Inc. All rights reserved.