Autocontinuity and convergence theorems for the Choquet integral

Our aim is to provide some convergence theorems for the Choquet integral with respect to various notions of convergence. For instance, the dominated convergence theorem for almost uniform convergence is related to autocontinuous set functions. Autocontinuity can also be related to convergence in measure, strict convergence or mean convergence. Whereas the monotone convergence theorem for almost uniform convergence is related to monotone autocontinuity, a weaker version than autocontinuity.

On Properties of the Choquet Integral of Interval-Valued Functions

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of interval-valued functions. We also discuss convergence in the (C) mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem for the Choquet integral of measurable interval-valued functions