5 research outputs found
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.
Complex Fuzzy Set-Valued Complex Fuzzy Measures and Their Properties
Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail
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