集值函数的对偶半模模糊积分

Semi-conormed fuzzy integrals of set-valued functions

为了将函数的对偶半模模糊积分推广到集值函数的情形,要建立一种新的非可加集值积分理论。仿照Aumann积分的方式,用集值函数的单值可测选择的对偶半模模糊积分,定义集值函数的对偶半模模糊积分,并给出了其性质及收敛定理。这些是函数的对偶半模模糊积分有关结果的推广,同时是一种新的集值积分。

The semi-conormed fuzzy integral of functions was extended to the case of set-valued functions to develop a new theory on non-additive set-valued integrals. The present paper uses a method similar to Aumann's integral to define the semi-conormed fuzzy integral of set-valued functions using the semi-conormed fuzzy integral of single-valued measurable selections of set-valued functions and to describe its properties and convergence theorems. These results extend the semi-conormed fuzzy integral of single-valued functions to a new kind of set-valued integrals.