中文摘要：

研究了集值函数关于模糊测度Choquet积分的分析性质：讨论了集值函数Choquet积分的计算方法,给出了集值函数Choquet积分的表示定理和Radon-Nikodym性质,并且对集值函数Choquet积分的原函数进行了刻划。最后,对集值函数关于模糊测度Choquet积分定义进行了改进,提出了集值函数＂上方函数＂和＂下方函数＂概念,实现了对集值函数关于模糊测度的Choquet积分的控制。

英文摘要：

The analytic properties of the Choquet integral of set-valued functions with respect to fuzzy measures are dis- cussed, such as the characteristics of the primitive, representation of integral, differentiability of the primitive, and so on. Firstly, based on the previous results, the calculation of Choquet integral of set-valued function is investigated, and a representation theorem of Choquet integral for set-valued function is obtained as a Radon-Nikodym property in some sense. In addition, the characteristics of the primitive of the Choquet integral for set valued functions are given. Final- ly, the definition of the Choquet integral of set-valued functions with respect to fuzzy measures is improved, and the concepts of the above functions and below function of the set-valued functions are proposed, which achieved the domi- nation of the Choquet integral of set-valued functions with respect to fuzzy measures.