中文摘要：

按照集值积分的经典定义方法，不可避免地涉及集值函数和集值测度两方面的选择问题。本文利用集值函数关于非可加测度的实值Choquet积分，定义和讨论了集值函数关于非可加集值测度的Choquet积分，并刻画了其原函数性质。结果表明，弱零可加性、零可加性、凸零可加性、伪度量性质以及Darboux性质在其不定积分中均可遗传到其原函数中。

英文摘要：

It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a mul- tisubmeasure according to the classical definition method of the set-valued integral. The Choquet integral of a set-valued function with respect to a multisubmeasure is defined and discussed by using the real-valued Choquet integral of the set- valued function with respect to the non-additive measure, and some basic properties are characterized. It shows that a lot of characters could be well kept to their primitives such as the weakly null-additive, null-additive, converse null-addi- tive, the pseudometric property and the Darboux property, and so on.