JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (08): 62-71.doi: 10.6040/j.issn.1671-9352.0.2014.340

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Choquet integral of set-valued functions with respect to multisubmeasures

GONG Zeng-tai, WEI Zhao-qi   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2014-07-02 Online:2015-08-20 Published:2015-07-31

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Abstract: It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a multisubmeasure 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-additive, the pseudometric property and the Darboux property, and so on.

Key words: set-valued functions, multisubmeasures, Choquet integral

CLC Number: 

  • O175.8
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