On the equivalence of the Choquet integral and the pan-integrals from above

Huadong Lv, Ya Chen, Yao Ouyang and Hongxia Sun

Applied Mathematics and Computation, 2019, vol. 361, issue C, 15-21

Abstract: A monotone measure μ is said to have dual (M)-property if for any A ⊂ B, there exists C with A ⊂ C ⊂ B such that μ(C)=μ(A)andμ(B)=μ(C)+μ(B∖C). By using this concept, we study the relationship of the Choquet integral and the pan-integral from above. We prove that the Choquet integral coincides with the pan-integral from above if μ has dual (M)-property. When the underlying space is finite, we prove that the dual (M)-property is also necessary for the coincidence of these two integrals. Thus we provide a necessary and sufficient condition for the equivalence of the Choquet integral and the pan-integral from above on a finite space.

Keywords: Monotone measure; Choquet integral; Pan-integral from above; Dual (M)-property (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:15-21

DOI: 10.1016/j.amc.2019.05.010

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