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

Author

Listed:
  • Lv, Huadong
  • Chen, Ya
  • Ouyang, Yao
  • Sun, Hongxia

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.

Suggested Citation

  • Lv, Huadong & Chen, Ya & Ouyang, Yao & Sun, Hongxia, 2019. "On the equivalence of the Choquet integral and the pan-integrals from above," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 15-21.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:15-21
    DOI: 10.1016/j.amc.2019.05.010
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    References listed on IDEAS

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    1. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
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