Interval-valued Choquet integral for set-valued mappings: definitions, integral representations and primitive characteristics

Zengtai Gong; Xuyang Kou; Ting Xie; Zengtai Gong; Xuyang Kou; Ting Xie

doi:10.3934/math.2020404

AIMS Mathematics

2020, Volume 5, Issue 6: 6277-6297. doi: 10.3934/math.2020404

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Research article

Interval-valued Choquet integral for set-valued mappings: definitions, integral representations and primitive characteristics

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
College of Social Development and Public Administration, Northwest Normal University, Lanzhou 730070, China

Received: 03 May 2020 Accepted: 29 July 2020 Published: 06 August 2020
MSC : 26E50, 28E10

In this paper, a new kind of real-valued major Choquet integral, real-valued minor Choquet integral and interval-valued Choquet integrals for set-valued functions is introduced and investigated. The representations of the Choquet integral of set-valued functions with respect to a fuzzy measure are given. In particular, we focus on the case of the distorted Lebesgue measure as a fuzzy measure. Furthermore, the characteristics of the primitive of Choquet integral for set-valued functions are given as Radon-Nikodym property in some sense.
- set-valued functions,
- Choquet integral
Citation: Zengtai Gong, Xuyang Kou, Ting Xie. Interval-valued Choquet integral for set-valued mappings: definitions, integral representations and primitive characteristics[J]. AIMS Mathematics, 2020, 5(6): 6277-6297. doi: 10.3934/math.2020404

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Abstract

In this paper, a new kind of real-valued major Choquet integral, real-valued minor Choquet integral and interval-valued Choquet integrals for set-valued functions is introduced and investigated. The representations of the Choquet integral of set-valued functions with respect to a fuzzy measure are given. In particular, we focus on the case of the distorted Lebesgue measure as a fuzzy measure. Furthermore, the characteristics of the primitive of Choquet integral for set-valued functions are given as Radon-Nikodym property in some sense.

References

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