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Pan-integrals of set-valued functions based on fuzzy measures

被引：2
|
作者：
Kang, Tong [1 ,2 ]
Wu, Dongsheng [3 ]
Li, Jun [1 ,4 ]
机构：
[1] Commun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China
[2] Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China
[3] Univ Alabama Huntsville, Dept Math Sci, Huntsville, AL 35899 USA
[4] Commun Univ China, Sch Sci, Beijing 100024, Peoples R China
来源：
FUZZY SETS AND SYSTEMS | 2023年 / 468卷
基金：
中国国家自然科学基金;
关键词：
Fuzzy measure; Pan-integral; Set-valued function; Set-valued pan-integral; CHOQUET INTEGRALS;
D O I：
10.1016/j.fss.2023.108632
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We propose the set-valued pan-integral of set-valued function based on number-valued fuzzy measure and present some basic properties. By means of a preorder on the class of all nonempty set of R1, we show the monotonicity of set-valued pan-integral in the sense of the preorder. We introduce an equivalence relation based on the preorder and demonstrate the linearity of set-valued pan-integral in the sense of the equivalence relation. The relationships of the set-valued pan-integral and the set-valued Choquet integral are discussed. Chebyshev's inequality of set-valued pan-integrals is shown. An open problem concerning the linearity of the set-valued pan-integral is raised.& COPY; 2023 Elsevier B.V. All rights reserved.
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页数：15
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