Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures

被引:1
|
作者
Yan, Leifan [1 ,2 ]
Kang, Tong [2 ,3 ]
Zhang, Huai [4 ]
机构
[1] Commun Univ China, Key Lab Media Audio & Video, Minist Educ, Beijing 100024, Peoples R China
[2] Commun Univ China, Sch Data Sci & Media Intelligence, Beijing 100024, Peoples R China
[3] Commun Univ China, Sch Sci, Beijing 100024, Peoples R China
[4] Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China
基金
中国国家自然科学基金;
关键词
set-valued function; fuzzy measure; decomposition integral; choquet integral; pan-integral; concave integral; CHOQUET INTEGRALS; CONCAVE; EQUIVALENCE;
D O I
10.3390/math11133013
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integrals, such as the Aumann integral based on the classical Lebesgue integral, the set-valued Choquet, pan-, concave and Shilkret integrals of set-valued functions with regard to capacity, etc. Some basic properties are presented and the monotonicity of the integrals in the sense of different types of the preorder relations are shown. By means of the monotonicity, the Chebyshev inequalities of decomposition integrals for set-valued functions are established. As a special case, we show the linearity of concave integrals of set-valued functions in terms of the equivalence relation based on a kind of preorder. The coincidences among the set-valued Choquet, the set-valued pan-integral and the set-valued concave integral are presented.
引用
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页数:14
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