Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures
被引:1
|
作者:
Yan, Leifan
论文数: 0引用数: 0
h-index: 0
机构:
Commun Univ China, Key Lab Media Audio & Video, Minist Educ, Beijing 100024, Peoples R China
Commun Univ China, Sch Data Sci & Media Intelligence, Beijing 100024, Peoples R ChinaCommun Univ China, Key Lab Media Audio & Video, Minist Educ, Beijing 100024, Peoples R China
Yan, Leifan
[1
,2
]
Kang, Tong
论文数: 0引用数: 0
h-index: 0
机构:
Commun Univ China, Sch Data Sci & Media Intelligence, Beijing 100024, Peoples R China
Commun Univ China, Sch Sci, Beijing 100024, Peoples R ChinaCommun Univ China, Key Lab Media Audio & Video, Minist Educ, Beijing 100024, Peoples R China
Kang, Tong
[2
,3
]
Zhang, Huai
论文数: 0引用数: 0
h-index: 0
机构:
Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R ChinaCommun Univ China, Key Lab Media Audio & Video, Minist Educ, Beijing 100024, Peoples R China
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
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.
机构:
Commun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China
Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R ChinaCommun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China
Kang, Tong
Wu, Dongsheng
论文数: 0引用数: 0
h-index: 0
机构:
Univ Alabama Huntsville, Dept Math Sci, Huntsville, AL 35899 USACommun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China
Wu, Dongsheng
Li, Jun
论文数: 0引用数: 0
h-index: 0
机构:
Commun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China
Commun Univ China, Sch Sci, Beijing 100024, Peoples R ChinaCommun Univ China, State Key Lab Media Convergence & Commun, Beijing 100024, Peoples R China