Real-valued Choquet integrals for set-valued mappings |
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Institution: | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China |
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Abstract: | In this paper a new kind of real-valued Choquet integrals for set-valued mappings is introduced, and some elementary properties of this kind of Choquet integrals are studied. Convergence theorems of a sequence of Choquet integrals for set-valued mappings are shown. However, in the case of the monotone convergence theorem of the nonincreasing sequence of Choquet integrals for set-valued mappings, we point out that the integrands must be closed. Specially, this kind of real-valued Choquet integrals for set-valued mappings can be regarded as the Choquet integrals for single-valued functions. |
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Keywords: | Fuzzy measure Set-valued mapping Choquet integral Monotone convergence |
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