| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 397670 | International Journal of Approximate Reasoning | 2014 | 6 Pages |
•A new kind of Choquet integrals for set-valued mappings is introduced.•Elementary properties and convergence theorems are shown.•In the case of the monotone convergence theorem of the nonincreasing sequence, the integrands must be closed.•This kind of Choquet integrals for set-valued mappings can be regarded as the Choquet integrals for single-valued functions.
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.
