The Shapley Values on Fuzzy Coalition Games with Concave Integral Form
A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/231508 |
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| _version_ | 1849683549241737216 |
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| author | Jinhui Pang Xiang Chen Shujin Li |
| author_facet | Jinhui Pang Xiang Chen Shujin Li |
| author_sort | Jinhui Pang |
| collection | DOAJ |
| description | A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions. |
| format | Article |
| id | doaj-art-d4a2d8552fc84f4983c290985dcb9946 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d4a2d8552fc84f4983c290985dcb99462025-08-20T03:23:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/231508231508The Shapley Values on Fuzzy Coalition Games with Concave Integral FormJinhui Pang0Xiang Chen1Shujin Li2Library, Beijing Institute of Technology, Beijing 100081, ChinaPatent Examination Cooperation Center of the Patent Office, State Intellectual Property Office of P.R.C, Beijing 100088, ChinaDepartment of Information Management, The Central Institute for Correctional Police, Baoding 071000, ChinaA generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.http://dx.doi.org/10.1155/2014/231508 |
| spellingShingle | Jinhui Pang Xiang Chen Shujin Li The Shapley Values on Fuzzy Coalition Games with Concave Integral Form Journal of Applied Mathematics |
| title | The Shapley Values on Fuzzy Coalition Games with Concave Integral Form |
| title_full | The Shapley Values on Fuzzy Coalition Games with Concave Integral Form |
| title_fullStr | The Shapley Values on Fuzzy Coalition Games with Concave Integral Form |
| title_full_unstemmed | The Shapley Values on Fuzzy Coalition Games with Concave Integral Form |
| title_short | The Shapley Values on Fuzzy Coalition Games with Concave Integral Form |
| title_sort | shapley values on fuzzy coalition games with concave integral form |
| url | http://dx.doi.org/10.1155/2014/231508 |
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