{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:19:47Z","timestamp":1777702787023,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>In this study, a new characteristic function with combined weighted form is developed to fuzzy cooperative games based on the BUM functions. By establishing efficiency, symmetry and additivity axioms, a Shapley function with combined weighted form is presented for fuzzy cooperative games. The proposed Shapley function considers not only the weighted average value of the marginal contribution, but also the collective cooperation tendency of players. Moreover, some desirable properties are introduced simultaneously. We show that the Shapley function with combined weighted form belong to fuzzy core when the fuzzy cooperative games is strong convex. Finally, a numerical example is provided to illustrate the validity of the proposed Shapley function.<\/jats:p>","DOI":"10.3233\/ifs-131055","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T18:45:01Z","timestamp":1575312301000},"page":"953-964","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["The Shapley function for n-person fuzzy cooperative games with combined weighted form"],"prefix":"10.1177","volume":"27","author":[{"given":"Jian","family":"Lin","sequence":"first","affiliation":[{"name":"School of Management and Economics, Beijing Institute of Technology, Beijing, China"},{"name":"College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Management and Economics, Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,1]]},"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-131055","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-131055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:36:55Z","timestamp":1777455415000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-131055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.3233\/IFS-131055"],"URL":"https:\/\/doi.org\/10.3233\/ifs-131055","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1]]}}}