{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:33:11Z","timestamp":1777703591847,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,7,18]],"date-time":"2019-07-18T00:00:00Z","timestamp":1563408000000},"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":[[2019,9,9]]},"abstract":"<jats:p>This paper proposes the concept of interval-valued average tree solution (\u201cAT solution\u201d for short) of graph cooperative games with interval-valued payoffs, and develop an effective and a direct simplified method for solving a subclass of interval-valued graph cooperative games. In this method, the interval-valued AT solution is proved to be a monotonic and non-decreasing function of coalitions\u2019 values under specific condition. Hence, the lower and upper bounds of interval-valued AT solutions of graph cooperative games can be obtained directly by using the lower and upper bounds of the interval-valued coalitions\u2019 payoffs, respectively. The proposed method gives better results than general interval subtraction and the partial subtraction operator methods. In addition, some important properties of the interval-valued AT solutions of interval-valued graph cooperative games are discussed. At last, the applicability and superiority of the proposed approach is demonstrated by comparing with other methods.<\/jats:p>","DOI":"10.3233\/jifs-190042","type":"journal-article","created":{"date-parts":[[2019,7,19]],"date-time":"2019-07-19T10:39:55Z","timestamp":1563532795000},"page":"2913-2923","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["A graph cooperative game with interval-valued payoffs and its simplified solving method"],"prefix":"10.1177","volume":"37","author":[{"given":"Libang","family":"Lai","sequence":"first","affiliation":[{"name":"Fujian Chuanzheng Communications College, Fuzhou, Fujian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Management, Fujian Agriculture and Forestry University, Fuzhou, Fujian, China"},{"name":"Business School, Sichuan University, Chengdu, Sichuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dengfeng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, University of Electronic Science and Technology of China, Chengdu, Sichuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,7,18]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-009-0116-0"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2012.08.002"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2013.784765"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12351-015-0183-z"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12351-016-0233-1"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-16117"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-009-0096-0"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.06.005"},{"key":"e_1_3_2_10_2","first-page":"205","article-title":"Integration des applications measurables dont la valeur est un compact convexe","volume":"10","author":"Hukuhara M.","year":"1967","unstructured":"HukuharaM., Integration des applications measurables dont la valeur est un compact convexe, Funkcialaj Ekvacioj 10 (1967), 205\u2013223.","journal-title":"Funkcialaj Ekvacioj"},{"key":"e_1_3_2_11_2","article-title":"Methods and Applications of Interval Analysis","author":"Moore R.","year":"1979","unstructured":"MooreR., Methods and Applications of Interval Analysis. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1979).","journal-title":"Society for Industrial and Applied Mathematics (SIAM)"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2011.01.007"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12351-016-0260-y"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2.3.225"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.05.013"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2015.09.029"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2007.03.007"},{"key":"e_1_3_2_18_2","first-page":"203","article-title":"Average tree solution and subcore for acyclic graph games","volume":"51","author":"Talman A.J.J.","year":"2008","unstructured":"TalmanA.J.J. and YamamotoY., Average tree solution and subcore for acyclic graph games, Journal of the operational research society 51 (2008), 203\u2013212.","journal-title":"Journal of the operational research society"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.geb.2009.10.002"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.07.023"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00199-013-0796-5"},{"key":"e_1_3_2_22_2","doi-asserted-by":"crossref","unstructured":"NieC.P. and Zhang.Q. Fuzzy Average Tree Solution for Graph Games with Fuzzy Coalitions In Fuzzy Information & Engineering and Operations Research & Management. Springer Berlin Heidelberg (2014).","DOI":"10.1007\/978-3-642-38667-1_41"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-16080"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00182-009-0194-1"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.06.009"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2004.831154"},{"key":"e_1_3_2_27_2","first-page":"220","article-title":"Study on profit allocation of enterprise\u2019s original innovation with an industry-university-research cooperative mode based on the Shapley value","volume":"22","author":"Li B.Z.","year":"2013","unstructured":"LiB.Z. and LuoX.F., Study on profit allocation of enterprise\u2019s original innovation with an industry-university-research cooperative mode based on the Shapley value, Operations Research and Management Science 22 (2013), 220\u2013224. (in Chinese).","journal-title":"Operations Research and Management Science"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.08.001"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190042","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-190042","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-190042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:04Z","timestamp":1777455544000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-190042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,18]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,9,9]]}},"alternative-id":["10.3233\/JIFS-190042"],"URL":"https:\/\/doi.org\/10.3233\/jifs-190042","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,18]]}}}