{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:45:12Z","timestamp":1777704312663,"version":"3.51.4"},"reference-count":20,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T00:00:00Z","timestamp":1534464000000},"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":[[2018,10]]},"abstract":"<jats:p>The aim of this paper is to extend the concept of the solidarity value to interval-valued (IV) cooperative games and develop a fast and simplified method for computing the IV solidarity values for a special class of IV cooperative games under some weaker conditions. In the method, we find a size (or coalition) monotonicity-like condition so that we can compute the IV solidarity values of a special class of IV cooperative games via determining their lower and upper bounds by utilizing the lower and upper bounds of the IV coalitions\u2019 values, respectively. In addition, some important and useful properties of IV solidarity values are discussed and the feasibility and applicability of the method proposed in this paper are verified with numerical examples as well as comparison analysis with existing methods is conducted.<\/jats:p>","DOI":"10.3233\/jifs-18217","type":"journal-article","created":{"date-parts":[[2018,8,17]],"date-time":"2018-08-17T11:23:15Z","timestamp":1534504995000},"page":"3653-3660","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["A simplified method of interval-valued solidarity values for a special class of interval-valued cooperative games"],"prefix":"10.1177","volume":"35","author":[{"given":"Yin-Fang","family":"Ye","sequence":"first","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China"}]},{"given":"Deng-Feng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Fuzhou University, Fuzhou, Fujian, China"}]}],"member":"179","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"1","article-title":"Shapley-like values for interval bankruptcy games","volume":"3","author":"Branzei R.","year":"2003","unstructured":"BranzeiR., DimitrovD. and TijsS., Shapley-like values for interval bankruptcy games, Economics Bulletin 3 (2003), 1\u20138.","journal-title":"Economics Bulletin"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-009-0116-0"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2012.08.002"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-141438"},{"key":"e_1_3_2_6_2","first-page":"243","article-title":"An axiomatization of the interval Shapley value and on some interval solution concepts","volume":"8","author":"Palanci O.","year":"2015","unstructured":"PalanciO., Alparslan G\u00f6kS.Z. and WeberG.W., An axiomatization of the interval Shapley value and on some interval solution concepts, Contributions to Game Theory and Management 8 (2015), 243\u2013251.","journal-title":"Contributions to Game Theory and Management"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00291-015-0422-y"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-010-0141-z"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmateco.2011.08.008"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161890"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970906"},{"key":"e_1_3_2_12_2","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s12351-016-0260-y","article-title":"Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method","volume":"18","author":"Li D.-F.","year":"2018","unstructured":"LiD.-F. and YeY.F., Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method, Operational Research: An International Journal 18 (2018), 205\u2013220.","journal-title":"Operational Research: An International Journal"},{"key":"e_1_3_2_13_2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/s12351-016-0233-1","article-title":"Nonlinear programming method for interval-valued n-person cooperative games","volume":"17","author":"Hong F.X.","year":"2017","unstructured":"HongF.X. and LiD.-F, Nonlinear programming method for interval-valued n-person cooperative games, Operational Research: An International Journal 17 (2017), 479\u2013497.","journal-title":"Operational Research: An International Journal"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01242845"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.12.015"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2011.08.011"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2015.12.002"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11238-017-9586-z"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-015-0525-x"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2014.03.005"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2017.12.006"}],"container-title":["Journal of Intelligent &amp; 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