{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T02:47:29Z","timestamp":1780627649413,"version":"3.54.1"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100000923","name":"Ministerio de Educaci\u00f3n, Cultura y Deporte (ES)","doi-asserted-by":"publisher","award":["TIN2014-59543-P"],"award-info":[{"award-number":["TIN2014-59543-P"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p> We investigate the role of some game solutions, such the Shapley and the Banzhaf values, as probability transformations. The first one coincides with the pignistic transformation proposed in the Transferable Belief Model; the second one is not efficient in general, leading us to consider its normalized version. We study a number of particular models of lower probabilities: minitive measures, coherent lower probabilities, as well as the lower probabilities induced by comparative or distortion models. For them, we provide some alternative expressions of the Shapley and Banzhaf values and study under which conditions they belong to the core of the lower probability. <\/jats:p>","DOI":"10.1142\/s0218488518500411","type":"journal-article","created":{"date-parts":[[2018,11,2]],"date-time":"2018-11-02T03:35:05Z","timestamp":1541129705000},"page":"917-947","source":"Crossref","is-referenced-by-count":20,"title":["Shapley and Banzhaf Values as Probability Transformations"],"prefix":"10.1142","volume":"26","author":[{"given":"Enrique","family":"Miranda","sequence":"first","affiliation":[{"name":"Department of Statistics and O.R., University of Oviedo, C\/Federico Garc\u00eda Lorca, No. 18, Oviedo 33007, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6534-1613","authenticated-orcid":false,"given":"Ignacio","family":"Montes","sequence":"additional","affiliation":[{"name":"Department of Statistics and O.R., University of Oviedo, C\/Federico Garc\u00eda Lorca, No. 18, Oviedo 33007, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2018,11,27]]},"reference":[{"key":"p_4","first-page":"169","author":"Dubois D.","year":"1998","journal-title":"Dordrecht"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2005.03.001"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488595000049"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2004.05.003"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7373(89)80032-X"},{"issue":"3","key":"p_11","first-page":"341","volume":"44","author":"Williams P.","year":"1982","journal-title":"by G. 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