{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T14:17:44Z","timestamp":1648822664633},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Info. Tech. Dec. Mak."],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p> Based on the leximin and leximax preferences, we consider two threshold preference relations on the set X of alternatives, each of which is characterized by an n-dimensional vector (n \u2265 2) with integer components varying between 1 and m(m \u2265 2). We determine explicitly in terms of binomial coefficients the unique utility function for each of the two relations, which in addition maps X onto the natural 'interval' [Formula: see text], where [Formula: see text] is the quotient set of X with respect to the indifference relation I on X induced by the threshold preference. This permits us to evaluate all equivalence classes and indifference classes of the threshold order on X, present an algorithm of ordering the monotone representatives of indifference classes, and restore the indifference class of an alternative via its ordinal number with respect to the threshold preference order. <\/jats:p>","DOI":"10.1142\/s021962201350034x","type":"journal-article","created":{"date-parts":[[2013,12,12]],"date-time":"2013-12-12T09:29:43Z","timestamp":1386840583000},"page":"1201-1222","source":"Crossref","is-referenced-by-count":3,"title":["THE THRESHOLD DECISION MAKING EFFECTUATED BY THE ENUMERATING PREFERENCE FUNCTION"],"prefix":"10.1142","volume":"12","author":[{"given":"FUAD T.","family":"ALESKEROV","sequence":"first","affiliation":[{"name":"Department of Mathematics for Economics, National Research University Higher School of Economics, 20 Myasnitskaya Street, Moscow 101000, Russian Federation"},{"name":"Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VYACHESLAV V.","family":"CHISTYAKOV","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Research University, Higher School of Economics, 25\/12 Bol'shaya Pech\u00ebrskaya Street, Nizhny Novgorod 603155, Russian Federation"},{"name":"Laboratory of Algorithms and Technologies for Network Analysis, National Research University, Higher School of Economics, 136 Rodionova Street, Nizhny Novgorod 603093, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,12,12]]},"reference":[{"key":"rf1","volume-title":"Abstract Measurement Theory","author":"Narens L.","year":"1985"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1983-027-4"},{"key":"rf3","volume-title":"Decision Processes","author":"Debreu G.","year":"1954"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00277-1"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1983-0682730-4"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.2307\/2296323"},{"key":"rf7","volume-title":"Collective Choice and Social Welfare","author":"Sen A. K.","year":"1970"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s00355-010-0454-9"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2013.05.140"},{"key":"rf10","doi-asserted-by":"crossref","DOI":"10.21236\/AD0708563","volume-title":"Utility Theory for Decision Making","author":"Fishburn P. C.","year":"1970"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4542-9"},{"key":"rf12","volume-title":"Set Theory","author":"Hausdorff F.","year":"2005"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.2307\/2296854"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0176-2680(86)90015-7"},{"key":"rf15","first-page":"45","author":"Chistyakov V. V.","journal-title":"Control Sciences"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1134\/S106456240702038X"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2010.01.041"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1134\/S1064562408040388"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2006.09.002"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/0041-5553(75)90040-3"},{"key":"rf21","volume-title":"Concrete Mathematics. A Foundation for Computer Science","author":"Graham R. L.","year":"1994"}],"container-title":["International Journal of Information Technology &amp; Decision Making"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021962201350034X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:12:12Z","timestamp":1565197932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021962201350034X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11]]},"references-count":21,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2013,12,12]]},"published-print":{"date-parts":[[2013,11]]}},"alternative-id":["10.1142\/S021962201350034X"],"URL":"https:\/\/doi.org\/10.1142\/s021962201350034x","relation":{},"ISSN":["0219-6220","1793-6845"],"issn-type":[{"value":"0219-6220","type":"print"},{"value":"1793-6845","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11]]}}}