{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T20:54:51Z","timestamp":1648673691967},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2010,10]]},"abstract":"<jats:p> The paper considers the analytical solution methods of the maximizing entropy or minimizing variance with fixed orness level problems and the maximizing orness with fixed entropy or variance value problems together. It proves that both of these two kinds of problems have common necessary conditions for their optimal solutions. The optimal solutions have the same forms and can be seen as the same OWA (ordered weighted averaging) weighting vectors from different points of view. The problems of minimizing orness problems with fixed entropy or variance constraints and their analytical solutions are proposed. Then these conclusions are extended to the corresponding RIM (regular increasing monotone) quantifier problems, which can be seen as the continuous case of OWA problems with free dimension. The analytical optimal solutions are obtained with variational methods. <\/jats:p>","DOI":"10.1142\/s0218488510006684","type":"journal-article","created":{"date-parts":[[2010,9,13]],"date-time":"2010-09-13T05:50:41Z","timestamp":1284357041000},"page":"515-538","source":"Crossref","is-referenced-by-count":0,"title":["THE RELATIONSHIPS BETWEEN TWO VARIABILITY AND ORNESS OPTIMIZATION PROBLEMS FOR OWA OPERATOR WITH RIM QUANTIFIER EXTENSIONS"],"prefix":"10.1142","volume":"18","author":[{"given":"XINWANG","family":"LIU","sequence":"first","affiliation":[{"name":"School of Economics and Management, Southeast University, Nanjing, 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/21.87068"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-111X(199601)11:1<49::AID-INT3>3.0.CO;2-Z"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6123-1"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1109\/91.842149"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0888-613X(01)00042-1"},{"key":"rf6","first-page":"937","volume":"31","author":"Kacprzyk J.","journal-title":"Control and Cybernetics"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.806319"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2003.821866"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2004.834814"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1002\/int.20075"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCA.2005.853488"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(94)00109-O"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00007-0"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2003.09.001"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.04.006"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(02)00267-1"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2004.09.003"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2005.11.003"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1080\/03081079408935212"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00254-0"},{"key":"rf22","first-page":"511","volume":"14","author":"Ahn B. 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