{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:37:15Z","timestamp":1777703835437,"version":"3.51.4"},"reference-count":54,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T00:00:00Z","timestamp":1495497600000},"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":[[2017,5,23]]},"abstract":"<jats:p>In most real life investment situations future security returns are represented mainly based on expert\u2019s judgments due to the occurrence of unexpected incidents in economic and social changes or lack of historical data. In order to tackle such uncertainties, the returns of the securities are evaluated by the experts instead of historical data. In this study, a multi-objective uncertain portfolio selection model has been proposed by defining average return as expected value, risk as variance and divergence among security returns as cross-entropy where the security returns are considered as uncertain variables. The transformed deterministic form of the proposed model is presented by considering security returns as linear uncertain variables. The deterministic model is then solved by using two multi-objective genetic algorithms (MOGAs), namely, Nondominated Sorting Genetic Algorithm II (NSGA-II) and Archive-Based hYbrid Scatter Search (AbYSS). We use a dataset from the Shenzhen Stock Exchange to illustrate the performance of the algorithms. Finally, a comparative study is performed in terms of certain performance matrices among NSGA-II and AbYSS.<\/jats:p>","DOI":"10.3233\/jifs-169212","type":"journal-article","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T14:44:07Z","timestamp":1495809847000},"page":"4467-4483","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":27,"title":["Cross-entropy based multi-objective uncertain portfolio selection problem"],"prefix":"10.1177","volume":"32","author":[{"given":"Mohuya B.","family":"Kar","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Heritage Institute of Technology, Kolkata, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saibal","family":"Majumder","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samarjit","family":"Kar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tandra","family":"Pal","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2017,5,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2007.913109"},{"key":"e_1_3_2_3_2","first-page":"3234","volume-title":"2006 IEEE Congress on Evolutionary Computation, Sheraton Vancouver Wall Center Vancouver","author":"Zhou A.","year":"2006","unstructured":"ZhouA., JinY., ZhangQ., SendhoB. and TsangE., Combining model-based and genetics-based offspring generation for multiobjective optimization using a convergence criterion, in 2006 IEEE Congress on Evolutionary Computation, Sheraton Vancouver Wall Center Vancouver, BC, Canada, 2006, pp. 3234\u20133241."},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89484-1"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8"},{"key":"e_1_3_2_7_2","first-page":"3","article-title":"Why is there a need for uncertainty theory?","volume":"6","author":"Liu B.","year":"2012","unstructured":"LiuB., Why is there a need for uncertainty theory? Journal of Uncertain System 6 (2012), 3\u201310.","journal-title":"Journal of Uncertain System"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40467-015-0036-6"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2006.1597059"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.39.12.1552"},{"key":"e_1_3_2_11_2","first-page":"416","article-title":"Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization","author":"Fonseca C.M.","year":"1993","unstructured":"FonsecaC.M. and FlemingP.J., Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization, Proceedings of the Fifth International Conference on Genetic Algorithms, 1993, pp. 416\u2013423.","journal-title":"Proceedings of the Fifth International Conference on Genetic Algorithms"},{"key":"e_1_3_2_12_2","volume-title":"Dept Elec Comput Eng, Graduate School of Eng, Air Force Inst Technol","author":"Van Veldhuizen D.A.","year":"1998","unstructured":"Van VeldhuizenD.A. and LamontG.B., Multiobjective evolutionary algorithm research: A history and analysis, Technical Report TR-98-03, Dept Elec Comput Eng, Graduate School of Eng, Air Force Inst Technol, Wright-Patterson, AFB, OH, 1998."},{"key":"e_1_3_2_13_2","first-page":"117","article-title":"Mean-risk analysis with risk associated with below-target returns","volume":"67","author":"Fishburn D.C.","year":"1977","unstructured":"FishburnD.C., Mean-risk analysis with risk associated with below-target returns, American Economical Review 67 (1977), 117\u2013126.","journal-title":"American Economical Review"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.797969"},{"key":"e_1_3_2_15_2","first-page":"103","article-title":"SPEA2: Improving the Strength Pareto Evolutionary Algorithm","author":"Zitzler E.","year":"2001","unstructured":"ZitzlerE., LaumannsM. and ThieleL., SPEA2: Improving the Strength Pareto Evolutionary Algorithm, Computer Engineering and Networks Laboratory Technical Report Department of Electrical Engineering, 2001, p. 103.","journal-title":"Computer Engineering and Networks Laboratory Technical Report Department of Electrical Engineering"},{"key":"e_1_3_2_16_2","first-page":"13","article-title":"A template for scatter search and path relinking","volume":"1363","author":"Glover F.","year":"1997","unstructured":"GloverF., A template for scatter search and path relinking, Lecture Notes in Computer Science 1363 (1997), 13\u201354.","journal-title":"Lecture Notes in Computer Science"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.15807\/jorsj.38.137"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.37.5.519"},{"issue":"1","key":"e_1_3_2_19_2","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"Markowitz H.","year":"1952","unstructured":"MarkowitzH., Portfolio selection, Journal of Finance 7(1) (1952), 77\u201391.","journal-title":"Journal of Finance"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.2307\/2330119"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2011.05.014"},{"key":"e_1_3_2_22_2","first-page":"82","article-title":"A niched Pareto genetic algorithm for multi-objective optimization","author":"Horn J.","year":"1994","unstructured":"HornJ., NafploitisN. and GoldbergD.E., A niched Pareto genetic algorithm for multi-objective optimization, Proceedings of the First IEEE Conference on Evolutionary Computation, 1994, pp. 82\u201387.","journal-title":"Proceedings of the First IEEE Conference on Evolutionary Computation"},{"key":"e_1_3_2_23_2","first-page":"9","article-title":"The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization","author":"Knowles J.","year":"1999","unstructured":"KnowlesJ. and CorneD., The Pareto archived evolution strategy: A new baseline algorithm for multiobjective optimization, Proceedings of the 1999 Congress on Evolutionary Computation CEC 99, 1999, pp. 9\u2013105.","journal-title":"Proceedings of the 1999 Congress on Evolutionary Computation CEC 99"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.996017"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2317693"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.irfa.2008.04.004"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-014-1457-8"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1162\/evco.1994.2.3.221"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2008.01.086"},{"key":"e_1_3_2_30_2","unstructured":"JorionP.H. Value at Risk: A new benchmark for measuring derivatives risk Irwin Professional Publishers (1996)."},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2007.892759"},{"key":"e_1_3_2_32_2","first-page":"44","article-title":"Possibilistic mean-variance-skewness portfolio selection models","volume":"8","author":"Bhattacharyya R.","year":"2011","unstructured":"BhattacharyyaR. and KarS., Possibilistic mean-variance-skewness portfolio selection models, International Journal of Operations Research 8 (2011), 44\u201356.","journal-title":"International Journal of Operations Research"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.10.039"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1186\/2195-5468-1-16"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.08.017"},{"key":"e_1_3_2_36_2","volume-title":"Engineering optimization: Theory and practice","author":"Rao S.S.","year":"1996","unstructured":"RaoS.S., Engineering optimization: Theory and practice, 3rd edn. John Wiley & Sons, New Jersey, 1996.","edition":"3"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.21314\/JOR.2000.038"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02408382"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.02.049"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2007-00356"},{"key":"e_1_3_2_41_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2008.924200"},{"key":"e_1_3_2_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.06.009"},{"key":"e_1_3_2_43_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11214-0"},{"key":"e_1_3_2_44_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-010-9094-x"},{"key":"e_1_3_2_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.11.119"},{"key":"e_1_3_2_46_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9125-x"},{"key":"e_1_3_2_47_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.06.017"},{"key":"e_1_3_2_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.12.018"},{"key":"e_1_3_2_49_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2009.05.003"},{"key":"e_1_3_2_50_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.10.048"},{"key":"e_1_3_2_51_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2015.12.016"},{"key":"e_1_3_2_52_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2016.07.011"},{"key":"e_1_3_2_53_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.43.10.1437"},{"key":"e_1_3_2_54_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2009.02.007"},{"key":"e_1_3_2_55_2","article-title":"Developments of mean-variance model for portfolio selection in uncertain environment","author":"Qin Z.","year":"2009","unstructured":"QinZ., KarS. and LiX., Developments of mean-variance model for portfolio selection in uncertain environment, Technical Report (2009).","journal-title":"Technical Report"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-169212","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-169212","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-169212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:44Z","timestamp":1777455584000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-169212"}},"subtitle":[],"editor":[{"given":"Xiaoxia","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Qun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Qing","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2017,5,23]]},"references-count":54,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2017,5,23]]}},"alternative-id":["10.3233\/JIFS-169212"],"URL":"https:\/\/doi.org\/10.3233\/jifs-169212","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,23]]}}}