{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:37:50Z","timestamp":1777703870906,"version":"3.51.4"},"reference-count":38,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T00:00:00Z","timestamp":1530144000000},"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":[[2018,7,27]]},"abstract":"<jats:p>This paper proposes a new definition of cross entropy for uncertain random variables, and derives a formula. Moreover, this paper introduces generalized cross entropy for uncertain random variables, and discusses its properties. Based on the definition of cross entropy, a cross entropy chance distribution model of degree-constrained minimum spanning tree (DCMST) problem is proposed. An algorithm is designed here to solve the model. Finally, a numerical example is provided to illustrate the effectiveness of the proposed model and algorithm.<\/jats:p>","DOI":"10.3233\/jifs-18268","type":"journal-article","created":{"date-parts":[[2018,6,29]],"date-time":"2018-06-29T16:42:05Z","timestamp":1530290525000},"page":"1193-1204","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":11,"title":["A new definition of cross entropy for uncertain random variables and its application"],"prefix":"10.1177","volume":"35","author":[{"given":"Lifen","family":"Jia","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tsinghua University, Beijing, China"}]},{"given":"Xiangfeng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Technology and Management, University of International Business and Economics, Beijing, China"}]},{"given":"Xin","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences and Physics, North China Electric Power University, Beijing, China."}]}],"member":"179","published-online":{"date-parts":[[2018,6,28]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161161"},{"key":"e_1_3_2_3_2","article-title":"Partial triangular entropy of uncertain random variables and its application","author":"Ahmadzade H.","unstructured":"AhmadzadeH., GaoR., DehghanM.H. and AhmadiR., Partial triangular entropy of uncertain random variables and its application, Journal of Ambient Intelligence and Humanized Computing. DOI: 10.1007\/s12652-017-0565-6","journal-title":"Journal of Ambient Intelligence and Humanized Computing"},{"issue":"4","key":"e_1_3_2_4_2","first-page":"292","article-title":"Partial quadratic entropy of uncertain random variables","volume":"10","author":"Ahmadzade H.","year":"2016","unstructured":"AhmadzadeH., GaoR. and ZareiH., Partial quadratic entropy of uncertain random variables, Journal of Uncertain Systems 10(4) (2016), 292\u2013301.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_5_2","first-page":"37","article-title":"O jist\u00e9m probl\u00e9mu minim\u00e1ln\u00edm, ce Mor P\u0159\u00edrodov\u00e9d Spol v Brn\u011b","volume":"3","author":"Bor\u00fcvka O.","year":"1926","unstructured":"Bor\u00fcvkaO., O jist\u00e9m probl\u00e9mu minim\u00e1ln\u00edm, ce Mor P\u0159\u00edrodov\u00e9d Spol v Brn\u011b, Pr&rsquo;a 3 (1926), 37\u201358.","journal-title":"Pr&rsquo;a"},{"issue":"4","key":"e_1_3_2_6_2","first-page":"1081","article-title":"Ant colony optimization approaches to the degree-constrained minimum spanning tree problem","volume":"24","author":"Bau Y.T.","year":"2008","unstructured":"BauY.T., HoC.K. and EveH.T., Ant colony optimization approaches to the degree-constrained minimum spanning tree problem, Journal of Information Science and Engineering 24(4) (2008), 1081\u20131094.","journal-title":"Journal of Information Science and Engineering"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-010-9073-2"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1965.1082452"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.21681"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2016.07.054"},{"issue":"5","key":"e_1_3_2_11_2","first-page":"747","article-title":"Degree-constrained minimum spanning tree problem of uncertain random network, of Ambient Intelligence and Humanized Computing","volume":"8","author":"Gao X.","year":"2017","unstructured":"GaoX., JiaL.F. and KarS., Degree-constrained minimum spanning tree problem of uncertain random network, of Ambient Intelligence and Humanized Computing, Journal 8(5) (2017), 747\u2013757.","journal-title":"Journal"},{"key":"e_1_3_2_12_2","unstructured":"GaoX. JiaL.F. and KarS. A new definition of cross-entropy for uncertain variables Soft Computing. 10.1007\/s00500-017-2534-6"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2016.07.006"},{"key":"e_1_3_2_14_2","doi-asserted-by":"crossref","unstructured":"GaoR. and RalescuD.A. Convergence in distribution for uncertain random variables IEEE Transactions on Fuzzy Systems. DOI: 10.1109\/TFUZZ.2017.2724021","DOI":"10.1109\/TFUZZ.2017.2724021"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/4235.850653"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"issue":"1","key":"e_1_3_2_17_2","first-page":"3","article-title":"Fuzzy process, hybrid process and uncertain process","volume":"2","author":"Liu B.","year":"2008","unstructured":"LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems 2(1) (2008), 3\u201316.","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"e_1_3_2_18_2","first-page":"3","article-title":"Some research problems in uncertainty theory","volume":"3","author":"Liu B.","year":"2009","unstructured":"LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems 3(1) (2009), 3\u201310.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89484-1"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8"},{"issue":"1","key":"e_1_3_2_21_2","first-page":"3","article-title":"Uncertain random graph and uncertain random network","volume":"8","author":"Liu B.","year":"2014","unstructured":"LiuB., Uncertain random graph and uncertain random network, Journal of Uncertain Systems 8(1) (2014), 3\u201312.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0935-0"},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9149-2"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1142\/S021848851450024X"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-017-0465-9"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/0305-0548(80)90022-2"},{"key":"e_1_3_2_27_2","first-page":"104","article-title":"An efficient evolutionary algorithm for the degreeconstrained minimum spanning tree problem","volume":"1","author":"Raidl G.R.","year":"2000","unstructured":"RaidlG.R., An efficient evolutionary algorithm for the degreeconstrained minimum spanning tree problem, IEEE Transactions on Evolutionary Computation 1 (2000), 104\u2013111.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10845-014-1015-3"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40467-014-0015-3"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488517500210"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.enavi.2015.06.008"},{"key":"e_1_3_2_32_2","doi-asserted-by":"publisher","DOI":"10.1080\/01969722.2012.637012"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.1142\/S012905411350007X"},{"key":"e_1_3_2_34_2","first-page":"157","article-title":"Approach to the drgree-constrained minimum spanning tree problem using genetic algorithm","volume":"3","author":"Zhou G.G.","year":"1997","unstructured":"ZhouG.G. and GenM.S., Approach to the drgree-constrained minimum spanning tree problem using genetic algorithm, Engineering Design and Automation 3 (1997), 157\u2013165.","journal-title":"Engineering Design and Automation"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2015.2466080"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.7232\/iems.2013.12.1.009"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.12720\/jcm.9.5.385-390"},{"key":"e_1_3_2_38_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488515500038"},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.1080\/01969722.2010.511552"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18268","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18268","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:51Z","timestamp":1777455591000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,28]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,7,27]]}},"alternative-id":["10.3233\/JIFS-18268"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18268","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,28]]}}}