{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:29:52Z","timestamp":1777703392190,"version":"3.51.4"},"reference-count":39,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2016,11,11]],"date-time":"2016-11-11T00:00:00Z","timestamp":1478822400000},"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":[[2017,1,13]]},"abstract":"<jats:p>This paper introduces arithmetic operations for LR mixed fuzzy random variables commonly used in practice for modeling fuzzy stochastic phenomena. The operations are proposed based on mean chance measure, which as a natural extension of both the probability of a random event and the credibility of a fuzzy event, measures the mean or expected (in the sense of probability) credibility that the fuzzy random event occurs. Following from the proposed operational laws, the mean chance distributions of LR mixed fuzzy random variables can be deduced explicitly rather than obtained by simulation, which will provide greater convenience for the decision making or optimization in mixed fuzzy and random environments. Furthermore, some important conclusions on the expected value operator defined via the mean chance measure as well as applications of the proposed arithmetic operations in system reliability analysis are also presented.<\/jats:p>","DOI":"10.3233\/jifs-152173","type":"journal-article","created":{"date-parts":[[2016,11,15]],"date-time":"2016-11-15T10:38:15Z","timestamp":1479206295000},"page":"451-466","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Arithmetic operations for LR mixed fuzzy random variables via mean chance measure with applications"],"prefix":"10.1177","volume":"32","author":[{"given":"Ke","family":"Wang","sequence":"first","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Management, Shanghai University, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan A.","family":"Ralescu","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,11,11]]},"reference":[{"key":"e_1_3_2_2_2","article-title":"Reliability analysis in presence of random variables and fuzzy variables","volume":"2015","author":"Cui L.","year":"2015","unstructured":"CuiL., L\u00fcZ. and LiG., Reliability analysis in presence of random variables and fuzzy variables, Journal of Applied Mathematics 2015 (2015).","journal-title":"Journal of Applied Mathematics"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207727808941724"},{"key":"e_1_3_2_4_2","unstructured":"DuboisD. and PradeH. Fuzzy Sets and Systems: Theory of Applications New York: Academic 1980."},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2006.05.002"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.10.035"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9133-x"},{"key":"e_1_3_2_8_2","doi-asserted-by":"crossref","unstructured":"KruseR. and MeyerK.D. Statistics with Vague Data Dordrecht: D. Reidel Publishing Company 1987.","DOI":"10.1007\/978-94-009-3943-1_8"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0255(78)90019-1"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2011.04.014"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130836"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2006.03.013"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-008-0308-x"},{"issue":"2","key":"e_1_3_2_14_2","first-page":"57","article-title":"Credibilistic parameter estimation and its application in fuzzy portfolio selection","volume":"8","author":"Li X.","year":"2011","unstructured":"LiX., QinZ. and RalescuD., Credibilistic parameter estimation and its application in fuzzy portfolio selection, Iranian Journal of Fuzzy Systems 8(2) (2011), 57\u201365.","journal-title":"Iranian Journal of Fuzzy Systems"},{"issue":"4","key":"e_1_3_2_15_2","first-page":"77","article-title":"Fuzzy train energy consumption minimization model and algorithm","volume":"8","author":"Li X.","year":"2011","unstructured":"LiX., RalescuD. and TangT., Fuzzy train energy consumption minimization model and algorithm, Iranian Journal of Fuzzy Systems 8(4) (2011), 77\u201391.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1080\/09544828.2012.753995"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.963757"},{"key":"e_1_3_2_18_2","unstructured":"LiuB. Uncertainty Theory: An Introduction to Its Axiomatic Foundations Berlin: Springer-Verlag 2004."},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-006-0016-x"},{"key":"e_1_3_2_20_2","unstructured":"LiuB. Uncertainty Theory (2nd ed.) Berlin: Springer 2007."},{"issue":"1","key":"e_1_3_2_21_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 Systems 6(1) (2012), 3\u201310.","journal-title":"Journal of Uncertain Systems"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.800692"},{"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":"10.1109\/TFUZZ.2006.890677"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.05.033"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023447217758"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2004.03.010"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0305-0548(03)00235-1"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.08.022"},{"key":"e_1_3_2_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90093-4"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130813"},{"issue":"1","key":"e_1_3_2_32_2","first-page":"57","article-title":"On convergence of series of fuzzy real numbers","volume":"39","author":"Tripathy B.C.","year":"2012","unstructured":"TripathyB.C. and DasP.C., On convergence of series of fuzzy real numbers, Kuwait Journal of Science and Engineering 39(1A) (2012), 57\u201370.","journal-title":"Kuwait Journal of Science and Engineering"},{"key":"e_1_3_2_33_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2012-0582"},{"key":"e_1_3_2_34_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0853-1"},{"issue":"6","key":"e_1_3_2_35_2","first-page":"1547","article-title":"Reliability optimization of a seriesparallel system with fuzzy random lifetimes","volume":"5","author":"Wang S.","year":"2009","unstructured":"WangS. and WatadaJ., Reliability optimization of a seriesparallel system with fuzzy random lifetimes, International Journal of Innovative Computing, Information and Control 5(6) (2009), 1547\u20131558.","journal-title":"International Journal of Innovative Computing, Information and Control"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(78)90029-5"},{"key":"e_1_3_2_38_2","first-page":"69","volume-title":"Mathematical Frontiers of the Social and Policy Sciences","author":"Zadeh L.A.","year":"1979","unstructured":"ZadehL.A., A theory of approximate reasoning, In Mathematical Frontiers of the Social and Policy Sciences, HayesJ.,MichieD., and ThrallR.M. (eds.), Cororado: Westview Press, 1979, pp. 69\u2013129."},{"key":"e_1_3_2_39_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151712"},{"key":"e_1_3_2_40_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2015.1086578"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-152173","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-152173","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-152173","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:38:37Z","timestamp":1777455517000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-152173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,11]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1,13]]}},"alternative-id":["10.3233\/JIFS-152173"],"URL":"https:\/\/doi.org\/10.3233\/jifs-152173","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,11]]}}}