{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:40:22Z","timestamp":1761489622472},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,4,12]],"date-time":"2015-04-12T00:00:00Z","timestamp":1428796800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2016,12]]},"DOI":"10.1007\/s10479-015-1863-z","type":"journal-article","created":{"date-parts":[[2015,4,11]],"date-time":"2015-04-11T13:24:12Z","timestamp":1428758652000},"page":"853-866","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A new concept for fuzzy variable based non-linear programming problem with application on system reliability via genetic algorithm approach"],"prefix":"10.1007","volume":"247","author":[{"given":"G. S.","family":"Mahapatra","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B. S.","family":"Mahapatra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. K.","family":"Roy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,4,12]]},"reference":[{"issue":"1","key":"1863_CR1","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s10479-013-1402-8","volume":"212","author":"L Baoliang","year":"2014","unstructured":"Baoliang, L., Lirong, C., & Yanqing, W. (2014). Interval reliability for aggregated Markov repairable system with repair time omission. Annals of Operations Research, 212(1), 169\u2013183.","journal-title":"Annals of Operations Research"},{"key":"1863_CR2","doi-asserted-by":"crossref","first-page":"1972","DOI":"10.1016\/j.eswa.2011.08.047","volume":"39","author":"A Baykasoglu","year":"2012","unstructured":"Baykasoglu, A., & Gocken, T. (2012). A direct solution approach to fuzzy mathematical programs with fuzzy decision variables. Expert System with Applications, 39, 1972\u20131978.","journal-title":"Expert System with Applications"},{"issue":"3","key":"1863_CR3","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0165-0114(00)00122-6","volume":"125","author":"CR Bector","year":"2002","unstructured":"Bector, C. R., & Chandra, S. (2002). On duality in linear programming under fuzzy environment. Fuzzy Sets and System, 125(3), 317\u2013325.","journal-title":"Fuzzy Sets and System"},{"issue":"4","key":"1863_CR4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1287\/mnsc.17.4.B141","volume":"17","author":"RE Bellmann","year":"1970","unstructured":"Bellmann, R. E., & Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Science, 17(4), 141\u2013164.","journal-title":"Management Science"},{"issue":"1","key":"1863_CR5","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1016\/j.eswa.2011.07.126","volume":"39","author":"R Bosma","year":"2012","unstructured":"Bosma, R., van den Berg, J., Kaymak, U., Udo, H., & Verreth, J. (2012). A generic methodology for developing fuzzy decision models. Expert Systems with Applications, 39(1), 1200\u20131210.","journal-title":"Expert Systems with Applications"},{"key":"1863_CR6","unstructured":"Cao, B.Y. (2004). Multi-objective linear programming model with T-fuzzy variables, Journal of Fuzzy Mathematics, 12(2), 425\u2013432."},{"key":"1863_CR7","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0165-0114(89)90042-0","volume":"29","author":"D Chanas","year":"1989","unstructured":"Chanas, D. (1989). Fuzzy programming in multiobjective linear programming-a parametric approach. Fuzzy Sets and Systems, 29, 303\u2013313.","journal-title":"Fuzzy Sets and Systems"},{"issue":"7","key":"1863_CR8","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s00500-005-0483-y","volume":"10","author":"JR Chang","year":"2006","unstructured":"Chang, J. R., Chang, K. H., Liao, S. H., & Cheng, C. H. (2006). The reliability of general vague fault-tree analysis on weapon systems fault diagnosis. Soft Computing, 10(7), 531\u2013542.","journal-title":"Soft Computing"},{"issue":"3","key":"1863_CR9","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s00500-009-0403-7","volume":"14","author":"KH Chang","year":"2010","unstructured":"Chang, K. H., Cheng, C. H., & Chang, Y. C. (2010). Reprioritization of failures in a silane supply system using an intuitionistic fuzzy set ranking technique. Soft Computing, 14(3), 285\u2013298.","journal-title":"Soft Computing"},{"issue":"12","key":"1863_CR10","doi-asserted-by":"crossref","first-page":"10943","DOI":"10.1016\/j.eswa.2012.03.030","volume":"39","author":"S Chatterjee","year":"2012","unstructured":"Chatterjee, S., & Bandopadhyay, S. (2012). Reliability estimation using a genetic algorithm-based artificial neural network: An application to a load\u2013haul\u2013dump machine. Expert System Applications, 39(12), 10943\u201310951.","journal-title":"Expert System Applications"},{"issue":"2","key":"1863_CR11","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182\u2013197.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"11","key":"1863_CR12","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1002\/nme.2944","volume":"84","author":"JJ Durillo","year":"2010","unstructured":"Durillo, J. J., Nebro, A. J., Luna, F., Coello Coello, C. A., & Alba, E. (2010). Convergence speed in multi-objective metaheuristics: Efficiency criteria and empirical study. International Journal for Numerical Methods in Engineering, 84(11), 1344\u20131375.","journal-title":"International Journal for Numerical Methods in Engineering"},{"key":"1863_CR13","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.cie.2012.09.015","volume":"64","author":"H Garg","year":"2013","unstructured":"Garg, H., & Sharma, S. P. (2013). Multi-objective reliability-redundancy allocation problem using particle swarm optimizzation. Computers & Industrial Engineering, 64, 247\u2013255.","journal-title":"Computers & Industrial Engineering"},{"key":"1863_CR14","volume-title":"Adaptation in natural and artificial systems","author":"HJ Holland","year":"1975","unstructured":"Holland, H. J. (1975). Adaptation in natural and artificial systems. Michigan: University of Michigan."},{"key":"1863_CR15","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1016\/j.ins.2010.01.006","volume":"180","author":"DH Hong","year":"2010","unstructured":"Hong, D. H. (2010). Blackwell\u2019s theorem for T-related fuzzy variables. Informations sciences, 180, 1769\u20131777.","journal-title":"Informations sciences"},{"key":"1863_CR16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0165-0114(00)00068-3","volume":"122","author":"F Hsu","year":"2001","unstructured":"Hsu, F., & Fu, L. (2001). A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping. Fuzzy Sets and Systems, 122, 83\u2013106.","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"1863_CR17","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s10479-011-0839-x","volume":"209","author":"PK Jeffrey","year":"2013","unstructured":"Jeffrey, P. K., Steven, M. C., & Mark, E. O. (2013). Reliability of manufacturing equipment in complex environments. Annals of Operations Research, 209(1), 231\u2013254.","journal-title":"Annals of Operations Research"},{"issue":"1","key":"1863_CR18","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/3477.907564","volume":"31","author":"U Kaymak","year":"2001","unstructured":"Kaymak, U., & Sousa, J. M. C. (2001). Model predictive control using fuzzy decision functions. IEEE Transactions on Systems, Man and Cybernetics. Part B, Cybernetics, 31(1), 54\u201365.","journal-title":"IEEE Transactions on Systems, Man and Cybernetics. Part B, Cybernetics"},{"issue":"1","key":"1863_CR19","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1023\/A:1021998611875","volume":"8","author":"U Kaymak","year":"2003","unstructured":"Kaymak, U., & Sousa, J. M. C. (2003). Weighted constraint aggregation in fuzzy optimization. Constraints, 8(1), 29\u201346.","journal-title":"Constraints"},{"key":"1863_CR20","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.apor.2012.10.007","volume":"39","author":"ML Koc","year":"2013","unstructured":"Koc, M. L., & Balas, C. E. (2013). Reliability analysis of a rubble mound breakwater using the theory of fuzzy random variables. Applied Ocean Research, 39, 83\u201388.","journal-title":"Applied Ocean Research"},{"key":"1863_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-48753-8","volume-title":"Fuzzy mathematical programming methods and application","author":"YJ Lai","year":"1992","unstructured":"Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming methods and application. Berlin: Springer."},{"key":"1863_CR22","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.orl.2008.09.004","volume":"37","author":"X Li","year":"2009","unstructured":"Li, X., Yan, R., & Zuo, M. J. (2009). Evaluating a warm standby system with components having proportional hazard rates. Operation Research Letters, 37, 56\u201360.","journal-title":"Operation Research Letters"},{"issue":"1","key":"1863_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10479-013-1491-4","volume":"212","author":"C Lirong","year":"2014","unstructured":"Lirong, C., Haijun, L., & Susan, H. X. (2014). Stochastic methods in reliability and risk management. Annals of Operations Research, 212(1), 1\u20132.","journal-title":"Annals of Operations Research"},{"key":"1863_CR24","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0165-0114(00)00114-7","volume":"122","author":"X Liu","year":"2001","unstructured":"Liu, X. (2001). Measuring the satisfaction of constraints in fuzzy linear programming. Fuzzy Sets and System, 122, 263\u2013275.","journal-title":"Fuzzy Sets and System"},{"issue":"1","key":"1863_CR25","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1016\/j.amc.2005.04.105","volume":"174","author":"GS Mahapatra","year":"2006","unstructured":"Mahapatra, G. S., & Roy, T. K. (2006). Fuzzy multi-objective mathematical programming on reliability optimization model. Applied Mathematics and Computation, 174(1), 643\u2013659.","journal-title":"Applied Mathematics and Computation"},{"issue":"2","key":"1863_CR26","first-page":"151","volume":"5","author":"GS Mahapatra","year":"2012","unstructured":"Mahapatra, G. S., & Roy, T. K. (2012). Reliability evaluation of bridge system with fuzzy reliability of components using interval nonlinear programming. Electronic Journal of Applied Statistical Analysis, 5(2), 151\u2013163.","journal-title":"Electronic Journal of Applied Statistical Analysis"},{"key":"1863_CR27","doi-asserted-by":"crossref","first-page":"743","DOI":"10.3233\/IFS-131032","volume":"27","author":"GS Mahapatra","year":"2014","unstructured":"Mahapatra, G. S., Mahapatra, B. S., & Roy, P. K. (2014). Network reliability evaluation for fuzzy components: An interval programming approach. Journal of Intelligent and Fuzzy Systems, 27, 743\u2013751.","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"1863_CR28","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1016\/j.fss.2007.05.005","volume":"158","author":"N Mahdavi-Amiri","year":"2007","unstructured":"Mahdavi-Amiri, N., & Nasseri, S. H. (2007). Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets and Systems, 158, 1961\u20131978.","journal-title":"Fuzzy Sets and Systems"},{"issue":"3","key":"1863_CR29","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0165-0114(94)90097-3","volume":"66","author":"HR Maleki","year":"1994","unstructured":"Maleki, H. R., Tata, M., & Mashinchi, M. (1994). Linear programming with fuzzy variables. Fuzzy Sets and System, 66(3), 301\u2013306.","journal-title":"Fuzzy Sets and System"},{"issue":"3","key":"1863_CR30","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s11081-006-9973-8","volume":"7","author":"D Padmanabhan","year":"2006","unstructured":"Padmanabhan, D., Agarwal, H., Renaud, J. E., & Batill, S. M. (2006). A study using Monte Carlo simulation for failure probability calculation in reliability-based optimization. Optimization and Engineering, 7(3), 297\u2013316.","journal-title":"Optimization and Engineering"},{"issue":"5","key":"1863_CR31","doi-asserted-by":"crossref","first-page":"1454","DOI":"10.1016\/j.cam.2010.08.031","volume":"235","author":"R Qin","year":"2011","unstructured":"Qin, R., Liu, Y., & Liu, Z. (2011). Methods of critical value reduction for type-2 fuzzy variables and their applications. Journal of Computational and Applied Mathematics, 235(5), 1454\u20131481.","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"1863_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-1633-4","volume-title":"Fuzzy Sets and Interactive multi-objective Optimization","author":"M Sakawa","year":"1993","unstructured":"Sakawa, M. (1993). Fuzzy Sets and Interactive multi-objective Optimization. New York: Plenum Press."},{"key":"1863_CR33","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/S0377-2217(02)00449-6","volume":"149","author":"C Satnciulescu","year":"2003","unstructured":"Satnciulescu, C., Fortemps, Ph, Installe, M., & Wertz, V. (2003). Multiobjective fuzzy linear programming problem with fuzzy decision variables. European Journal of Operational Research, 149, 654\u2013675.","journal-title":"European Journal of Operational Research"},{"issue":"4","key":"1863_CR34","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1109\/TEVC.2010.2064321","volume":"15","author":"O Schutze","year":"2011","unstructured":"Schutze, O., Lara, A., & Coello Coello, C. A. (2011). On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Transactions on Evolutionary Computation, 15(4), 444\u2013455.","journal-title":"IEEE Transactions on Evolutionary Computation"},{"issue":"2","key":"1863_CR35","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0165-0114(98)00052-9","volume":"111","author":"T Shaocheng","year":"2000","unstructured":"Shaocheng, T., Jiantao, T., & Tao, W. (2000). Fuzzy adaptive control of non-linear systems. Fuzzy Sets and System, 111(2), 153\u2013167.","journal-title":"Fuzzy Sets and System"},{"issue":"3","key":"1863_CR36","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1162\/evco.1994.2.3.221","volume":"2","author":"N Srinivas","year":"1994","unstructured":"Srinivas, N., & Deb, K. (1994). Multi-objective function optimization using nondominated sorting genetic algorithms. Evolutionary computation, 2(3), 221\u2013248.","journal-title":"Evolutionary computation"},{"issue":"5","key":"1863_CR37","first-page":"970","volume":"53","author":"S Wang","year":"2011","unstructured":"Wang, S., & Watada, J. (2011). Some properties of T-independent fuzzy variables. Mathematical and Computer Modelling, 53(5), 970\u2013984.","journal-title":"Mathematical and Computer Modelling"},{"issue":"1","key":"1863_CR38","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1016\/j.amc.2005.04.106","volume":"174","author":"F Wu","year":"2006","unstructured":"Wu, F., Lu, J., & Zhang, G. (2006). A new approximate algorithm for solving multiple objective linear programming problems with fuzzy parameters. Applied Mathematics and Computation, 174(1), 524\u2013544.","journal-title":"Applied Mathematics and Computation"},{"issue":"1","key":"1863_CR39","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10479-012-1127-0","volume":"212","author":"Z Xiaoyan","year":"2014","unstructured":"Xiaoyan, Z., & Way, K. (2014). Importance measures in reliability and mathematical programming. Annals of Operations Research, 212(1), 241\u2013267.","journal-title":"Annals of Operations Research"},{"issue":"6","key":"1863_CR40","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1016\/j.camwa.2007.04.042","volume":"55","author":"F Xue","year":"2008","unstructured":"Xue, F., Tang, W., & Zhao, R. (2008). The expected value of a function of a fuzzy variable with a continuous membership function. Computers & Mathematics with Applications, 55(6), 1215\u20131224.","journal-title":"Computers & Mathematics with Applications"},{"key":"1863_CR41","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338\u2013353.","journal-title":"Information and Control"},{"key":"1863_CR42","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1016\/j.ress.2010.05.004","volume":"95","author":"X Zhong","year":"2010","unstructured":"Zhong, X., Ichchou, M., & Saidi, A. (2010). Reliability assessment of complex mechatronic systems using a modified nonparamertic belief propagation algorithm. Reliability Engineering and System Safety, 95, 1174\u20131185.","journal-title":"Reliability Engineering and System Safety"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1863-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-015-1863-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1863-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1863-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T19:51:53Z","timestamp":1598903513000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-015-1863-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,12]]},"references-count":42,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["1863"],"URL":"https:\/\/doi.org\/10.1007\/s10479-015-1863-z","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,12]]}}}