{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T01:16:48Z","timestamp":1784251008480,"version":"3.55.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T00:00:00Z","timestamp":1688947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2023,11]]},"DOI":"10.1007\/s40815-023-01558-2","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T19:03:17Z","timestamp":1689015797000},"page":"3103-3118","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Garbage Classification Game Based on Bilevel Multi-objective Optimization with Fuzzy Weight"],"prefix":"10.1007","volume":"25","author":[{"given":"Kaikai","family":"Qiao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"1558_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/J.APENERGY.2022.118736","author":"J Lv","year":"2022","unstructured":"Lv, J., Li, Y.P., Huang, G.H., Ding, Y.K., Li, X., Li, Y.: Planning energy economy and eco-environment nexus system under uncertainty: A copula-based stochastic multi-level programming method. Appl. Energy (2022). https:\/\/doi.org\/10.1016\/J.APENERGY.2022.118736","journal-title":"Appl. Energy"},{"issue":"1","key":"1558_CR2","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1016\/j.eswa.2014.08.006","volume":"42","author":"R Kadambur","year":"2015","unstructured":"Kadambur, R., Kotecha, P.: Multi-level production planning in a petrochemical industry using elitist teachingclearning-based-optimization. Expert Syst. Appl. 42(1), 628\u2013641 (2015)","journal-title":"Expert Syst. Appl."},{"issue":"2","key":"1558_CR3","doi-asserted-by":"publisher","first-page":"277","DOI":"10.12720\/sgce.2.2.277-282","volume":"2","author":"M Jin","year":"2013","unstructured":"Jin, M., Shi, R., Ning, Z., Yang, L.: Study on multi-level layout planning of electric vehicle charging stations based on an improved genetic algorithm. Int J Smart Grid Clean Energy 2(2), 277\u2013282 (2013)","journal-title":"Int J Smart Grid Clean Energy"},{"issue":"20","key":"1558_CR4","doi-asserted-by":"publisher","first-page":"6227","DOI":"10.1080\/00207543.2010.535043","volume":"49","author":"W Tao","year":"2011","unstructured":"Tao, W., Shi, L.Y.: Mathematical models for capacitated multi-level production planning problems with linked lot sizes. Int. J. Prod. Res. 49(20), 6227\u20136247 (2011)","journal-title":"Int. J. Prod. Res."},{"issue":"1","key":"1558_CR5","first-page":"786","volume":"188","author":"E Roghanian","year":"2007","unstructured":"Roghanian, E., Sadjadi, S.J., Aryanezhad, M.B.: A probabilistic bi-level linear multi-objective programming problem to supply chain planning. Appl. Math. Comput. 188(1), 786\u2013800 (2007)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1558_CR6","first-page":"67","volume":"19","author":"MB Aryanezhad","year":"2008","unstructured":"Aryanezhad, M.B., Roghanian, E.A.: A bi-level linear multi-objective decision making model with interval coefficients for supply chain coordination. Int. J. Ind. Eng. Prod. Res. 19(1), 67\u201374 (2008)","journal-title":"Int. J. Ind. Eng. Prod. Res."},{"key":"1558_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/J.EJOR.2021.07.052","author":"B Cta","year":"2021","unstructured":"Cta, B., Bg, C., Sl, A.: An iterative two-stage heuristic algorithm for a bilevel service network design and pricing model. Eur. J. Opera. Res. (2021). https:\/\/doi.org\/10.1016\/J.EJOR.2021.07.052","journal-title":"Eur. J. Opera. Res."},{"key":"1558_CR8","doi-asserted-by":"publisher","DOI":"10.1016\/J.KNOSYS.2022.108119","author":"XJ Zhou","year":"2022","unstructured":"Zhou, X.J., Tian, J.T., Wang, Z.Y., Yang, C.H., Huang, T.W., Xu, X.S.: Nonlinear bilevel programming approach for decentralized supply chain using a hybrid state transition algorithm. Knowledge-Based Syst. (2022). https:\/\/doi.org\/10.1016\/J.KNOSYS.2022.108119","journal-title":"Knowledge-Based Syst."},{"issue":"1","key":"1558_CR9","first-page":"51","volume":"162","author":"CG Shi","year":"2005","unstructured":"Shi, C.G., Lu, J., Zhang, G.Q.: An extended k th-best approach for linear bilevel programming. Appl. Math. Comput. 162(1), 51\u201363 (2005)","journal-title":"Appl. Math. Comput."},{"key":"1558_CR10","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/j.cor.2013.07.016","volume":"41","author":"X Pan","year":"2014","unstructured":"Pan, X., Li, Z.W.: An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions. Comput. Opera. Res. 41, 309\u2013318 (2014)","journal-title":"Comput. Opera. Res."},{"issue":"1","key":"1558_CR11","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1287\/ijoc.2019.0945","volume":"33","author":"T Kleinert","year":"2021","unstructured":"Kleinert, T., Schmidt, M.: Computing feasible points of bilevel problems with a penalty alternating direction method. Inform. J. Comput. 33(1), 198\u2013215 (2021)","journal-title":"Inform. J. Comput."},{"key":"1558_CR12","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1109\/TSMC.1981.4308712","volume":"11","author":"E Aiyoshi","year":"1981","unstructured":"Aiyoshi, E., Shimizu, K.: Hierarchical decentralized systems and its new solution by a barrier method optimization method. IEEE Trans. Syst. Man Cyber. 11, 444\u2013449 (1981)","journal-title":"IEEE Trans. Syst. Man Cyber."},{"issue":"12","key":"1558_CR13","doi-asserted-by":"publisher","first-page":"1111","DOI":"10.1109\/TAC.1984.1103455","volume":"29","author":"E Aiyoshi","year":"1984","unstructured":"Aiyoshi, E., Shimizu, K.: A solution method for the static constrained stackelberg problem via penalty method. IEEE Trans. Autom. Control 29(12), 1111\u20131114 (1984)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1558_CR14","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1109\/TAC.1981.1102607","volume":"26","author":"K Shimizu","year":"1981","unstructured":"Shimizu, K., Aiyoshi, E.: A new computational method for stackelberg and min-max problems by use a penalty method. IEEE Trans. Autom. Control 26, 460\u2013466 (1981)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"2","key":"1558_CR15","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1016\/S1474-6670(17)63658-9","volume":"14","author":"K Shimizu","year":"1981","unstructured":"Shimizu, K.: Two-level decision problems and their new solution methods by a penalty method. IFAC Proc. Vol. 14(2), 1303\u20131308 (1981)","journal-title":"IFAC Proc. Vol."},{"key":"1558_CR16","unstructured":"Bi, Z., Calamai, P., Conn, A.: An exact penalty function approach for the linear bilevel programming problem. Technical report, University of Waterloo, Department of Systems Design Engineering (1989)"},{"key":"1558_CR17","unstructured":"Bi, Z., Calamai,P., Conn, A.: An exact penalty function approach for the nonlinear bilevel programming problem. Technical report, University of Waterloo, Department of Systems Design Engineering (1989)"},{"key":"1558_CR18","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1007\/BF01096412","volume":"3","author":"D White","year":"1993","unstructured":"White, D., Anandalingam, G.: A penalty function approach for solving bilevel linear programs. J. Global Optim. 3, 397\u2013419 (1993)","journal-title":"J. Global Optim."},{"key":"1558_CR19","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.cor.2014.10.005","volume":"56","author":"J Gang","year":"2015","unstructured":"Gang, J., Yan, T., Lev, B., Xu, J., Shen, W., Yao, L.: A multi-objective bi-level location planning problem for stone industrial parks. Comput. Opera. Res. 56, 8\u201321 (2015)","journal-title":"Comput. Opera. Res."},{"issue":"6","key":"1558_CR20","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1007\/s00500-013-1015-9","volume":"17","author":"J Rada-Vilela","year":"2013","unstructured":"Rada-Vilela, J., Zhang, M., Seah, W.: A performance study on synchronicity and neighborhood size in particle swarm optimization. Soft Comput. 17(6), 1019\u20131030 (2013)","journal-title":"Soft Comput."},{"key":"1558_CR21","volume-title":"Optimization, learning and natural algorithms","author":"M Dorigo","year":"1992","unstructured":"Dorigo, M.: Optimization, learning and natural algorithms. Thesis Politecnico Di Milano Italy, Italy (1992)"},{"issue":"2","key":"1558_CR22","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1109\/TEVC.2009.2030331","volume":"14","author":"WN Chen","year":"2010","unstructured":"Chen, W.N., Zhang, J., Seah, W., Chen, W.N., Zhang, J., Chung, H., Zhong, W.L., Wu, W.G., Shi, Y.H.: A novel set-based particle swarm optimization method for discrete optimization problems. IEEE Trans. Evol. Comput. 14(2), 278\u2013300 (2010)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"2","key":"1558_CR23","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/0377-2217(95)00275-8","volume":"95","author":"VR Neppalli","year":"1996","unstructured":"Neppalli, V.R., Chen, C.L., Gupta, J.: Genetic algorithms for the two-stage bicriteria flowshop problem. Eur. J. Opera. Res. 95(2), 356\u2013373 (1996)","journal-title":"Eur. J. Opera. Res."},{"issue":"7","key":"1558_CR24","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s00500-006-0131-1","volume":"11","author":"RL Wang","year":"2007","unstructured":"Wang, R.L., Okazaki, K.: An improved genetic algorithm with conditional genetic operators and its application to set-covering problem. Soft. Comput. 11(7), 687\u2013694 (2007)","journal-title":"Soft. Comput."},{"issue":"6","key":"1558_CR25","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1109\/TCSVT.2009.2017309","volume":"19","author":"G Jeon","year":"2009","unstructured":"Jeon, G., You, J., Jeong, J.: Weighted fuzzy reasoning scheme for interlaced to progressive conversion. IEEE Trans. Circuits Syst. Video Technol. 19(6), 842\u2013855 (2009)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"issue":"3","key":"1558_CR26","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1109\/TEVC.2006.882428","volume":"11","author":"CK Goh","year":"2007","unstructured":"Goh, C.K., Tan, K.C.: An investigation on noisy environments in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 11(3), 354\u2013381 (2007)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"1558_CR27","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1162\/evco.2006.14.4.463","volume":"14","author":"K Deb","year":"2006","unstructured":"Deb, K., Gupta, H.: Introducing robustness in multi-objective optimization. Evol. Comput. 14(4), 463\u2013494 (2006)","journal-title":"Evol. Comput."},{"issue":"1080\/21693277","key":"1558_CR28","first-page":"1602486","volume":"10","author":"XX Wei","year":"2019","unstructured":"Wei, X.X., Yuan, S.C., Ye, Y.Q.: (2019) Optimizing facility layout planning for reconfigurable manufacturing system based on chaos genetic algorithm. Prod. Manufact. Res. 10(1080\/21693277), 1602486 (2019)","journal-title":"Prod. Manufact. Res."},{"key":"1558_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.energy.2018.03.174","author":"YQ Shen","year":"2018","unstructured":"Shen, Y.Q.: Improved chaos genetic algorithm based state of charge determination for lithium batteries in electric vehicles. Energy (2018). https:\/\/doi.org\/10.1016\/j.energy.2018.03.174","journal-title":"Energy"},{"key":"1558_CR30","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.procs.2017.03.076","volume":"107","author":"M Ru","year":"2017","unstructured":"Ru, M., Yin, S., Qu, Z.: Power and spectrum allocation in d2d networks based on coloring and chaos genetic algorithm. Proc. Comput. Sci. 107, 183\u2013189 (2017)","journal-title":"Proc. Comput. Sci."},{"issue":"2","key":"1558_CR31","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb, K., Agarwal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm Nsga ii. IEEE Trans. Evol. Comput. 6(2), 182\u2013197 (2002)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"4","key":"1558_CR32","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","volume":"18","author":"K Deb","year":"2014","unstructured":"Deb, K., Jain, H., Pratap, A., Meyarivan, T.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i Solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577\u2013601 (2014)","journal-title":"IEEE Trans. Evol. Comput"},{"issue":"6","key":"1558_CR33","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"QF Zhang","year":"2008","unstructured":"Zhang, Q.F., Li, H.: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712\u2013731 (2008)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"1558_CR34","volume-title":"J. Water Resour. Plan. Manag","author":"AM Baltar","year":"2008","unstructured":"Baltar, A.M., Fontane, D.G.: Use of multiobjective particle swarm optimization in water resources management. J. Water Resour. Plan. Manag. 134(3), 257\u2013265 (2008)"},{"key":"1558_CR35","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/657978","author":"J Xiong","year":"2013","unstructured":"Xiong, J., Tan, X., Yang, K.W., Chen, Y.W.: Fuzzy group decision making for multiobjective problems Tradeoff between consensus and robustness. J. Appl. Math. (2013). https:\/\/doi.org\/10.1155\/2013\/657978","journal-title":"J. Appl. Math."},{"key":"1558_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2020.106299","author":"J Dai","year":"2020","unstructured":"Dai, J., Chen, J.: Feature selection via normative fuzzy information weight with application into tumor classification. Appl. Soft Comput. (2020). https:\/\/doi.org\/10.1016\/j.asoc.2020.106299","journal-title":"Appl. Soft Comput."},{"issue":"2","key":"1558_CR37","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1109\/TFUZZ.2018.2852307","volume":"27","author":"ZJ Zhang","year":"2019","unstructured":"Zhang, Z.J.: A goal-programming-based heuristic approach to deriving fuzzy weights in analytic form from triangular fuzzy preference relations. IEEE Trans. Fuzzy Syst. 27(2), 234\u2013248 (2019)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1558_CR38","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2022.3200730","author":"HJ Liang","year":"2020","unstructured":"Liang, H.J., Chen, L., Pan, Y.N., Lam, H.-K.: Fuzzy-based robust precision consensus tracking for uncertain networked systems with cooperative-antagonistic interactions. IEEE Trans. Fuzzy Syst. (2020). https:\/\/doi.org\/10.1109\/TFUZZ.2022.3200730","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"11","key":"1558_CR39","doi-asserted-by":"publisher","first-page":"2296","DOI":"10.1016\/j.ins.2006.12.009","volume":"177","author":"MJ Zolghadri","year":"2007","unstructured":"Zolghadri, M.J., Mansoori, E.G.: Weighting fuzzy classification rules using receiver operating characteristics (roc) analysis. Inform. Sci. 177(11), 2296\u20132307 (2007)","journal-title":"Inform. Sci."},{"issue":"2","key":"1558_CR40","first-page":"5","volume":"14","author":"CH Qian","year":"2005","unstructured":"Qian, C.H., Zhang, L., Dai, B., Wang, J.Z.: Fuzzy weighted average with triangular fuzzy numbers and its application to the assessment and decision. Opera. Res. Manag. Sci. 14(2), 5\u20139 (2005)","journal-title":"Opera. Res. Manag. Sci."},{"issue":"1","key":"1558_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TEVC.2010.2051443","volume":"16","author":"LT Bui","year":"2012","unstructured":"Bui, L.T., Abbass, H.A., Barlow, M., Bender, A.: Robustness against the decision-makers attitude to risk in problems with conflicting objectives. Evol. Comput. IEEE Trans. 16(1), 1\u201319 (2012)","journal-title":"Evol. Comput. IEEE Trans."},{"key":"1558_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/J.ASOC.2022.109718","author":"KK Qiao","year":"2023","unstructured":"Qiao, K.K., Zhang, J.R., Chen, J.W.: Two effective heuristic methods of determining the numbers of fuzzy clustering centers based on bilevel programming. Appl. Soft Comput. (2023). https:\/\/doi.org\/10.1016\/J.ASOC.2022.109718","journal-title":"Appl. Soft Comput."},{"key":"1558_CR43","volume-title":"Solid waste management and recycling","author":"I Baud","year":"2005","unstructured":"Baud, I., Furedy, C., Post, J.: Solid waste management and recycling. Spring Netherlands, Netherlands (2005)"},{"issue":"4","key":"1558_CR44","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1007\/s10898-019-00796-9","volume":"76","author":"J Jiang","year":"2020","unstructured":"Jiang, J., Zhang, S., Lv, Y., Du, X., Yan, Z.: An admm-based locationcallocation algorithm for nonconvex constrained multi-source weber problem under gauge. J. Global Optim. 76(4), 793\u2013818 (2020)","journal-title":"J. Global Optim."},{"issue":"6","key":"1558_CR45","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1016\/S1004-4132(08)60213-3","volume":"19","author":"HC Li","year":"2008","unstructured":"Li, H.C., Wang, Y.P.: Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems. J. Syst. Eng. Electron. 19(6), 1157\u20131164 (2008)","journal-title":"J. Syst. Eng. Electron."},{"issue":"3","key":"1558_CR46","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1007\/s10915-015-0048-x","volume":"66","author":"W Deng","year":"2016","unstructured":"Deng, W., Yin, W.: On the global and linear convergence of the generalized alternating direction method of multipliers. J. Sci. Comput. 66(3), 889\u2013916 (2016)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1558_CR47","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01581204","volume":"55","author":"J Eckstein","year":"1992","unstructured":"Eckstein, J., Bertsekas, D.P.: On the douglas-rachford splitting method and the proximal point algorithm for maximal monotone operators. Math. Program. 55(1), 293\u2013318 (1992)","journal-title":"Math. Program."},{"key":"1558_CR48","doi-asserted-by":"crossref","unstructured":"Fukunaga, K.: Introduction to statistical pattern recognition. Academic Press, Boston (1990)","DOI":"10.1016\/B978-0-08-047865-4.50007-7"}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-023-01558-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-023-01558-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-023-01558-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,30]],"date-time":"2023-11-30T15:23:23Z","timestamp":1701357803000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-023-01558-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,10]]},"references-count":48,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["1558"],"URL":"https:\/\/doi.org\/10.1007\/s40815-023-01558-2","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,10]]},"assertion":[{"value":"1 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 May 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}