{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T22:32:34Z","timestamp":1767911554427,"version":"3.49.0"},"reference-count":94,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T00:00:00Z","timestamp":1617753600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T00:00:00Z","timestamp":1617753600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71901178"],"award-info":[{"award-number":["71901178"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71904084"],"award-info":[{"award-number":["71904084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71910107002"],"award-info":[{"award-number":["71910107002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1007\/s10479-021-04027-x","type":"journal-article","created":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T09:03:08Z","timestamp":1617786188000},"page":"173-210","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Data envelopment analysis cross efficiency evaluation with reciprocal behaviors"],"prefix":"10.1007","volume":"302","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4387-423X","authenticated-orcid":false,"given":"Feng","family":"Li","sequence":"first","affiliation":[]},{"given":"Han","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Qingyuan","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"Liang","family":"Liang","sequence":"additional","affiliation":[]},{"given":"Gang","family":"Kou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,4,7]]},"reference":[{"issue":"2","key":"4027_CR1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0377-2217(02)00068-1","volume":"140","author":"N Adler","year":"2002","unstructured":"Adler, N., Friedman, L., & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, 140(2), 249\u2013265.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4027_CR2","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1016\/j.ejor.2012.11.034","volume":"226","author":"J Alcaraz","year":"2013","unstructured":"Alcaraz, J., Ram\u00f3n, N., Ruiz, J. L., & Sirvent, I. (2013). Ranking ranges in cross-efficiency evaluations. European Journal of Operational Research, 226(3), 516\u2013521.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"4027_CR3","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s10479-018-2766-6","volume":"271","author":"Q An","year":"2018","unstructured":"An, Q., Meng, F., & Xiong, B. (2018). Interval cross efficiency for fully ranking decision making units using DEA\/AHP approach. Annals of Operations Research, 271(2), 297\u2013317.","journal-title":"Annals of Operations Research"},{"key":"4027_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2020.102235","author":"Q An","year":"2020","unstructured":"An, Q., Tao, X., & Xiong, B. (2020a). Benchmarking with data envelopment analysis: An agency perspective. Omega. https:\/\/doi.org\/10.1016\/j.omega.2020.102235","journal-title":"Omega"},{"issue":"2","key":"4027_CR5","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1016\/j.ejor.2019.11.031","volume":"283","author":"Q An","year":"2020","unstructured":"An, Q., Wang, P., Emrouznejad, A., & Hu, J. (2020b). Fixed cost allocation based on the principle of efficiency invariance in two-stage systems. European Journal of Operational Research, 283(2), 662\u2013675.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4027_CR6","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1023\/A:1015012121760","volume":"17","author":"TR Anderson","year":"2002","unstructured":"Anderson, T. R., Hollingsworth, K., & Inman, L. (2002). The fixed weighting nature of a cross-evaluation model. Journal of Productivity Analysis, 17(3), 249\u2013255.","journal-title":"Journal of Productivity Analysis"},{"key":"4027_CR7","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.cie.2018.08.028","volume":"125","author":"S Ang","year":"2018","unstructured":"Ang, S., Chen, M., & Yang, F. (2018). Group cross-efficiency evaluation in data envelopment analysis: An application to Taiwan hotels. Computers & Industrial Engineering, 125, 190\u2013199.","journal-title":"Computers & Industrial Engineering"},{"issue":"9","key":"4027_CR8","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1287\/mnsc.30.9.1078","volume":"30","author":"RD Banker","year":"1984","unstructured":"Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078\u20131092.","journal-title":"Management Science"},{"issue":"1","key":"4027_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0377-2217(91)90331-O","volume":"52","author":"A Boussofiane","year":"1991","unstructured":"Boussofiane, A., Dyson, R. G., & Thanassoulis, E. (1991). Applied data envelopment analysis. European Journal of Operational Research, 52(1), 1\u201315.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR10","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.knosys.2015.10.023","volume":"92","author":"J Cao","year":"2016","unstructured":"Cao, J., Chen, G., Khoveyni, M., Eslami, R., & Yang, G. (2016). Specification of a performance indicator using the evidential-reasoning approach. Knowledge-Based Systems, 92, 138\u2013150.","journal-title":"Knowledge-Based Systems"},{"key":"4027_CR11","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.cie.2018.04.017","volume":"120","author":"M Carrillo","year":"2018","unstructured":"Carrillo, M., & Jorge, J. M. (2018a). An alternative neutral approach for cross-efficiency evaluation. Computers & Industrial Engineering, 120, 137\u2013145.","journal-title":"Computers & Industrial Engineering"},{"key":"4027_CR12","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.orp.2018.08.005","volume":"5","author":"M Carrillo","year":"2018","unstructured":"Carrillo, M., & Jorge, J. M. (2018b). Integrated approach for computing aggregation weights in cross-efficiency evaluation. Operations Research Perspectives, 5, 256\u2013264.","journal-title":"Operations Research Perspectives"},{"issue":"6","key":"4027_CR13","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/0377-2217(78)90138-8","volume":"2","author":"A Charnes","year":"1978","unstructured":"Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429\u2013444.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4027_CR14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ejor.2019.06.053","volume":"280","author":"L Chen","year":"2020","unstructured":"Chen, L., Huang, Y., Li, M. J., & Wang, Y. M. (2020a). Meta-frontier analysis using cross-efficiency method for performance evaluation. European Journal of Operational Research, 280(1), 219\u2013229.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR15","doi-asserted-by":"crossref","first-page":"102072","DOI":"10.1016\/j.omega.2019.05.008","volume":"96","author":"L Chen","year":"2020","unstructured":"Chen, L., & Wang, Y. M. (2020). DEA target setting approach within the cross efficiency framework. Omega, 96, 102072.","journal-title":"Omega"},{"issue":"1","key":"4027_CR16","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10479-019-03491-w","volume":"288","author":"L Chen","year":"2020","unstructured":"Chen, L., Wang, Y., & Huang, Y. (2020b). Cross-efficiency aggregation method based on prospect consensus process. Annals of Operations Research, 288(1), 115\u2013135.","journal-title":"Annals of Operations Research"},{"issue":"3","key":"4027_CR17","doi-asserted-by":"crossref","first-page":"e12461","DOI":"10.1111\/exsy.12461","volume":"37","author":"L Chen","year":"2020","unstructured":"Chen, L., Wu, F. M., Wang, Y. M., & Li, M. J. (2020c). Analysis of the environmental efficiency in China based on the DEA cross-efficiency approach under different policy objectives. Expert Systems, 37(3), e12461.","journal-title":"Expert Systems"},{"issue":"14","key":"4027_CR18","doi-asserted-by":"crossref","first-page":"10721","DOI":"10.1007\/s00500-019-04576-1","volume":"24","author":"X Chen","year":"2020","unstructured":"Chen, X., Liu, X., Wang, W., & Gong, Z. (2020d). Behavioral DEA model and its application to the efficiency evaluation of manufacturing transformation and upgrading in the Yangtze River Delta. Soft Computing, 24(14), 10721\u201310738.","journal-title":"Soft Computing"},{"issue":"1\u20132","key":"4027_CR19","first-page":"1","volume":"278","author":"Y Chen","year":"2019","unstructured":"Chen, Y., Cook, W. D., & Lim, S. (2019). Preface: DEA and its applications in operations and data analytics. Annals of Operations Research, 278(1\u20132), 1\u20134.","journal-title":"Annals of Operations Research"},{"key":"4027_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/s12351-019-00484-2","author":"I Contreras","year":"2019","unstructured":"Contreras, I., & Hinojosa, M. A. (2019). A note on \u201cThe cross-efficiency in the optimistic\u2013pessimistic framework.\u201d Operational Research. https:\/\/doi.org\/10.1007\/s12351-019-00484-2","journal-title":"Operational Research"},{"issue":"6","key":"4027_CR21","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/j.omega.2009.12.001","volume":"38","author":"WD Cook","year":"2010","unstructured":"Cook, W. D., Liang, L., & Zhu, J. (2010). Measuring performance of two-stage network structures by DEA: A review and future perspective. Omega, 38(6), 423\u2013430.","journal-title":"Omega"},{"issue":"5","key":"4027_CR22","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1080\/01605682.2018.1457482","volume":"70","author":"M Davtalab-Olyaie","year":"2019","unstructured":"Davtalab-Olyaie, M. (2019). A secondary goal in DEA cross-efficiency evaluation: A \u201cone home run is much better than two doubles\u201d criterion. Journal of the Operational Research Society, 70(5), 807\u2013816.","journal-title":"Journal of the Operational Research Society"},{"issue":"3","key":"4027_CR23","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1057\/palgrave.jors.2601253","volume":"53","author":"DK Despotis","year":"2002","unstructured":"Despotis, D. K. (2002). Improving the discriminating power of DEA: Focus on globally efficient units. Journal of the Operational Research Society, 53(3), 314\u2013323.","journal-title":"Journal of the Operational Research Society"},{"issue":"3","key":"4027_CR24","first-page":"205","volume":"33","author":"J Doyle","year":"1995","unstructured":"Doyle, J., & Green, R. (1995). Cross-evaluation in DEA: Improving discrimination among DMUs. INFOR: Information Systems and Operational Research, 33(3), 205\u2013222.","journal-title":"INFOR: Information Systems and Operational Research"},{"issue":"5","key":"4027_CR25","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1057\/jors.1994.84","volume":"45","author":"J Doyle","year":"1994","unstructured":"Doyle, J., & Green, R. (1994). Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the Operational Research Society, 45(5), 567\u2013578.","journal-title":"Journal of the Operational Research Society"},{"issue":"2","key":"4027_CR26","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/j.ejor.2011.10.031","volume":"218","author":"M Falagario","year":"2012","unstructured":"Falagario, M., Sciancalepore, F., Costantino, N., & Pietroforte, R. (2012). Using a DEA-cross efficiency approach in public procurement tenders. European Journal of Operational Research, 218(2), 523\u2013529.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR250","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.cie.2019.07.053","volume":"136","author":"L Fang","year":"2019","unstructured":"Fang, L., & Yang, J. (2019). An integrated ranking approach using cross-efficiency intervals and the cumulative prospect theory. Computers & Industrial Engineering, 136, 556\u2013574.","journal-title":"Computers & Industrial Engineering"},{"issue":"3","key":"4027_CR27","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1257\/jep.14.3.159","volume":"14","author":"E Fehr","year":"2000","unstructured":"Fehr, E., & G\u00e4chter, S. (2000). Fairness and retaliation: The economics of reciprocity. The Journal of Economic Perspectives, 14(3), 159\u2013181.","journal-title":"The Journal of Economic Perspectives"},{"issue":"1","key":"4027_CR28","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1515\/JSSI-2015-0014","volume":"3","author":"R Guo","year":"2015","unstructured":"Guo, R., Dong, Y., Wang, M., & Li, Y. (2015). DEA cross-efficiency evaluation method based on good relationship. Journal of Systems Science and Information, 3(1), 14\u201324.","journal-title":"Journal of Systems Science and Information"},{"issue":"1","key":"4027_CR29","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1051\/ro\/2016023","volume":"51","author":"GR Jahanshahloo","year":"2017","unstructured":"Jahanshahloo, G. R., Sadeghi, J., & Khodabakhshi, M. (2017). Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis. RAIRO-Operations Research, 51(1), 253\u2013260.","journal-title":"RAIRO-Operations Research"},{"key":"4027_CR30","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1016\/j.omega.2018.02.004","volume":"83","author":"C Kao","year":"2019","unstructured":"Kao, C., & Liu, S. T. (2019). Cross efficiency measurement and decomposition in two basic network systems. Omega, 83, 70\u201379.","journal-title":"Omega"},{"key":"4027_CR31","doi-asserted-by":"crossref","first-page":"102192","DOI":"10.1016\/j.omega.2020.102192","volume":"95","author":"C Kao","year":"2020","unstructured":"Kao, C., & Liu, S. T. (2020). A slacks-based measure model for calculating cross efficiency in data envelopment analysis. Omega, 95, 102192.","journal-title":"Omega"},{"issue":"12","key":"4027_CR32","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1016\/j.aml.2012.04.019","volume":"25","author":"M Khodabakhshi","year":"2012","unstructured":"Khodabakhshi, M., & Aryavash, K. (2012). Ranking all units in data envelopment analysis. Applied Mathematics Letters, 25(12), 2066\u20132070.","journal-title":"Applied Mathematics Letters"},{"issue":"2","key":"4027_CR33","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1007\/s12351-016-0243-z","volume":"17","author":"M Khodabakhshi","year":"2017","unstructured":"Khodabakhshi, M., & Aryavash, K. (2017). The cross-efficiency in the optimistic\u2013pessimistic framework. Operational Research, 17(2), 619\u2013632.","journal-title":"Operational Research"},{"issue":"8","key":"4027_CR34","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1080\/01605682.2019.1609892","volume":"71","author":"F Li","year":"2020","unstructured":"Li, F., Emrouznejad, A., Yang, G. L., & Li, Y. (2020a). Carbon emission abatement quota allocation in Chinese manufacturing industries: An integrated cooperative game data envelopment analysis approach. Journal of the Operational Research Society, 71(8), 1259\u20131288.","journal-title":"Journal of the Operational Research Society"},{"issue":"11","key":"4027_CR35","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1080\/01605682.2017.1409867","volume":"69","author":"F Li","year":"2018","unstructured":"Li, F., Liang, L., Li, Y., & Emrouznejad, A. (2018b). An alternative approach to decompose the potential gains from mergers. Journal of the Operational Research Society, 69(11), 1793\u20131802.","journal-title":"Journal of the Operational Research Society"},{"key":"4027_CR36","doi-asserted-by":"publisher","DOI":"10.1080\/01605682.2020.1718561","author":"F Li","year":"2020","unstructured":"Li, F., Yan, Z., Zhu, Q., Yin, M., & Kou, G. (2020b). Allocating a fixed cost across decision making units with explicitly considering efficiency rankings. Journal of the Operational Research Society. https:\/\/doi.org\/10.1080\/01605682.2020.1718561","journal-title":"Journal of the Operational Research Society"},{"key":"4027_CR37","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.eswa.2018.04.009","volume":"106","author":"F Li","year":"2018","unstructured":"Li, F., Zhu, Q., Chen, Z., & Xue, H. (2018b). A balanced data envelopment analysis cross-efficiency evaluation approach. Expert Systems with Applications, 106, 154\u2013168.","journal-title":"Expert Systems with Applications"},{"key":"4027_CR38","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.eswa.2017.12.002","volume":"96","author":"F Li","year":"2018","unstructured":"Li, F., Zhu, Q., & Liang, L. (2018c). Allocating a fixed cost based on a DEA-game cross efficiency approach. Expert Systems with Applications, 96, 196\u2013207.","journal-title":"Expert Systems with Applications"},{"issue":"1\u20132","key":"4027_CR39","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10479-018-2819-x","volume":"274","author":"F Li","year":"2019","unstructured":"Li, F., Zhu, Q., & Liang, L. (2019a). A new data envelopment analysis based approach for fixed cost allocation. Annals of Operations Research, 274(1\u20132), 347\u2013372.","journal-title":"Annals of Operations Research"},{"issue":"4","key":"4027_CR40","doi-asserted-by":"crossref","first-page":"e12334","DOI":"10.1111\/exsy.12334","volume":"37","author":"X Li","year":"2020","unstructured":"Li, X., Li, F., Zhao, N., & Zhu, Q. (2020c). Measuring environmental sustainability performance of freight transportation seaports in China: A data envelopment analysis approach based on the closest targets. Expert Systems, 37(4), e12334.","journal-title":"Expert Systems"},{"issue":"1\u20132","key":"4027_CR41","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s10479-018-2860-9","volume":"274","author":"Y Li","year":"2019","unstructured":"Li, Y., Li, F., Emrouznejad, A., Liang, L., & Xie, Q. (2019b). Allocating the fixed cost: An approach based on data envelopment analysis and cooperative game. Annals of Operations Research, 274(1\u20132), 373\u2013394.","journal-title":"Annals of Operations Research"},{"key":"4027_CR42","doi-asserted-by":"crossref","first-page":"102123","DOI":"10.1016\/j.omega.2019.102123","volume":"98","author":"Y Li","year":"2021","unstructured":"Li, Y., Wang, L., & Li, F. (2021). A data-driven prediction approach for sports team performance and its application to National Basketball Association. Omega, 98, 102123.","journal-title":"Omega"},{"issue":"2","key":"4027_CR43","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1016\/j.ijpe.2007.12.006","volume":"113","author":"L Liang","year":"2008","unstructured":"Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008a). Alternative secondary goals in DEA cross-efficiency evaluation. International Journal of Production Economics, 113(2), 1025\u20131030.","journal-title":"International Journal of Production Economics"},{"issue":"5","key":"4027_CR44","doi-asserted-by":"crossref","first-page":"1278","DOI":"10.1287\/opre.1070.0487","volume":"56","author":"L Liang","year":"2008","unstructured":"Liang, L., Wu, J., Cook, W. D., & Zhu, J. (2008b). The DEA game cross-efficiency model and its Nash equilibrium. Operations Research, 56(5), 1278\u20131288.","journal-title":"Operations Research"},{"issue":"1","key":"4027_CR45","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.ejor.2013.12.002","volume":"236","author":"S Lim","year":"2014","unstructured":"Lim, S., Oh, K. W., & Zhu, J. (2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236(1), 361\u2013368.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4027_CR46","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1057\/jors.2014.13","volume":"66","author":"S Lim","year":"2015","unstructured":"Lim, S., & Zhu, J. (2015). DEA cross-efficiency evaluation under variable returns to scale. Journal of the Operational Research Society, 66(3), 476\u2013487.","journal-title":"Journal of the Operational Research Society"},{"issue":"3","key":"4027_CR47","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1080\/01605682.2019.1567652","volume":"71","author":"R Lin","year":"2020","unstructured":"Lin, R. (2020). Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach. Journal of the Operational Research Society, 71(3), 505\u2013516.","journal-title":"Journal of the Operational Research Society"},{"issue":"1","key":"4027_CR48","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.ejor.2018.07.046","volume":"273","author":"HH Liu","year":"2019","unstructured":"Liu, H. H., Song, Y. Y., & Yang, G. L. (2019). Cross-efficiency evaluation in data envelopment analysis based on prospect theory. European Journal of Operational Research, 273(1), 364\u2013375.","journal-title":"European Journal of Operational Research"},{"issue":"5","key":"4027_CR50","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.omega.2012.11.004","volume":"41","author":"JS Liu","year":"2013","unstructured":"Liu, J. S., Lu, L. Y., Lu, W. M., & Lin, B. J. (2013). A survey of DEA applications. Omega, 41(5), 893\u2013902.","journal-title":"Omega"},{"key":"4027_CR51","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10479-017-2562-8","volume":"261","author":"S Liu","year":"2018","unstructured":"Liu, S. (2018). A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio. Annals of Operations Research, 261, 207\u2013232.","journal-title":"Annals of Operations Research"},{"issue":"1\u20132","key":"4027_CR52","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s10479-017-2524-1","volume":"259","author":"W Liu","year":"2017","unstructured":"Liu, W., Wang, Y. M., & Lv, S. (2017). An aggressive game cross-efficiency evaluation in data envelopment analysis. Annals of Operations Research, 259(1\u20132), 241\u2013258.","journal-title":"Annals of Operations Research"},{"issue":"12","key":"4027_CR53","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1002\/int.21685","volume":"29","author":"T Le\u00f3n","year":"2014","unstructured":"Le\u00f3n, T., Ram\u00f3n, N., Ruiz, J. L., & Sirvent, I. (2014). Using induced ordered weighted averaging operators for aggregation in cross-efficiency evaluations. International Journal of Intelligent Systems, 29(12), 1100\u20131116.","journal-title":"International Journal of Intelligent Systems"},{"issue":"2","key":"4027_CR54","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1504\/IJOR.2014.058953","volume":"19","author":"R Maddahi","year":"2014","unstructured":"Maddahi, R., Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., & Ebrahimnejad, A. (2014). Optimising proportional weights as a secondary goal in DEA cross-efficiency evaluation. International Journal of Operational Research, 19(2), 234\u2013245.","journal-title":"International Journal of Operational Research"},{"key":"4027_CR55","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s10479-018-2803-5","volume":"274","author":"H Omrani","year":"2019","unstructured":"Omrani, H., Shafaat, K., & Alizadeh, A. (2019). Integrated data envelopment analysis and cooperative game for evaluating energy efficiency of transportation sector: A case of Iran. Annals of Operations Research, 274, 471\u2013499.","journal-title":"Annals of Operations Research"},{"issue":"5","key":"4027_CR56","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1002\/int.22082","volume":"34","author":"A Oukil","year":"2019","unstructured":"Oukil, A. (2019). Embedding OWA under preference ranking for DEA cross-efficiency aggregation: Issues and procedures. International Journal of Intelligent Systems, 34(5), 947\u2013965.","journal-title":"International Journal of Intelligent Systems"},{"key":"4027_CR57","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.eswa.2019.01.067","volume":"125","author":"HH \u00d6rkc\u00fc","year":"2019","unstructured":"\u00d6rkc\u00fc, H. H., \u00d6zsoy, V. S., \u00d6rkc\u00fc, M., & Bal, H. (2019). A neutral cross efficiency approach for basic two stage production systems. Expert Systems with Applications, 125, 333\u2013344.","journal-title":"Expert Systems with Applications"},{"issue":"4","key":"4027_CR58","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1051\/ro\/2019052","volume":"54","author":"M \u00d6rkc\u00fc","year":"2020","unstructured":"\u00d6rkc\u00fc, M., \u00d6zsoy, V. S., & \u00d6rkc\u00fc, H. H. (2020). An optimistic-pessimistic DEA model based on game cross efficiency approach. RAIRO-Operations Research, 54(4), 1215\u20131230.","journal-title":"RAIRO-Operations Research"},{"issue":"2","key":"4027_CR59","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.ejor.2020.04.004","volume":"287","author":"H Pun","year":"2020","unstructured":"Pun, H., Chen, J., & Li, W. (2020). Channel strategy for manufacturers in the presence of service freeriders. European Journal of Operational Research, 287(2), 460\u2013479.","journal-title":"European Journal of Operational Research"},{"issue":"3","key":"4027_CR60","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1016\/j.ejor.2012.06.011","volume":"223","author":"JL Ruiz","year":"2012","unstructured":"Ruiz, J. L., & Sirvent, I. (2012). On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations. European Journal of Operational Research, 223(3), 732\u2013738.","journal-title":"European Journal of Operational Research"},{"issue":"32","key":"4027_CR61","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1002\/ev.1441","volume":"1986","author":"TR Sexton","year":"1986","unstructured":"Sexton, T. R., Silkman, R. H., & Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation, 1986(32), 73\u2013105.","journal-title":"New Directions for Program Evaluation"},{"issue":"2","key":"4027_CR62","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1080\/17457300.2018.1535510","volume":"26","author":"SR Seyedalizadeh Ganji","year":"2019","unstructured":"Seyedalizadeh Ganji, S. R., & Rassafi, A. A. (2019a). Measuring the road safety performance of Iranian provinces: A double-frontier DEA model and evidential reasoning approach. International Journal of Injury Control and Safety Promotion, 26(2), 156\u2013169.","journal-title":"International Journal of Injury Control and Safety Promotion"},{"issue":"2","key":"4027_CR63","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1007\/s12205-018-0401-3","volume":"23","author":"SR Seyedalizadeh Ganji","year":"2019","unstructured":"Seyedalizadeh Ganji, S. R., & Rassafi, A. A. (2019b). Road safety evaluation using a novel cross efficiency method based on double frontiers DEA and evidential reasoning approach. KSCE Journal of Civil Engineering, 23(2), 850\u2013865.","journal-title":"KSCE Journal of Civil Engineering"},{"key":"4027_CR64","doi-asserted-by":"crossref","first-page":"100706","DOI":"10.1016\/j.seps.2019.04.003","volume":"69","author":"SR Seyedalizadeh Ganji","year":"2020","unstructured":"Seyedalizadeh Ganji, S. R., Rassafi, A. A., & Bandari, S. J. (2020). Application of evidential reasoning approach and OWA operator weights in road safety evaluation considering the best and worst practice frontiers. Socio-Economic Planning Sciences, 69, 100706.","journal-title":"Socio-Economic Planning Sciences"},{"key":"4027_CR65","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1016\/j.measurement.2018.12.098","volume":"136","author":"SR Seyedalizadeh Ganji","year":"2019","unstructured":"Seyedalizadeh Ganji, S. R., Rassafi, A. A., & Xu, D. L. (2019). A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance. Measurement, 136, 668\u2013688.","journal-title":"Measurement"},{"issue":"3","key":"4027_CR66","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1016\/j.ejor.2020.08.055","volume":"290","author":"H Shi","year":"2021","unstructured":"Shi, H., Chen, S., Chen, L., & Wang, Y. (2021). A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior. European Journal of Operational Research, 290(3), 1098\u20131110.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR67","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.cie.2019.04.035","volume":"132","author":"H Shi","year":"2019","unstructured":"Shi, H., Wang, Y., & Chen, L. (2019). Neutral cross-efficiency evaluation regarding an ideal frontier and anti-ideal frontier as evaluation criteria. Computers & Industrial Engineering, 132, 385\u2013394.","journal-title":"Computers & Industrial Engineering"},{"issue":"2","key":"4027_CR68","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1111\/itor.12361","volume":"25","author":"L Song","year":"2018","unstructured":"Song, L., & Liu, F. (2018). An improvement in DEA cross-efficiency aggregation based on the Shannon entropy. International Transactions in Operational Research, 25(2), 705\u2013714.","journal-title":"International Transactions in Operational Research"},{"key":"4027_CR69","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.cie.2017.07.023","volume":"112","author":"M Song","year":"2017","unstructured":"Song, M., Zhu, Q., Peng, J., & Gonzalez, E. D. S. (2017). Improving the evaluation of cross efficiencies: A method based on Shannon entropy weight. Computers & Industrial Engineering, 112, 99\u2013106.","journal-title":"Computers & Industrial Engineering"},{"issue":"4","key":"4027_CR70","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1080\/19388160.2013.841500","volume":"9","author":"H Tsai","year":"2013","unstructured":"Tsai, H., Wu, J., & Sun, J. (2013). Cross-efficiency evaluation of Taiwan\u2019s international tourist hotels under competitive and cooperative relationships. Journal of China Tourism Research, 9(4), 413\u2013428.","journal-title":"Journal of China Tourism Research"},{"key":"4027_CR71","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2020.108020","author":"F Wang","year":"2021","unstructured":"Wang, F., Diabat, A., & Wu, L. (2021). Supply chain coordination with competing suppliers under price-sensitive stochastic demand. International Journal of Production Economics. https:\/\/doi.org\/10.1016\/j.ijpe.2020.108020","journal-title":"International Journal of Production Economics"},{"issue":"10","key":"4027_CR72","doi-asserted-by":"crossref","first-page":"358","DOI":"10.3390\/e18100358","volume":"18","author":"L Wang","year":"2016","unstructured":"Wang, L., Li, L., & Hong, N. (2016). Entropy cross-efficiency model for decision making units with interval data. Entropy, 18(10), 358.","journal-title":"Entropy"},{"issue":"1","key":"4027_CR73","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.ijpe.2010.07.032","volume":"128","author":"YM Wang","year":"2010","unstructured":"Wang, Y. M., & Chin, K. S. (2010). Some alternative models for DEA cross-efficiency evaluation. International Journal of Production Economics, 128(1), 332\u2013338.","journal-title":"International Journal of Production Economics"},{"issue":"5","key":"4027_CR74","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/j.omega.2010.10.007","volume":"39","author":"YM Wang","year":"2011","unstructured":"Wang, Y. M., & Chin, K. S. (2011). The use of OWA operator weights for cross-efficiency aggregation. Omega, 39(5), 493\u2013503.","journal-title":"Omega"},{"issue":"3","key":"4027_CR75","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.cie.2011.04.004","volume":"61","author":"YM Wang","year":"2011","unstructured":"Wang, Y. M., Chin, K. S., & Jiang, P. (2011a). Weight determination in the cross-efficiency evaluation. Computers & Industrial Engineering, 61(3), 497\u2013502.","journal-title":"Computers & Industrial Engineering"},{"key":"4027_CR76","doi-asserted-by":"crossref","first-page":"10312","DOI":"10.1016\/j.eswa.2011.02.116","volume":"38","author":"YM Wang","year":"2011","unstructured":"Wang, Y. M., Chin, K. S., & Luo, Y. (2011b). Cross-efficiency evaluation based on ideal and anti-ideal decision making units. Expert Systems with Applications, 38, 10312\u201310319.","journal-title":"Expert Systems with Applications"},{"issue":"1","key":"4027_CR77","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1057\/jors.2012.43","volume":"64","author":"YM Wang","year":"2013","unstructured":"Wang, Y. M., & Wang, S. (2013). Approaches to determining the relative importance weights for cross-efficiency aggregation in data envelopment analysis. Journal of the Operational Research Society, 64(1), 60\u201369.","journal-title":"Journal of the Operational Research Society"},{"issue":"2","key":"4027_CR78","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.ejor.2015.07.042","volume":"248","author":"J Wu","year":"2016","unstructured":"Wu, J., Chu, J., Sun, J., & Zhu, Q. (2016a). DEA cross-efficiency evaluation based on Pareto improvement. European Journal of Operational Research, 248(2), 571\u2013579.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR79","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.cie.2015.12.019","volume":"93","author":"J Wu","year":"2016","unstructured":"Wu, J., Chu, J., Sun, J., Zhu, Q., & Liang, L. (2016b). Extended secondary goal models for weights selection in DEA cross-efficiency evaluation. Computers & Industrial Engineering, 93, 143\u2013151.","journal-title":"Computers & Industrial Engineering"},{"issue":"20","key":"4027_CR80","doi-asserted-by":"crossref","first-page":"5990","DOI":"10.1080\/00207543.2016.1148278","volume":"54","author":"J Wu","year":"2016","unstructured":"Wu, J., Chu, J., Zhu, Q., Yin, P., & Liang, L. (2016c). DEA cross-efficiency evaluation based on satisfaction degree: An application to technology selection. International Journal of Production Research, 54(20), 5990\u20136007.","journal-title":"International Journal of Production Research"},{"issue":"4","key":"4027_CR81","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1016\/j.omega.2008.07.001","volume":"37","author":"J Wu","year":"2009","unstructured":"Wu, J., Liang, L., & Chen, Y. (2009a). DEA game cross-efficiency approach to Olympic rankings. Omega, 37(4), 909\u2013918.","journal-title":"Omega"},{"issue":"1","key":"4027_CR82","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1016\/j.eswa.2007.10.006","volume":"36","author":"J Wu","year":"2009","unstructured":"Wu, J., Liang, L., & Yang, F. (2009b). Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game. Expert Systems with Applications, 36(1), 872\u2013876.","journal-title":"Expert Systems with Applications"},{"issue":"23","key":"4027_CR83","doi-asserted-by":"crossref","first-page":"6726","DOI":"10.1080\/00207543.2011.618150","volume":"50","author":"J Wu","year":"2012","unstructured":"Wu, J., Sun, J., & Liang, L. (2012). DEA cross-efficiency aggregation method based upon Shannon entropy. International Journal of Production Research, 50(23), 6726\u20136736.","journal-title":"International Journal of Production Research"},{"issue":"5","key":"4027_CR84","doi-asserted-by":"crossref","first-page":"5162","DOI":"10.1016\/j.eswa.2010.10.046","volume":"38","author":"J Wu","year":"2011","unstructured":"Wu, J., Sun, J., Liang, L., & Zha, Y. (2011). Determination of weights for ultimate cross efficiency using Shannon entropy. Expert Systems with Applications, 38(5), 5162\u20135165.","journal-title":"Expert Systems with Applications"},{"issue":"4","key":"4027_CR85","doi-asserted-by":"crossref","first-page":"e12466","DOI":"10.1111\/exsy.12466","volume":"37","author":"X Wu","year":"2020","unstructured":"Wu, X., Chen, Y., Zhao, P., Guo, J., & Ma, Z. (2020). Study of haze emission efficiency based on new co-opetition data envelopment analysis. Expert Systems, 37(4), e12466.","journal-title":"Expert Systems"},{"issue":"2","key":"4027_CR86","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/j.ejor.2012.07.001","volume":"223","author":"F Yang","year":"2012","unstructured":"Yang, F., Ang, S., Xia, Q., & Yang, C. (2012). Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis. European Journal of Operational Research, 223(2), 483\u2013488.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"4027_CR87","first-page":"92","volume":"31","author":"F Yang","year":"2011","unstructured":"Yang, F., Xia, Q., & Liang, L. (2011). DEA cross efficiency evaluation method for competitive and cooperative decision making units. Systems Engineering-Theory & Practice, 31(1), 92\u201398.","journal-title":"Systems Engineering-Theory & Practice"},{"issue":"2","key":"4027_CR88","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.ejor.2013.05.017","volume":"231","author":"GL Yang","year":"2013","unstructured":"Yang, G. L., Yang, J. B., Liu, W. B., & Li, X. X. (2013). Cross-efficiency aggregation in DEA models using the evidential-reasoning approach. European Journal of Operational Research, 231(2), 393\u2013404.","journal-title":"European Journal of Operational Research"},{"key":"4027_CR89","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.jclepro.2018.10.271","volume":"209","author":"Z Yang","year":"2019","unstructured":"Yang, Z., & Wei, X. (2019). The measurement and influences of China\u2019s urban total factor energy efficiency under environmental pollution: Based on the game cross-efficiency DEA. Journal of Cleaner Production, 209, 439\u2013450.","journal-title":"Journal of Cleaner Production"},{"issue":"1\u20132","key":"4027_CR90","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10479-017-2669-y","volume":"278","author":"Y Yu","year":"2019","unstructured":"Yu, Y., Zhu, W., & Zhang, Q. (2019). DEA cross-efficiency evaluation and ranking method based on interval data. Annals of Operations Research, 278(1\u20132), 159\u2013175.","journal-title":"Annals of Operations Research"},{"issue":"2","key":"4027_CR91","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s10479-016-2165-9","volume":"258","author":"Y Zhang","year":"2017","unstructured":"Zhang, Y., Li, J., & Gou, Q. (2017). An allocation game model with reciprocal behavior and its applications in supply chain pricing decisions. Annals of Operations Research, 258(2), 347\u2013368.","journal-title":"Annals of Operations Research"},{"key":"4027_CR92","doi-asserted-by":"crossref","first-page":"106926","DOI":"10.1016\/j.cie.2020.106926","volume":"151","author":"Q Zhu","year":"2021","unstructured":"Zhu, Q., Li, F., Wu, J., & Sun, J. (2021a). Cross-efficiency evaluation in data envelopment analysis based on the perspective of fairness utility. Computers & Industrial Engineering, 151, 106926.","journal-title":"Computers & Industrial Engineering"},{"key":"4027_CR93","doi-asserted-by":"crossref","first-page":"107235","DOI":"10.1016\/j.ecolind.2020.107235","volume":"122","author":"Q Zhu","year":"2021","unstructured":"Zhu, Q., Li, X., Li, F., Wu, J., & Sun, J. (2021b). Analyzing the sustainability of China\u2019s industrial sectors: A data-driven approach with total energy consumption constraint. Ecological Indicators, 122, 107235.","journal-title":"Ecological Indicators"},{"key":"4027_CR94","doi-asserted-by":"crossref","first-page":"104817","DOI":"10.1016\/j.eneco.2020.104817","volume":"89","author":"Q Zhu","year":"2020","unstructured":"Zhu, Q., Li, X., Li, F., Wu, J., & Zhou, D. (2020). Energy and environmental efficiency of China\u2019s transportation sectors under the constraints of energy consumption and environmental pollutions. Energy Economics, 89, 104817.","journal-title":"Energy Economics"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04027-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-021-04027-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-021-04027-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T19:44:34Z","timestamp":1698867874000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-021-04027-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,7]]},"references-count":94,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["4027"],"URL":"https:\/\/doi.org\/10.1007\/s10479-021-04027-x","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,7]]},"assertion":[{"value":"3 March 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}