{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:52:41Z","timestamp":1777704761043,"version":"3.51.4"},"reference-count":37,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,1,4]],"date-time":"2018-01-04T00:00:00Z","timestamp":1515024000000},"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":[[2019,2,16]]},"abstract":"<jats:p>In the cross-efficiency model, when the decision making unit (DMU) self-evaluation efficiency value is optimal, the sets of input and output weights exhibit non-uniqueness, and the choice among alternative optimal solutions results in different peer- evaluation values, consequently leading to different cross-efficiency scores and rankings. In addition, the interval value constitutes the cross-efficiency value, which increases the uncertainty of the decision- making due to the information fuzziness. To solve this problem, a group decision-making method for cross-efficiency is proposed on the basis of hesitant fuzzy sets (HFSs). This method selects five optimal solutions. Moreover, given that the attitudes of decision-makers range from pessimistic to optimistic, this method introduces HFSs to the cross-efficiency matrix, and obtains the multi-objective optimization method to rank the alternatives based on the relative closeness degree. Finally, a classical numerical example is provided to illustrate the potential applications of the proposed method and its effectiveness in ranking DMUs.<\/jats:p>","DOI":"10.3233\/jifs-181477","type":"journal-article","created":{"date-parts":[[2019,1,4]],"date-time":"2019-01-04T10:35:00Z","timestamp":1546598100000},"page":"371-383","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["A novel cross-efficiency evaluation method under hesitant fuzzy environment"],"prefix":"10.1177","volume":"36","author":[{"given":"Jianping","family":"Fan","sequence":"first","affiliation":[{"name":"School of Economics and Management, Shanxi University, Taiyuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinrong","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Shanxi University, Taiyuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Shanxi University, Taiyuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Shanxi University, Taiyuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meiqin","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Shanxi University, Taiyuan, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,1,4]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(78)90138-8"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11430-014-4977-2"},{"issue":"10","key":"e_1_3_1_4_2","article-title":"A Novel Comparison of Probabilistic Hesitant Fuzzy Elements in Multi-Criteria Decision Making","volume":"177","author":"Song C.Y.","year":"2018","unstructured":"SongC.Y. XuZ.S and ZhaoH., A Novel Comparison of Probabilistic Hesitant Fuzzy Elements in Multi-Criteria Decision Making, Symmetry 177(10) (2018).","journal-title":"Symmetry"},{"issue":"1","key":"e_1_3_1_5_2","first-page":"92","article-title":"DEA cross efficiency evaluation method for competitive and cooperative decision making units","volume":"31","author":"Yang F.","year":"2011","unstructured":"YangF., XiaQ. and LiangL., DEA cross efficiency evaluation method for competitive and cooperative decision making units, Systems Engineering\u2014Theory & Practice 31(1) (2011), 92\u201398.","journal-title":"Systems Engineering\u2014Theory & Practice"},{"issue":"12","key":"e_1_3_1_6_2","first-page":"2237","article-title":"Ranking decision making units based on the weight set","volume":"30","author":"Bi G.","year":"2010","unstructured":"BiG., TaoC., LiangL. et al., Ranking decision making units based on the weight set, Systems Engineering\u2014Theory & Practice 30(12) (2010), 2237\u20132243.","journal-title":"Systems Engineering\u2014Theory & Practice"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.05.017"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-013-9162-0"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.1994.84"},{"issue":"10","key":"e_1_3_1_10_2","first-page":"1890","article-title":"Ranking approach of interval cross efficiency considering all weighting schemes","volume":"30","author":"Wu J.","year":"2008","unstructured":"WuJ. and LiangL., Ranking approach of interval cross efficiency considering all weighting schemes, Systems Engineering And Electronics 30(10) (2008), 1890\u20131894.","journal-title":"Systems Engineering And Electronics"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2015.07.042"},{"issue":"5","key":"e_1_3_1_12_2","first-page":"1293","article-title":"Dealing with interval DEA based on error propagation and entropy","volume":"35","author":"Fan J.P.","year":"2015","unstructured":"FanJ.P., YueW.Z. and WuM.Q., Dealing with interval DEA based on error propagation and entropy, Systems Engineering\u2014Theory & Practice 35(5) (2015), 1293\u20131303.","journal-title":"Systems Engineering\u2014Theory & Practice"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"issue":"2","key":"e_1_3_1_14_2","first-page":"19","article-title":"DEA Method for Three-Parameter Interval Cross Efficiency","volume":"13","author":"Wang K.","year":"2010","unstructured":"WangK. and WeiF.J., DEA Method for Three-Parameter Interval Cross Efficiency, Industrial Engineering Journal 13(2) (2010), 19\u201322.","journal-title":"Industrial Engineering Journal"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0487"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2010.05.035"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.09.002"},{"issue":"4","key":"e_1_3_1_19_2","first-page":"109","article-title":"The Constructing and Ranking of Interval Efficiency of DMUs in CCR Model","volume":"26","author":"Wang M.Q.","year":"2008","unstructured":"WangM.Q. and LiangL., The Constructing and Ranking of Interval Efficiency of DMUs in CCR Model, Systems Engineering 26(4) (2008), 109\u2013112.","journal-title":"Systems Engineering"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.2013.90"},{"key":"e_1_3_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jairtraman.2015.02.008"},{"key":"e_1_3_1_22_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2015\/710264","article-title":"Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix","author":"Hou Q.","year":"2015","unstructured":"HouQ. and ZhouX., Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix, Mathematical Problems in Engineering 2015, 1\u20137. doi: https:\/\/doi.org\/10.1155\/2015\/710264.","journal-title":"Mathematical Problems in Engineering"},{"issue":"11","key":"e_1_3_1_23_2","first-page":"62","article-title":"An Adaptive Group Evaluating Method for Cross-Efficiencies of Decision Making Units","volume":"22","author":"Zhang Q.P.","year":"2014","unstructured":"ZhangQ.P. LiuY.Z and JiangY.C., An Adaptive Group Evaluating Method for Cross-Efficiencies of Decision Making Units, Chinese Journal of Management Science 22(11) (2014), 62\u201371.","journal-title":"Chinese Journal of Management Science"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.12.002"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2011.11.010"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2004.11.010"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(01)00055-8"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1002\/ev.1441"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZY.2009.5276884"},{"issue":"6","key":"e_1_3_1_30_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V.","year":"2010","unstructured":"TorraV., Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6) (2010), 529\u2013539.","journal-title":"International Journal of Intelligent Systems"},{"key":"e_1_3_1_31_2","first-page":"297","article-title":"Hesitant fuzzy multiple attribute decision making method based on optimization of attribute weights","volume":"2","author":"Liu X.","year":"2016","unstructured":"LiuX., ZhuJ., ZhangS. et al., Hesitant fuzzy multiple attribute decision making method based on optimization of attribute weights, Control and Decision 2 (2016), 297\u2013302.","journal-title":"Control and Decision"},{"key":"e_1_3_1_32_2","first-page":"172","article-title":"Economic Benefits Evaluation of Urban Public Infrastructure Based on the DEA Cross-Efficiency Method","author":"Sun Y.","year":"2015","unstructured":"SunY., WangK.Y. and YaoX.D., Economic Benefits Evaluation of Urban Public Infrastructure Based on the DEA Cross-Efficiency Method, China Soft Science 2015, 172\u2013183.","journal-title":"China Soft Science"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2010.10.007"},{"key":"e_1_3_1_34_2","doi-asserted-by":"publisher","DOI":"10.1057\/jors.2012.43"},{"key":"e_1_3_1_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2009.10.024"},{"issue":"1","key":"e_1_3_1_36_2","first-page":"121","article-title":"Research the Resource Allocation Problem in Stochastic Weighted Cross Efficiency","volume":"23","author":"Cui Y.Q.","year":"2015","unstructured":"CuiY.Q., ZhangX., LuX. et al., Research the Resource Allocation Problem in Stochastic Weighted Cross Efficiency, Chinese Journal of Management Science 23(1) (2015), 121\u2013127.","journal-title":"Chinese Journal of Management Science"},{"key":"e_1_3_1_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2015.09.018"},{"key":"e_1_3_1_38_2","first-page":"177","article-title":"Cross Efficiency Evaluation Method Based on Maximizing Deviations","volume":"6","author":"Huang Z.S.","year":"2012","unstructured":"HuangZ.S., HuP. and NieJ.J., Cross Efficiency Evaluation Method Based on Maximizing Deviations, Operations Research and Management Science 6 (2012), 177\u2013181.","journal-title":"Operations Research and Management Science"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181477","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-181477","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-181477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:57Z","timestamp":1777455717000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-181477"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,4]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,2,16]]}},"alternative-id":["10.3233\/JIFS-181477"],"URL":"https:\/\/doi.org\/10.3233\/jifs-181477","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,4]]}}}