{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T03:25:30Z","timestamp":1774581930464,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T00:00:00Z","timestamp":1631836800000},"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":["71771140"],"award-info":[{"award-number":["71771140"]}],"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":["71471172"],"award-info":[{"award-number":["71471172"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010040","name":"Taishan Scholar Project of Shandong Province","doi-asserted-by":"publisher","award":["ts20151104"],"award-info":[{"award-number":["ts20151104"]}],"id":[{"id":"10.13039\/501100010040","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018563","name":"Social Science Planning Project of Shandong Province","doi-asserted-by":"crossref","award":["20CSDJ23"],"award-info":[{"award-number":["20CSDJ23"]}],"id":[{"id":"10.13039\/501100018563","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2020QG002"],"award-info":[{"award-number":["ZR2020QG002"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s40815-021-01161-3","type":"journal-article","created":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T05:04:22Z","timestamp":1631855062000},"page":"552-573","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Probabilistic Linguistic Z Number Decision-Making Method for Multiple Attribute Group Decision-Making Problems with Heterogeneous Relationships and Incomplete Probability Information"],"prefix":"10.1007","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8820-4427","authenticated-orcid":false,"given":"Fei","family":"Teng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lili","family":"Rong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peide","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,17]]},"reference":[{"key":"1161_CR1","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/j.ins.2013.08.054","volume":"261","author":"TY Chen","year":"2014","unstructured":"Chen, T.Y.: Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis. Inf. Sci. 261, 149\u2013169 (2014)","journal-title":"Inf. Sci."},{"key":"1161_CR2","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1214\/aoms\/1177698950","volume":"38","author":"A Dempster","year":"1967","unstructured":"Dempster, A.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38, 325\u2013339 (1967)","journal-title":"Ann. Math. Stat."},{"key":"1161_CR3","first-page":"1631869","volume":"2020","author":"XF Ding","year":"2020","unstructured":"Ding, X.F., Zhu, L.X., Lu, M.S., et al.: A novel linguistic Z-number QUALIFLEX method and its application to large group emergency decision making. Sci. Program. 2020, 1631869 (2020)","journal-title":"Sci. Program."},{"issue":"1","key":"1161_CR4","doi-asserted-by":"publisher","first-page":"719","DOI":"10.3233\/JIFS-172112","volume":"36","author":"X Feng","year":"2019","unstructured":"Feng, X., Liu, Q., Wei, C.: Probabilistic linguistic QUALIFLEX approach with possibility degree comparison. J. Intell. Fuzzy Syst. 36(1), 719\u2013730 (2019)","journal-title":"J. Intell. Fuzzy Syst."},{"issue":"2","key":"1161_CR5","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/S0165-0114(97)00168-1","volume":"92","author":"M Grabisch","year":"1997","unstructured":"Grabisch, M.: K-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92(2), 167\u2013189 (1997)","journal-title":"Fuzzy Sets Syst."},{"key":"1161_CR6","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2019.2955916","author":"J Huang","year":"2019","unstructured":"Huang, J., Xu, D.H., Liu, H.C., et al.: A new model for failure mode and effect analysis integrating linguistic Z-numbers and projection method. IEEE Trans. Fuzzy Syst. (2019). https:\/\/doi.org\/10.1109\/TFUZZ.2019.2955916","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1161_CR7","doi-asserted-by":"publisher","first-page":"105900","DOI":"10.1016\/j.asoc.2019.105900","volume":"86","author":"S Jiang","year":"2020","unstructured":"Jiang, S., Shi, H., Lin, W., et al.: A large group linguistic Z-DEMATEL approach for identifying key performance indicators in hospital performance management. Appl. Soft Comput. 86, 105900 (2020)","journal-title":"Appl. Soft Comput."},{"key":"1161_CR8","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2019.2940424","author":"A Labella","year":"2019","unstructured":"Labella, A., Rodriguez, R.M., Martinez, L.: Computing with comparative linguistic expressions and symbolic translation for decision making: ELICIT information. IEEE Trans. Fuzzy Syst. (2019). https:\/\/doi.org\/10.1109\/TFUZZ.2019.2940424","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"12","key":"1161_CR9","doi-asserted-by":"publisher","first-page":"1172","DOI":"10.1002\/int.21624","volume":"28","author":"F Meng","year":"2013","unstructured":"Meng, F., Tang, J.: Interval-valued intuitionistic fuzzy multiattribute group decision making based on cross entropy measure and Choquet integral. Int. J. Intell. Syst. 28(12), 1172\u20131195 (2013)","journal-title":"Int. J. Intell. Syst."},{"key":"1161_CR10","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.ins.2016.06.021","volume":"369","author":"Q Pang","year":"2016","unstructured":"Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128\u2013143 (2016)","journal-title":"Inf. Sci."},{"key":"1161_CR11","doi-asserted-by":"publisher","first-page":"2187","DOI":"10.1007\/s12652-019-01251-z","volume":"11","author":"D Qiao","year":"2020","unstructured":"Qiao, D., Shen, K., Wang, J., et al.: Multi-criteria PROMETHEE method based on possibility degree with Z-numbers under uncertain linguistic environment. J. Ambient. Intell. Humaniz. Comput. 11, 2187\u20132201 (2020)","journal-title":"J. Ambient. Intell. Humaniz. Comput."},{"key":"1161_CR12","doi-asserted-by":"publisher","first-page":"106517","DOI":"10.1016\/j.cie.2020.106517","volume":"145","author":"Z Ren","year":"2020","unstructured":"Ren, Z., Liao, H., Liu, Y.: Generalized Z-numbers with hesitant fuzzy linguistic information and its application to medicine selection for the patients with mild symptoms of the COVID-19. Comput. Ind. Eng. 145, 106517 (2020)","journal-title":"Comput. Ind. Eng."},{"issue":"1","key":"1161_CR13","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1109\/TFUZZ.2011.2170076","volume":"20","author":"RM Rodriguez","year":"2011","unstructured":"Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20(1), 109\u2013119 (2011)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1161_CR14","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/j.ins.2019.01.006","volume":"483","author":"H Seiti","year":"2019","unstructured":"Seiti, H., Hafezalkotob, A., Mart\u00ednez, L.: R-numbers, a new risk modeling associated with fuzzy numbers and its application to decision making. Inf. Sci. 483, 206\u2013231 (2019)","journal-title":"Inf. Sci."},{"key":"1161_CR15","doi-asserted-by":"publisher","DOI":"10.1515\/9780691214696","volume-title":"A Mathematical Theory of Evidence","author":"G Shafer","year":"1976","unstructured":"Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)"},{"key":"1161_CR16","unstructured":"Sugeno, M.: Theory of Fuzzy Integral and its Application (Ph.D. Dissertation), Tokyo Institute of Technology, Tokyo, Japan (1974)"},{"key":"1161_CR17","doi-asserted-by":"crossref","unstructured":"Tang, G., Chiclana, F., Lin, X.C., et al.: Interval type-2 fuzzy multi-attribute decision-making approaches for evaluating the service quality of Chinese commercial banks. Knowl. Based Syst. 193 (2020)","DOI":"10.1016\/j.knosys.2019.105438"},{"key":"1161_CR18","doi-asserted-by":"publisher","first-page":"106971","DOI":"10.1016\/j.cie.2020.106971","volume":"151","author":"F Teng","year":"2020","unstructured":"Teng, F., Liu, P.: A large group decision-making method based on a generalized Shapley probabilistic linguistic Choquet average operator and the TODIM method. Comput. Ind. Eng. 151, 106971 (2020)","journal-title":"Comput. Ind. Eng."},{"key":"1161_CR19","doi-asserted-by":"publisher","first-page":"98742","DOI":"10.1109\/ACCESS.2020.2994508","volume":"8","author":"AH Mahmoodi","year":"2020","unstructured":"Mahmoodi, A.H., Sadjadi, S.J., Sadi-Nezhad, S., et al.: Linguistic Z-number Bonferroni mean and Linguistic Z-number geometric Bonferroni mean operators: their applications in portfolio selection problems. IEEE Access 8, 98742\u201398760 (2020)","journal-title":"IEEE Access"},{"issue":"6","key":"1161_CR20","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1007\/s12559-017-9493-1","volume":"9","author":"JQ Wang","year":"2017","unstructured":"Wang, J.Q., Cao, Y.X., Zhang, H.Y.: Multi-criteria decision-making method based on distance measure and choquet integral for linguistic Z-numbers. Cogn. Comput. 9(6), 827\u2013842 (2017)","journal-title":"Cogn. Comput."},{"key":"1161_CR21","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.ins.2014.07.034","volume":"288","author":"J Wang","year":"2014","unstructured":"Wang, J., Wu, J., Wang, J., et al.: Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 288, 55\u201372 (2014)","journal-title":"Inf. Sci."},{"issue":"7","key":"1161_CR22","doi-asserted-by":"publisher","first-page":"1190","DOI":"10.3390\/math8071190","volume":"8","author":"XK Wang","year":"2020","unstructured":"Wang, X.K., Wang, Y.T., Wang, J.Q., et al.: A TODIM-PROMETHEE II based multi-criteria group decision making method for risk evaluation of water resource carrying capacity under probabilistic linguistic Z-number circumstances. Mathematics 8(7), 1190 (2020)","journal-title":"Mathematics"},{"key":"1161_CR23","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.omega.2005.12.003","volume":"36","author":"XT Wang","year":"2008","unstructured":"Wang, X.T., Triantaphyllou, E.: Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega 36, 45\u201363 (2008)","journal-title":"Omega"},{"issue":"1\u20134","key":"1161_CR24","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.ins.2004.02.003","volume":"168","author":"ZS Xu","year":"2004","unstructured":"Xu, Z.S.: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf. Sci. 168(1\u20134), 171\u2013184 (2004)","journal-title":"Inf. Sci."},{"issue":"2","key":"1161_CR25","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1080\/18756891.2016.1150003","volume":"9","author":"AM Yaakob","year":"2016","unstructured":"Yaakob, A.M., Gegov, A.: Interactive TOPSIS based group decision making methodology using Z-numbers. International Journal of Computational Intelligence Systems 9(2), 311\u2013324 (2016)","journal-title":"International Journal of Computational Intelligence Systems"},{"issue":"1","key":"1161_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/21.259681","volume":"24","author":"JB Yang","year":"1994","unstructured":"Yang, J.B., Singh, M.G.: An evidential reasoning approach for multiple-attribute decision making with uncertainty. IEEE Trans. Syst. Man Cybern. 24(1), 1\u201318 (1994)","journal-title":"IEEE Trans. Syst. Man Cybern."},{"issue":"3","key":"1161_CR27","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1109\/TSMCA.2002.802746","volume":"32","author":"JB Yang","year":"2002","unstructured":"Yang, J.B., Xu, D.L.: On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 32(3), 289\u2013304 (2002)","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans"},{"key":"1161_CR28","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.ins.2019.11.001","volume":"513","author":"J Ye","year":"2020","unstructured":"Ye, J., Xu, Z., Gou, X.: Virtual linguistic trust degree-based evidential reasoning approach and its application to emergency response assessment of railway station. Inf. Sci. 513, 341\u2013359 (2020)","journal-title":"Inf. Sci."},{"key":"1161_CR29","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning-Part I. Inf. Sci. 8, 199\u2013249 (1975)","journal-title":"Inf. Sci."},{"key":"1161_CR30","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","volume":"8","author":"LA Zadeh","year":"1975","unstructured":"Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning pt II. Inf. Sci. 8, 301\u2013357 (1975)","journal-title":"Inf. Sci."},{"key":"1161_CR31","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0020-0255(75)90017-1","volume":"9","author":"LA Zadeh","year":"1975","unstructured":"Zadeh, L.A.: The concept of a linguistic variable and its applications to approximate reasoning pt III. Inf. Sci. 9, 43\u201380 (1975)","journal-title":"Inf. Sci."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01161-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-021-01161-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01161-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T18:26:43Z","timestamp":1644258403000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-021-01161-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,17]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["1161"],"URL":"https:\/\/doi.org\/10.1007\/s40815-021-01161-3","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"value":"1562-2479","type":"print"},{"value":"2199-3211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,17]]},"assertion":[{"value":"1 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}