{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T14:02:19Z","timestamp":1762351339252,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"14","license":[{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,26]],"date-time":"2022-03-26T00:00:00Z","timestamp":1648252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2017MG027"],"award-info":[{"award-number":["ZR2017MG027"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s10489-021-03081-z","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T01:03:41Z","timestamp":1648515821000},"page":"16832-16851","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Novel consistency and consensus of generalized intuitionistic fuzzy preference relations with application in group decision making"],"prefix":"10.1007","volume":"52","author":[{"given":"Huan Tian","family":"Xie","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3666-1188","authenticated-orcid":false,"given":"Zhen Ming","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Ze Shui","family":"Xu","sequence":"additional","affiliation":[]},{"given":"Zun Wei","family":"Fu","sequence":"additional","affiliation":[]},{"given":"Wei","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,26]]},"reference":[{"key":"3081_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy set. Fuzzy Sets and Systems 20:87\u201396","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR2","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.fss.2018.08.009","volume":"362","author":"F Ahmed","year":"2019","unstructured":"Ahmed F, Kilic K (2019) Fuzzy analytic hierarchy process: A performance analysis of various algorithms. Fuzzy Sets and Systems 362:110\u2013128","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR3","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/0165-0114(94)90084-1","volume":"67","author":"SM Chen","year":"1994","unstructured":"Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67:163\u2013172","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR4","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/S0165-0114(96)00339-9","volume":"97","author":"F Chiclana","year":"1998","unstructured":"Chiclana F, Herrera F, Herrera-Viedma E (1998) Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations. Fuzzy Sets and Systems 97:33\u201348","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR5","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/S0165-0114(00)00004-X","volume":"122","author":"F Chiclana","year":"2001","unstructured":"Chiclana F, Herrera F, Herrera-Viedma E (2001) Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets and Systems 122:277\u2013291","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR6","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1109\/TFUZZ.2008.2008028","volume":"17","author":"F Chiclana","year":"2009","unstructured":"Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2009) Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Transactions on Fuzzy Systems 17:14\u201323","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR7","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1109\/21.229476","volume":"23","author":"WL Gau","year":"1993","unstructured":"Gau WL, Buehrer DJ (1993) Vague sets. IEEE Transactions on Systems, Man, and Cybernetics 23:610\u2013614","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics"},{"key":"3081_CR8","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1109\/TFUZZ.2013.2249586","volume":"22","author":"KH Guo","year":"2014","unstructured":"Guo KH (2014) Amount of information and attitudinal based method for ranking Atanassov\u2019s intuitionistic fuzzy values. IEEE Transactions on Fuzzy Systems 22:177\u2013188","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR9","doi-asserted-by":"publisher","first-page":"1187","DOI":"10.1016\/j.cie.2009.05.007","volume":"57","author":"Z Gong","year":"2009","unstructured":"Gong Z, Li L, Zhou F, Yao T (2009) Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations. Computers & Industrial Engineering 57:1187\u20131193","journal-title":"Computers & Industrial Engineering"},{"key":"3081_CR10","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1109\/TSMCB.2006.875872","volume":"B37","author":"E Herrera-Viedma","year":"2007","unstructured":"Herrera-Viedma E, Chiclana F, Herrera F, Alonso S (2007) Group decision-making model with incomplete fuzzy preference relations based on additive consistency. IEEE Transactions on Systems, Man and Cybernetics, Part B37:176\u2013189","journal-title":"IEEE Transactions on Systems, Man and Cybernetics, Part"},{"key":"3081_CR11","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0165-0114(98)00271-1","volume":"114","author":"DH Hong","year":"2000","unstructured":"Hong DH, ChoiC H (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114:103\u2013113","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR12","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.knosys.2016.01.017","volume":"97","author":"F Jin","year":"2016","unstructured":"Jin F, Ni Z, Chen H, Li Y (2016) Approaches to group decision making with intuitionistic fuzzy preference relations based on multiplicative consistency. Knowledge-Based Systems 97:48\u201359","journal-title":"Knowledge-Based Systems"},{"key":"3081_CR13","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.asoc.2017.06.056","volume":"60","author":"Y Li","year":"2017","unstructured":"Li Y, Zhang H, Dong Y (2017) The interactive consensus reaching process with the minimum and uncertain cost in group decision making. Applied Soft Computing 60:202\u2013212","journal-title":"Applied Soft Computing"},{"key":"3081_CR14","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.inffus.2018.12.004","volume":"52","author":"C Li","year":"2019","unstructured":"Li C, Dong Y, Xu Y, Chiclana F, Herrera-Viedma E, Herrera F (2019) An overview on managing additive consistency of reciprocal preference elations for consistency-driven decision making and fusion: Taxonomy and future directions. Information Fusion 52:143\u2013156","journal-title":"Information Fusion"},{"key":"3081_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.fss.2011.11.009","volume":"198","author":"X Liu","year":"2012","unstructured":"Liu X, Pan Y, Xu Y, Yu S (2012) Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations. Fuzzy Sets and Systems 198:1\u201319","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR16","doi-asserted-by":"publisher","first-page":"1669","DOI":"10.1109\/TFUZZ.2014.2302495","volume":"22","author":"HC Liao","year":"2014","unstructured":"Liao HC, Xu ZS (2014) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Transactions on Fuzzy Systems 22:1669\u20131681","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR17","unstructured":"Liao HC, Xu ZS, Consistency and consensus of intuitionistic duzzy preference relations in group decision making, Imprecision and Uncertainty in Information Representation and Processing, Studies in Fuzziness and Soft Computing 332"},{"key":"3081_CR18","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/s10700-018-9297-0","volume":"18","author":"JP Liu","year":"2019","unstructured":"Liu JP, Song JM, Chen HY (2019) Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations. Fuzzy Optimization and Decision Making 18:345\u2013370","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"3081_CR19","doi-asserted-by":"publisher","first-page":"1786","DOI":"10.1007\/s40815-020-00882-1","volume":"22","author":"P Liu","year":"2020","unstructured":"Liu P, Ali A, Rehman N, Shah SIA (2020) Another view on intuitionistic fuzzy preference relation-based aggregation operators and their Applications. International Journal of Fuzzy Systems 22:1786\u20131800","journal-title":"International Journal of Fuzzy Systems"},{"key":"3081_CR20","doi-asserted-by":"publisher","first-page":"4041","DOI":"10.3233\/JIFS-200200","volume":"39","author":"F Liu","year":"2020","unstructured":"Liu F, Tan X, Yang H, Zhao H (2020) Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency. Journal of Intelligent & Fuzzy Systems 39:4041\u20134058","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"3081_CR21","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1016\/j.ins.2018.04.040","volume":"451\u2013452","author":"ZM Ma","year":"2018","unstructured":"Ma ZM, Xu ZS (2018) Hyperbolic scales involving appetites-based intuitionistic multiplicative preference relations for group decision making. Information Sciences 451\u2013452:310\u2013325","journal-title":"Information Sciences"},{"key":"3081_CR22","doi-asserted-by":"publisher","first-page":"2615","DOI":"10.3934\/jimo.2020086","volume":"17","author":"ZM Ma","year":"2021","unstructured":"Ma ZM, Xu ZS, Yang W (2021) Approach to the consistency and consensus of Pythagorean fuzzy preference relations based on their partial orders in group decision making. Journal of Industrial and Management Optimization 17:2615\u20132638","journal-title":"Journal of Industrial and Management Optimization"},{"key":"3081_CR23","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/j.inffus.2018.05.001","volume":"46","author":"FY Meng","year":"2019","unstructured":"Meng FY, Tang J, Fujita H (2019) Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making. Information Fusion 46:77\u201390","journal-title":"Information Fusion"},{"key":"3081_CR24","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/0165-0114(78)90001-5","volume":"1","author":"SA Orlovsky","year":"1978","unstructured":"Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems 1:155\u2013167","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR25","volume-title":"The Analytic Hierarchy Process","author":"TL Saaty","year":"1980","unstructured":"Saaty TL (1980) The Analytic Hierarchy Process. McGraw-Hill, New York, NY"},{"key":"3081_CR26","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/0165-0114(84)90032-0","volume":"12","author":"T Tanino","year":"1984","unstructured":"Tanino T (1984) Fuzzy preferenceorderingsingroupdecisionmaking. Fuzzy Sets and Systems 12:117\u2013131","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR27","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.ins.2016.08.019","volume":"372","author":"S Wan","year":"2016","unstructured":"Wan S, Xu G, Dong J (2016) A novel method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Information Sciences 372:53\u201371","journal-title":"Information Sciences"},{"key":"3081_CR28","doi-asserted-by":"publisher","first-page":"6377","DOI":"10.1016\/j.apm.2013.01.021","volume":"37","author":"ZJ Wang","year":"2013","unstructured":"Wang ZJ (2013) Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations. Applied Mathematical Modelling 37:6377\u20136388","journal-title":"Applied Mathematical Modelling"},{"key":"3081_CR29","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s10700-014-9205-1","volume":"14","author":"ZJ Wang","year":"2015","unstructured":"Wang ZJ (2015) Geometric consistency based interval weight elicitation from intuitionistic preference relations using logarithmic least square optimization. Fuzzy Optimization and Decision Making 14:289\u2013310","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"3081_CR30","doi-asserted-by":"publisher","first-page":"2555","DOI":"10.1109\/TFUZZ.2019.2941174","volume":"28","author":"ZJ Wang","year":"2020","unstructured":"Wang ZJ (2020) A representable uninorm based intuitionistic fuzzy analytic hierarchy process. IEEE Transactions on Fuzzy Systems 28:2555\u20132569","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR31","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.asoc.2015.09.058","volume":"42","author":"H Wang","year":"2016","unstructured":"Wang H, Xu ZS (2016) Interactive algorithms for improving incomplete linguistic preference relations based on consistency measures. Applied Soft Computing 42:66\u201379","journal-title":"Applied Soft Computing"},{"key":"3081_CR32","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/j.knosys.2014.07.024","volume":"71","author":"J Wu","year":"2014","unstructured":"Wu J, Chiclana F (2014) Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus uilding. Knowledge-Based Systems 71:187\u2013200","journal-title":"Knowledge-Based Systems"},{"key":"3081_CR33","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1109\/TFUZZ.2016.2646749","volume":"26","author":"J Wu","year":"2018","unstructured":"Wu J, Chiclana F, Liao H (2018) Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors. IEEE Transactions on Fuzzy Systems 26:193\u2013202","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR34","doi-asserted-by":"publisher","first-page":"1179","DOI":"10.1109\/TFUZZ.2006.890678","volume":"15","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 15:1179\u20131187","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"3081_CR35","doi-asserted-by":"publisher","first-page":"2363","DOI":"10.1016\/j.ins.2006.12.019","volume":"177","author":"ZS Xu","year":"2007","unstructured":"Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Information Sciences 177:2363\u20132379","journal-title":"Information Sciences"},{"key":"3081_CR36","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1002\/int.20494","volume":"26","author":"ZS Xu","year":"2011","unstructured":"Xu ZS, Cai XQ, Szmidt E (2011) Algorithms for estimating missing elements of incomplete intuitionistic preference relations. International Journal of Intelligent Systems 26:787\u2013813","journal-title":"International Journal of Intelligent Systems"},{"key":"3081_CR37","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/j.ins.2015.08.034","volume":"328","author":"Y Xu","year":"2016","unstructured":"Xu Y, Herrera F, Wang HM (2016) A distance-based framework to deal with ordinal and additive inconsistencies for fuzzy reciprocal preference relations. Information Sciences 328:189\u2013205","journal-title":"Information Sciences"},{"key":"3081_CR38","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.fss.2018.09.009","volume":"362","author":"Y Xu","year":"2019","unstructured":"Xu Y, Herrera F (2019) Visualizing andrectifying different inconsistencies for fuzzyreciprocal preference relations. Fuzzy Sets and Systems 362:85\u2013109","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR39","doi-asserted-by":"crossref","unstructured":"Xia M, Xu ZS, Chen J (2013) Algorithms for improving consistency or consensus of reciprocal $$ \\left[0,1\\right] $$-valued preference relations. Fuzzy Sets and Systems 216:108\u2013133","DOI":"10.1016\/j.fss.2012.09.016"},{"key":"3081_CR40","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.knosys.2015.12.007","volume":"98","author":"G Xu","year":"2016","unstructured":"Xu G, Wan S, Wang F, Dong J, Zeng Y (2016) Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations. Knowledge-Based Systems 98:30\u201343","journal-title":"Knowledge-Based Systems"},{"key":"3081_CR41","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/j.ins.2018.10.044","volume":"477","author":"Y Yang","year":"2019","unstructured":"Yang Y, Wang X, Xu ZS (2019) The multiplicative consistency threshold of intuitionistic fuzzypreference relation. Information Sciences 477:349\u2013368","journal-title":"Information Sciences"},{"key":"3081_CR42","doi-asserted-by":"publisher","first-page":"4342","DOI":"10.1007\/s10489-020-01796-z","volume":"50","author":"W Yang","year":"2020","unstructured":"Yang W, Jhang ST, Shi SG, Xu ZS, Ma ZM (2020) A novel additive consistency for intuitionistic fuzzy preference relations in group decision making. Applied Intelligence 50:4342\u20134356","journal-title":"Applied Intelligence"},{"key":"3081_CR43","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/s00500-020-05472-9","volume":"25","author":"W Yang","year":"2021","unstructured":"Yang W, Jhang ST, Fu ZW, Xu ZS, Ma ZM (2021) A novel method to derive the intuitionistic fuzzy priority vectors from intuitionistic fuzzy preference relations. Soft Computing 25:147\u2013159","journal-title":"Soft Computing"},{"key":"3081_CR44","unstructured":"Yang W, Jhang ST, Shi SG, Ma ZM, Representable uninorm-based consistencies for intuitionistic fuzzy preference relations in group decision making, submitted to Expert Systems with Applications"},{"key":"3081_CR45","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10700-012-9118-9","volume":"12","author":"XM Zhang","year":"2012","unstructured":"Zhang XM, Xu ZS (2012) A new method for ranking intuitionistic fuzzy values and its application in multi-attribute decision making. Fuzzy Optimization and Decision Making 12:135\u2013146","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"3081_CR46","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.fss.2015.04.009","volume":"282","author":"H Zhang","year":"2016","unstructured":"Zhang H (2016) Group decision making based on multiplicative consistent reciprocal preference relations. Fuzzy Sets and Systems 282:31\u201346","journal-title":"Fuzzy Sets and Systems"},{"key":"3081_CR47","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.ins.2017.06.006","volume":"414","author":"Y Zhang","year":"2017","unstructured":"Zhang Y, Xu ZS, Liao H (2017) A consensus process for group decision making with probabilistic linguistic preference relations. Information Sciences 414:260\u2013275","journal-title":"Information Sciences"},{"key":"3081_CR48","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1109\/TFUZZ.2019.2957259","volume":"29","author":"HJ Zhang","year":"2021","unstructured":"Zhang HJ, Li CC, Liu YT, Dong YC (2021) Modelling personalized individual semantics and consensus in comparative linguistic expression preference relations with self-confidence: An optimization-based approach. IEEE Transactions on Fuzzy Systems 29:627\u2013640","journal-title":"IEEE Transactions on Fuzzy Systems"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-021-03081-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-021-03081-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-021-03081-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,10]],"date-time":"2022-11-10T09:27:09Z","timestamp":1668072429000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-021-03081-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,26]]},"references-count":48,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["3081"],"URL":"https:\/\/doi.org\/10.1007\/s10489-021-03081-z","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"type":"print","value":"0924-669X"},{"type":"electronic","value":"1573-7497"}],"subject":[],"published":{"date-parts":[[2022,3,26]]},"assertion":[{"value":"6 December 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}