{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T05:13:24Z","timestamp":1768713204799,"version":"3.49.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,3,25]],"date-time":"2017-03-25T00:00:00Z","timestamp":1490400000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper Res Int J"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s12351-017-0307-8","type":"journal-article","created":{"date-parts":[[2017,3,25]],"date-time":"2017-03-25T07:01:20Z","timestamp":1490425280000},"page":"783-815","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["On extension of multiplicative consistency to interval fuzzy preference relations"],"prefix":"10.1007","volume":"19","author":[{"given":"Jana","family":"Krej\u010d\u00ed","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,3,25]]},"reference":[{"key":"307_CR1","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1002\/int.20262","volume":"23","author":"S Alonso","year":"2008","unstructured":"Alonso S, Chiclana F, Herrera F, Herrera-Viedma E, Alcal\u00e1-Fdez E, Porcel C (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23:155\u2013175","journal-title":"Int J Intell Syst"},{"key":"307_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1057\/jors.2013.135","volume":"66","author":"M Brunelli","year":"2015","unstructured":"Brunelli M, Fedrizzi M (2015) Axiomatic properties of inconsistency indices for pairwise comparisons. J Oper Res Soc 66:1\u201315","journal-title":"J Oper Res Soc"},{"key":"307_CR3","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 Trans Fuzzy Syst 17:14\u201323","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"307_CR4","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.knosys.2016.10.005","volume":"114","author":"Y Dong","year":"2016","unstructured":"Dong Y, Li CC, Chiclana F, Herrera F, Herrera-Viedma E (2016) Average-case consistency measurement and analysis of interval-valued reciprocal preference relations. Knowl Based Syst 114:108\u2013117","journal-title":"Knowl Based Syst"},{"key":"307_CR5","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1023\/B:FODM.0000013071.63614.3d","volume":"3","author":"M Enea","year":"2004","unstructured":"Enea M, Piazza T (2004) Project selection by constrained fuzzy AHP. Fuzzy Optim Decis Mak 3:39\u201362","journal-title":"Fuzzy Optim Decis Mak"},{"key":"307_CR6","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1142\/S0218488515500440","volume":"23","author":"M Fedrizzi","year":"2015","unstructured":"Fedrizzi M, Krej\u010d\u00ed J (2015) A note on the paper fuzzy analytic hierarchy process: Fallacy of the popular methods. Int J Uncertain Fuzziness Knowl Based Syst 23:965\u2013970","journal-title":"Int J Uncertain Fuzziness Knowl Based Syst"},{"key":"307_CR7","unstructured":"Fedrizzi M, Pereira RAM (1995) Positive fuzzy matrices, dominant eigenvalues and an extension of saaty\u2019s analytic hierarchy process. In: Proceedings of 6th world congress of international fuzzy systems association, Sao Paulo, Brazil, pp 245\u2013247"},{"key":"307_CR8","doi-asserted-by":"publisher","first-page":"4877","DOI":"10.1016\/j.ins.2010.08.019","volume":"180","author":"S Gen\u00e7","year":"2010","unstructured":"Gen\u00e7 S, Boran FE, Akay D, Xu Z (2010) Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations. Inf Sci 180:4877\u20134891","journal-title":"Inf Sci"},{"key":"307_CR9","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1109\/TSMCB.2006.875872","volume":"37","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 Trans Syst Man Cybern B Cybern B 37:176\u2013189","journal-title":"IEEE Trans Syst Man Cybern B Cybern B"},{"key":"307_CR10","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1016\/j.ejor.2014.03.021","volume":"237","author":"M Hu","year":"2014","unstructured":"Hu M, Ren P, Lan J, Wang J, Zheng W (2014) Note on \u2019some models for deriving the priority weights from interval fuzzy preference relations\u2019. Eur J Oper Res 237:771\u2013773","journal-title":"Eur J Oper Res"},{"key":"307_CR11","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0165-0114(86)90014-X","volume":"18","author":"J Kacprzyk","year":"1986","unstructured":"Kacprzyk J (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst 18:105\u2013118","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR12","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/s005000050038","volume":"2","author":"GJ Klir","year":"1998","unstructured":"Klir GJ, Yuan B (1998) Constrained fuzzy arithmetic: basic questions and some answers. Soft Comput 2:100\u2013108","journal-title":"Soft Comput"},{"key":"307_CR13","doi-asserted-by":"publisher","unstructured":"Krej\u010d\u00ed J (2015) Additively reciprocal fuzzy pairwise comparison matrices and multiplicative fuzzy priorities. Soft Comput. doi:\n                    10.1007\/s00500-015-2000-2","DOI":"10.1007\/s00500-015-2000-2"},{"key":"307_CR14","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.fss.2016.03.006","volume":"315","author":"J Krej\u010d\u00ed","year":"2016","unstructured":"Krej\u010d\u00ed J (2016a) Fuzzy eigenvector method for obtaining normalized fuzzy weights from fuzzy pairwise comparison matrices. Fuzzy Sets Syst 315:26\u201343","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR15","doi-asserted-by":"publisher","DOI":"10.1093\/imaman\/dpw006","author":"J Krej\u010d\u00ed","year":"2016","unstructured":"Krej\u010d\u00ed J (2016b) Obtaining fuzzy priorities from additively reciprocal fuzzy pairwise comparison matrices. IMA J Manag Math. doi:\n                    10.1093\/imaman\/dpw006","journal-title":"IMA J Manag Math"},{"key":"307_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2017.03.002","author":"J Krej\u010d\u00ed","year":"2017","unstructured":"Krej\u010d\u00ed J (2017) On additive consistency of interval fuzzy preference relations. Comput Ind Eng. doi:\n                    10.1016\/j.cie.2017.03.002","journal-title":"Comput Ind Eng"},{"key":"307_CR17","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s10700-016-9241-0","volume":"16","author":"J Krej\u010d\u00ed","year":"2017","unstructured":"Krej\u010d\u00ed J, Pavla\u010dka O, Tala\u0161ov\u00e1 J (2017) A fuzzy extension of analytic hierarchy process based on the constrained fuzzy arithmetic. Fuzzy Optim Decis Mak 16:89\u2013110","journal-title":"Fuzzy Optim Decis Mak"},{"key":"307_CR18","doi-asserted-by":"publisher","first-page":"2686","DOI":"10.1016\/j.fss.2009.01.010","volume":"160","author":"F Liu","year":"2009","unstructured":"Liu F (2009) Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst 160:2686\u20132700","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR19","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.ins.2011.09.019","volume":"185","author":"F Liu","year":"2012","unstructured":"Liu F, Zhang WG, Fu JH (2012) A new method of obtaining the priority weights from an interval fuzzy preference relation. Inf Sci 185:32\u201342","journal-title":"Inf Sci"},{"key":"307_CR20","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1007\/s00500-013-1006-x","volume":"17","author":"WA Lodwick","year":"2013","unstructured":"Lodwick WA, Jenkins OA (2013) Constrained intervals and interval spaces. Soft Comput 17:1393\u20131402","journal-title":"Soft Comput"},{"key":"307_CR21","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0165-0114(81)90003-8","volume":"3","author":"N Nurmi","year":"1981","unstructured":"Nurmi N (1981) Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets Syst 3:249\u2013259","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR22","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/0165-0114(78)90001-5","volume":"1","author":"SA Orlovski","year":"1978","unstructured":"Orlovski SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155\u2013167","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR23","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 preference orderings in group decision making. Fuzzy Sets Syst 12:117\u2013131","journal-title":"Fuzzy Sets Syst"},{"key":"307_CR24","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.knosys.2015.06.020","volume":"89","author":"R Ure\u00f1a","year":"2015","unstructured":"Ure\u00f1a R, Chiclana F, Fujita H, Herrera-Viedma E (2015a) Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations. Knowl Based Syst 89:86\u201396","journal-title":"Knowl Based Syst"},{"key":"307_CR25","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.ins.2014.12.061","volume":"302","author":"R Ure\u00f1a","year":"2015","unstructured":"Ure\u00f1a R, Chiclana F, Morente-Molinera JA, Herrera-Viedma E (2015b) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14\u201332","journal-title":"Inf Sci"},{"key":"307_CR26","first-page":"67","volume":"27","author":"J Wang","year":"2012","unstructured":"Wang J, Lan J, Ren P, Luo Y (2012) Some programming models to derive priority weights from additive interval fuzzy preference relations. Knowl Based Syst 27:67\u201377","journal-title":"Knowl Based Syst"},{"key":"307_CR27","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/j.cie.2014.09.011","volume":"77","author":"ZJ Wang","year":"2014","unstructured":"Wang ZJ (2014) A note on incomplete interval fuzzy preference relations and their applications. Comput Ind Eng 77:65\u201369","journal-title":"Comput Ind Eng"},{"key":"307_CR28","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.ins.2015.03.074","volume":"314","author":"ZJ Wang","year":"2015","unstructured":"Wang ZJ (2015a) Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean. Inf Sci 314:169\u2013183","journal-title":"Inf Sci"},{"key":"307_CR29","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1016\/j.ejor.2015.06.015","volume":"274","author":"ZJ Wang","year":"2015","unstructured":"Wang ZJ (2015b) A note on a goal proggramming model for incomplete interval multiplicative preference relations and its application in group decision-making. Eur J Oper Res 274:867\u2013871","journal-title":"Eur J Oper Res"},{"key":"307_CR30","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.ins.2012.01.019","volume":"193","author":"ZJ Wang","year":"2012","unstructured":"Wang ZJ, Li KW (2012) Goal programming approaches to deriving interval weights based on interval fuzzy preference relations. Inf Sci 193:180\u2013198","journal-title":"Inf Sci"},{"key":"307_CR31","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 (2014a) Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowl Based Syst 71:187\u2013200","journal-title":"Knowl Based Syst"},{"key":"307_CR32","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.knosys.2014.01.017","volume":"59","author":"J Wu","year":"2014","unstructured":"Wu J, Chiclana F (2014b) A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations. Knowl Based Syst 59:97\u2013107","journal-title":"Knowl Based Syst"},{"key":"307_CR33","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1142\/S0219622011004701","volume":"10","author":"M Xia","year":"2011","unstructured":"Xia M, Xu Z (2011) Some issues on multiplicative consistency of interval reciprocal relations. Int J Inf Technol Decis Mak 10:1043\u20131065","journal-title":"Int J Inf Technol Decis Mak"},{"key":"307_CR34","doi-asserted-by":"publisher","first-page":"1499","DOI":"10.1007\/s00500-013-1156-x","volume":"18","author":"Y Xu","year":"2014","unstructured":"Xu Y, Li KW, Wang H (2014a) Consistency test and weight generation for additive interval fuzzy preference relations. Soft Comput 18:1499\u20131513","journal-title":"Soft Comput"},{"key":"307_CR35","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.cie.2013.10.010","volume":"67","author":"Y Xu","year":"2014","unstructured":"Xu Y, Li KW, Wang H (2014b) Incomplete interval fuzzy preference relations and their applications. Comput Ind Eng 67:93\u2013103","journal-title":"Comput Ind Eng"},{"key":"307_CR36","doi-asserted-by":"publisher","first-page":"1500","DOI":"10.1109\/TSMCB.2006.888925","volume":"37","author":"Z Xu","year":"2007","unstructured":"Xu Z (2007) Multiple-attribute group decision making with different formats of preference information on attributes. IEEE Trans Syst Man Cybern B Cybern 37:1500\u20131511","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"key":"307_CR37","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1016\/j.ejor.2006.11.011","volume":"184","author":"Z Xu","year":"2008","unstructured":"Xu Z, Chen J (2008) Some models for deriving the priority weights from interval fuzzy preference relations. Eur J Oper Res 184:266\u2013280","journal-title":"Eur J Oper Res"}],"container-title":["Operational Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-017-0307-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12351-017-0307-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12351-017-0307-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T13:09:18Z","timestamp":1566306558000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12351-017-0307-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,25]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["307"],"URL":"https:\/\/doi.org\/10.1007\/s12351-017-0307-8","relation":{},"ISSN":["1109-2858","1866-1505"],"issn-type":[{"value":"1109-2858","type":"print"},{"value":"1866-1505","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,25]]},"assertion":[{"value":"2 November 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 March 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2017","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2017","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}