{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T10:01:31Z","timestamp":1767866491547,"version":"3.49.0"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["737459"],"award-info":[{"award-number":["737459"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cent Eur J Oper Res"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s10100-020-00735-0","type":"journal-article","created":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T19:03:54Z","timestamp":1609959834000},"page":"1051-1069","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A framework of incorporating confidence levels to deal with uncertainty in pairwise comparisons"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2947-7470","authenticated-orcid":false,"given":"Georgia","family":"Dede","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Kamalakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimosthenis","family":"Anagnostopoulos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,1,6]]},"reference":[{"issue":"4","key":"735_CR1","first-page":"521","volume":"43","author":"JM Alho","year":"1997","unstructured":"Alho JM, Kangas J (1997) Analyzing uncertainties in experts\u2019 opinions of forest plan performance. For Sci 43(4):521\u2013528","journal-title":"For Sci"},{"issue":"04","key":"735_CR2","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1142\/S0218488506004114","volume":"14","author":"JA Alonso","year":"2006","unstructured":"Alonso JA, Lamata MT (2006) Consistency in the analytic hierarchy process: a new approach. Int J Uncertain Fuzziness Knowl Based Syst 14(04):445\u2013459","journal-title":"Int J Uncertain Fuzziness Knowl Based Syst"},{"issue":"9226","key":"735_CR3","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/S0140-6736(00)02502-2","volume":"356","author":"SS Anand","year":"2000","unstructured":"Anand SS, Yusuf S, Vuksan V, Devanesen S, Teo KK, Montague PA, Kelemen L, Yi C, Lonn E, Gerstein H et al (2000) Differences in risk factors, atherosclerosis, and cardiovascular disease between ethnic groups in canada: the study of health assessment and risk in ethnic groups (share). Lancet 356(9226):279\u2013284","journal-title":"Lancet"},{"issue":"18","key":"735_CR4","doi-asserted-by":"publisher","first-page":"3851","DOI":"10.1080\/00207540410001699183","volume":"42","author":"R Banuelas","year":"2004","unstructured":"Banuelas R, Antony J (2004) Modified analytic hierarchy process to incorporate uncertainty and managerial aspects. Int J Prod Res 42(18):3851\u20133872","journal-title":"Int J Prod Res"},{"issue":"12","key":"735_CR5","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1057\/palgrave.jors.2600474","volume":"48","author":"J Barzilai","year":"1997","unstructured":"Barzilai J (1997) Deriving weights from pairwise comparison matrices. J Oper Res Soc 48(12):1226\u20131232","journal-title":"J Oper Res Soc"},{"issue":"3","key":"735_CR6","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1002\/(SICI)1099-1360(199805)7:3<123::AID-MCDA181>3.0.CO;2-8","volume":"7","author":"J Barzilai","year":"1998","unstructured":"Barzilai J (1998) Consistency measures for pairwise comparison matrices. J Multi-Criteria Decis Anal 7(3):123\u2013132","journal-title":"J Multi-Criteria Decis Anal"},{"key":"735_CR7","doi-asserted-by":"publisher","DOI":"10.1533\/9780857099471","volume-title":"Probability and random variables","author":"GP Beaumont","year":"2005","unstructured":"Beaumont GP (2005) Probability and random variables. Elsevier, London"},{"issue":"1","key":"735_CR8","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/S0377-2217(01)00230-2","volume":"140","author":"M Beynon","year":"2002","unstructured":"Beynon M (2002) Ds\/ahp method: a mathematical analysis, including an understanding of uncertainty. Eur J Oper Res 140(1):148\u2013164","journal-title":"Eur J Oper Res"},{"issue":"2","key":"735_CR9","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0165-0114(89)90187-5","volume":"29","author":"C Boender","year":"1989","unstructured":"Boender C, De Graan J, Lootsma F (1989) Multi-criteria decision analysis with fuzzy pairwise comparisons. Fuzzy Sets Syst 29(2):133\u2013143","journal-title":"Fuzzy Sets Syst"},{"issue":"6","key":"735_CR10","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1016\/S0305-0548(03)00042-X","volume":"31","author":"EU Choo","year":"2004","unstructured":"Choo EU, Wedley WC (2004) A common framework for deriving preference values from pairwise comparison matrices. Comput Oper Res 31(6):893\u2013908","journal-title":"Comput Oper Res"},{"issue":"2","key":"735_CR11","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1016\/j.ejor.2014.08.037","volume":"241","author":"G Dede","year":"2015","unstructured":"Dede G, Kamalakis T, Sphicopoulos T (2015) Convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi-criteria decision making problems. Eur J Oper Res 241(2):458\u2013468","journal-title":"Eur J Oper Res"},{"issue":"2","key":"735_CR12","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1016\/j.ejor.2016.01.059","volume":"252","author":"G Dede","year":"2016","unstructured":"Dede G, Kamalakis T, Sphicopoulos T (2016) Theoretical estimation of the probability of weight rank reversal in pairwise comparisons. Eur J Oper Res 252(2):587\u2013600","journal-title":"Eur J Oper Res"},{"issue":"11","key":"735_CR13","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1364\/JOCN.3.000850","volume":"3","author":"G Dede","year":"2011","unstructured":"Dede G, Kamalakis T, Varoutas D (2011) Evaluation of optical wireless technologies in home networking: an analytical hierarchy process approach. J Opt Commun Netw 3(11):850\u2013859","journal-title":"J Opt Commun Netw"},{"issue":"3","key":"735_CR14","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/S0888-613X(99)00025-0","volume":"21","author":"H Deng","year":"1999","unstructured":"Deng H (1999) Multicriteria analysis with fuzzy pairwise comparison. Int J Approx Reason 21(3):215\u2013231","journal-title":"Int J Approx Reason"},{"issue":"8","key":"735_CR15","doi-asserted-by":"publisher","first-page":"2321","DOI":"10.1007\/s00500-014-1426-2","volume":"19","author":"Y Dong","year":"2015","unstructured":"Dong Y, Chen X, Li C-C, Hong W-C, Xu Y (2015) Consistency issues of interval pairwise comparison matrices. Soft Comput 19(8):2321\u20132335","journal-title":"Soft Comput"},{"issue":"2","key":"735_CR16","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1016\/j.ejor.2014.03.045","volume":"238","author":"I Durbach","year":"2014","unstructured":"Durbach I, Lahdelma R, Salminen P (2014) The analytic hierarchy process with stochastic judgements. Eur J Oper Res 238(2):552\u2013559","journal-title":"Eur J Oper Res"},{"issue":"1","key":"735_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ejor.2012.04.038","volume":"223","author":"IN Durbach","year":"2012","unstructured":"Durbach IN, Stewart TJ (2012) Modeling uncertainty in multi-criteria decision analysis. Eur J Oper Res 223(1):1\u201314","journal-title":"Eur J Oper Res"},{"issue":"2","key":"735_CR18","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.ejor.2012.01.010","volume":"219","author":"T Entani","year":"2012","unstructured":"Entani T, Sugihara K (2012) Uncertainty index based interval assignment by interval ahp. Eur J Oper Res 219(2):379\u2013385","journal-title":"Eur J Oper Res"},{"issue":"01","key":"735_CR19","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1142\/S0219622007002356","volume":"6","author":"H Eskandari","year":"2007","unstructured":"Eskandari H, Rabelo L (2007) Handling uncertainty in the analytic hierarchy process: a stochastic approach. Int J Inf Technol Decis Making 6(01):177\u2013189","journal-title":"Int J Inf Technol Decis Making"},{"issue":"8","key":"735_CR20","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1002\/nla.318","volume":"10","author":"A Farkas","year":"2003","unstructured":"Farkas A, Lancaster P, R\u00f3zsa P (2003) Consistency adjustments for pairwise comparison matrices. Numer Linear Algebra with Appl 10(8):689\u2013700","journal-title":"Numer Linear Algebra with Appl"},{"issue":"4","key":"735_CR21","doi-asserted-by":"publisher","first-page":"950","DOI":"10.1198\/106186002394","volume":"11","author":"A Genz","year":"2002","unstructured":"Genz A, Bretz F (2002) Comparison of methods for the computation of multivariate t probabilities. J Comput Graph Stat 11(4):950\u2013971","journal-title":"J Comput Graph Stat"},{"issue":"7\u20138","key":"735_CR22","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1016\/j.mcm.2007.03.015","volume":"46","author":"N Gerdsri","year":"2007","unstructured":"Gerdsri N, Kocaoglu DF (2007) Applying the analytic hierarchy process (ahp) to build a strategic framework for technology roadmapping. Math Comput Model 46(7\u20138):1071\u20131080","journal-title":"Math Comput Model"},{"issue":"3","key":"735_CR23","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1111\/j.1540-5414.2003.02274.x","volume":"34","author":"ED Hahn","year":"2003","unstructured":"Hahn ED (2003) Decision making with uncertain judgments: a stochastic formulation of the analytic hierarchy process. Decis Sci 34(3):443\u2013466","journal-title":"Decis Sci"},{"issue":"2","key":"735_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF03216919","volume":"37","author":"S Heldsinger","year":"2010","unstructured":"Heldsinger S, Humphry S (2010) Using the method of pairwise comparison to obtain reliable teacher assessments. Austr Educ Res 37(2):1\u201319","journal-title":"Austr Educ Res"},{"key":"735_CR25","volume-title":"Introduction to numerical analysis","author":"FB Hildebrand","year":"1987","unstructured":"Hildebrand FB (1987) Introduction to numerical analysis. Courier Corporation, New York"},{"key":"735_CR26","unstructured":"https:\/\/github.com\/gdede hua\/confidence_levels_framework"},{"issue":"11","key":"735_CR27","first-page":"14336","volume":"38","author":"A Ishizaka","year":"2011","unstructured":"Ishizaka A, Labib A (2011) Review of the main developments in the analytic hierarchy process. Expert Syst Appl 38(11):14336\u201314345","journal-title":"Expert Syst Appl"},{"issue":"6","key":"735_CR28","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1093\/jigpal\/jzp062","volume":"18","author":"WW Koczkodaj","year":"2010","unstructured":"Koczkodaj WW, Szarek SJ (2010) On distance-based inconsistency reduction algorithms for pairwise comparisons. Logic J IGPL 18(6):859\u2013869","journal-title":"Logic J IGPL"},{"issue":"1","key":"735_CR29","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/0377-2217(85)90114-6","volume":"22","author":"M Kok","year":"1985","unstructured":"Kok M, Lootsma F (1985) Pairwise-comparison methods in multiple objective programming, with applications in a long-term energy-planning model. Eur J Oper Res 22(1):44\u201355","journal-title":"Eur J Oper Res"},{"issue":"5","key":"735_CR30","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1016\/S0305-0548(03)00022-4","volume":"31","author":"M Kwiesielewicz","year":"2004","unstructured":"Kwiesielewicz M, Van Uden E (2004) Inconsistent and contradictory judgements in pairwise comparison method in the ahp. Comput Oper Res 31(5):713\u2013719","journal-title":"Comput Oper Res"},{"issue":"6","key":"735_CR31","doi-asserted-by":"publisher","first-page":"1824","DOI":"10.1016\/j.cor.2005.05.037","volume":"34","author":"F Limayem","year":"2007","unstructured":"Limayem F, Yannou B (2007) Selective assessment of judgmental inconsistencies in pairwise comparisons for group decision rating. Comput Oper Res 34(6):1824\u20131841","journal-title":"Comput Oper Res"},{"issue":"7","key":"735_CR32","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1016\/j.mcm.2007.03.025","volume":"46","author":"NJZ Mamat","year":"2007","unstructured":"Mamat NJZ, Daniel JK (2007) Statistical analyses on time complexity and rank consistency between singular value decomposition and the duality approach in ahp: A case study of faculty member selection. Math Comput Model 46(7):1099\u20131106","journal-title":"Math Comput Model"},{"issue":"5","key":"735_CR33","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1109\/TSMCB.2002.1033190","volume":"32","author":"M Marimin","year":"2002","unstructured":"Marimin M, Umano M, Hatono I, Tamura H (2002) Hierarchical semi-numeric method for pairwise fuzzy group decision making. IEEE Trans Syst Man Cybern Part B (Cybernetics) 32(5):691\u2013700","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybernetics)"},{"issue":"3","key":"735_CR34","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/S0377-2217(03)00432-6","volume":"159","author":"L Mikhailov","year":"2004","unstructured":"Mikhailov L (2004) A fuzzy approach to deriving priorities from interval pairwise comparison judgements. Eur J Oper Res 159(3):687\u2013704","journal-title":"Eur J Oper Res"},{"issue":"2","key":"735_CR35","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1002\/mcda.319","volume":"11","author":"I Millet","year":"2002","unstructured":"Millet I, Wedley WC (2002) Modelling risk and uncertainty with the analytic hierarchy process. J Multi-Criteria Decis Anal 11(2):97\u2013107","journal-title":"J Multi-Criteria Decis Anal"},{"issue":"11","key":"735_CR36","doi-asserted-by":"publisher","first-page":"1604","DOI":"10.1016\/j.fss.2009.10.011","volume":"161","author":"J Ram\u00edk","year":"2010","unstructured":"Ram\u00edk J, Korviny P (2010) Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets Syst 161(11):1604\u20131613","journal-title":"Fuzzy Sets Syst"},{"key":"735_CR37","volume-title":"Mathematical statistics and data analysis","author":"J Rice","year":"2006","unstructured":"Rice J (2006) Mathematical statistics and data analysis. Nelson Education, Toronto"},{"issue":"1","key":"735_CR38","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0377-2217(02)00227-8","volume":"145","author":"TL Saaty","year":"2003","unstructured":"Saaty TL (2003) Decision-making with the ahp: why is the principal eigenvector necessary. Eur J Oper Res 145(1):85\u201391","journal-title":"Eur J Oper Res"},{"key":"735_CR39","volume-title":"Decision making for leaders: the analytic hierarchy process for decisions in a complex world","author":"TL Saaty","year":"2008","unstructured":"Saaty TL (2008) Decision making for leaders: the analytic hierarchy process for decisions in a complex world. RWS Publications, Pittsburgh"},{"issue":"2","key":"735_CR40","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/BF03191825","volume":"102","author":"TL Saaty","year":"2008","unstructured":"Saaty TL (2008b) Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy\/network process. Rev Real Acad Cienc Exactas Fisicas y Nat Ser A Mat 102(2):251\u2013318","journal-title":"Rev Real Acad Cienc Exactas Fisicas y Nat Ser A Mat"},{"issue":"2","key":"735_CR41","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0022-2496(84)90027-0","volume":"28","author":"TL Saaty","year":"1984","unstructured":"Saaty TL, Vargas LG (1984) Inconsistency and rank preservation. J Math Psychol 28(2):205\u2013214","journal-title":"J Math Psychol"},{"issue":"1","key":"735_CR42","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/0377-2217(87)90275-X","volume":"32","author":"TL Saaty","year":"1987","unstructured":"Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32(1):107\u2013117","journal-title":"Eur J Oper Res"},{"issue":"2","key":"735_CR43","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1016\/j.ejor.2014.10.024","volume":"242","author":"S Siraj","year":"2015","unstructured":"Siraj S, Mikhailov L, Keane JA (2015) Contribution of individual judgments toward inconsistency in pairwise comparisons. Eur J Oper Res 242(2):557\u2013567","journal-title":"Eur J Oper Res"},{"issue":"3","key":"735_CR44","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1111\/j.1540-5915.1997.tb01326.x","volume":"28","author":"A Stam","year":"1997","unstructured":"Stam A, Silva APD (1997) Stochastic judgments in the ahp: the measurement of rank reversal probabilities. Decis Sci 28(3):655\u2013688","journal-title":"Decis Sci"},{"issue":"3","key":"735_CR45","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1016\/S0377-2217(03)00418-1","volume":"158","author":"K Sugihara","year":"2004","unstructured":"Sugihara K, Ishii H, Tanaka H (2004) Interval priorities in ahp by interval regression analysis. Eur J Oper Res 158(3):745\u2013754","journal-title":"Eur J Oper Res"},{"issue":"3","key":"735_CR46","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1111\/0824-7935.00163","volume":"17","author":"K Sugihara","year":"2001","unstructured":"Sugihara K, Tanaka H (2001) Interval evaluations in the analytic hierarchy process by possibility analysis. Comput Intel 17(3):567\u2013579","journal-title":"Comput Intel"},{"key":"735_CR47","doi-asserted-by":"crossref","unstructured":"Triantaphyllou E (2000) Multi-criteria decision making methods. In: Multi-criteria decision making methods: a comparative study, pp 5\u201321. Springer","DOI":"10.1007\/978-1-4757-3157-6_2"},{"issue":"6","key":"735_CR48","doi-asserted-by":"publisher","first-page":"2396","DOI":"10.1109\/TSMCB.2004.837348","volume":"34","author":"RR Yager","year":"2004","unstructured":"Yager RR (2004) Modeling prioritized multicriteria decision making. IEEE Trans Syst Man Cybern Part B (Cybernetics) 34(6):2396\u20132404","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybernetics)"},{"key":"735_CR49","doi-asserted-by":"crossref","unstructured":"Yang X, Yan L, Zeng L (2013) How to handle uncertainties in ahp: The cloud delphi hierarchical analysis. Information Sciences 222:384\u2013404. Including Special Section on New Trends in Ambient Intelligence and Bio-inspired Systems","DOI":"10.1016\/j.ins.2012.08.019"},{"issue":"2","key":"735_CR50","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/0377-2217(91)90135-I","volume":"53","author":"MS Zahir","year":"1991","unstructured":"Zahir MS (1991) Incorporating the uncertainty of decision judgements in the analytic hierarchy process. Eur J Oper Res 53(2):206\u2013216","journal-title":"Eur J Oper Res"}],"container-title":["Central European Journal of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-020-00735-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10100-020-00735-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-020-00735-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,26]],"date-time":"2022-05-26T20:31:55Z","timestamp":1653597115000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10100-020-00735-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,6]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["735"],"URL":"https:\/\/doi.org\/10.1007\/s10100-020-00735-0","relation":{},"ISSN":["1435-246X","1613-9178"],"issn-type":[{"value":"1435-246X","type":"print"},{"value":"1613-9178","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,6]]},"assertion":[{"value":"10 December 2020","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}