{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T23:29:28Z","timestamp":1779924568243,"version":"3.53.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2008,6,19]],"date-time":"2008-06-19T00:00:00Z","timestamp":1213833600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cent Eur J Oper Res"],"published-print":{"date-parts":[[2008,12]]},"DOI":"10.1007\/s10100-008-0063-1","type":"journal-article","created":{"date-parts":[[2008,6,18]],"date-time":"2008-06-18T15:39:18Z","timestamp":1213803558000},"page":"345-358","source":"Crossref","is-referenced-by-count":35,"title":["Solution of the least squares method problem of pairwise comparison matrices"],"prefix":"10.1007","volume":"16","author":[{"given":"S\u00e1ndor","family":"Boz\u00f3ki","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2008,6,19]]},"reference":[{"key":"63_CR1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0167-6377(87)90026-5","volume":"6","author":"J Barzilai","year":"1987","unstructured":"Barzilai J, Cook WD, Golany B (1987) Consistent weights for judgements matrices of the relative importance of alternatives. Oper Res Lett 6: 131\u2013134","journal-title":"Oper Res Lett"},{"key":"63_CR2","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF00940197","volume":"54","author":"E Blankmeyer","year":"1987","unstructured":"Blankmeyer E (1987) Approaches to consistency adjustments. J Optim Theory Appl 54: 479\u2013488","journal-title":"J Optim Theory Appl"},{"key":"63_CR3","unstructured":"de Borda JC (1781) M\u00e9moire sur les \u00e9lectiones au scrutin. Histoire de l\u2019Acad\u00e9mie Royale des Sciences, Paris"},{"key":"63_CR4","first-page":"17","volume":"11","author":"S Boz\u00f3ki","year":"2003","unstructured":"Boz\u00f3ki S (2003) A method for solving LSM problems of small size in the AHP. Central Eur J Oper Res 11: 17\u201333","journal-title":"Central Eur J Oper Res"},{"key":"63_CR5","first-page":"255","volume":"13","author":"S Boz\u00f3ki","year":"2005","unstructured":"Boz\u00f3ki S, Lewis R (2005) Solving the Least Squares Method problem in the AHP for 3\u00a0\u00d7\u00a03 and 4\u00a0\u00d7\u00a04 matrices. Central Eur J Oper Res 13: 255\u2013270","journal-title":"Central Eur J Oper Res"},{"key":"63_CR6","first-page":"121","volume":"23","author":"S Boz\u00f3ki","year":"2006","unstructured":"Boz\u00f3ki S (2006) Weights from the least squares approximation of pairwise comparison matrices (in Hungarian, S\u00falyok meghat\u00e1roz\u00e1sa p\u00e1ros \u00f6sszehasonl\u00edt\u00e1s m\u00e1trixok legkisebb n\u00e9gyzetes k\u00f6zel\u00edt\u00e9se alapj\u00e1n). Alkal-mazott Matematikai Lapok 23: 121\u2013137","journal-title":"Alkal-mazott Matematikai Lapok"},{"key":"63_CR7","unstructured":"Buchberger B (1965) On Finding a Vector Space Basis of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal (in German). Ph.D. Dissertation, University of Innsbruck, Department of Mathematics, Austria"},{"key":"63_CR8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1177\/014662168601000106","volume":"10","author":"DV Budescu","year":"1986","unstructured":"Budescu DV, Zwick R, Rapoport A (1986) A comparison of the Eigenvector Method and the Geometric Mean procedure for ratio scaling. Appl Psychol Measure 10: 69\u201378","journal-title":"Appl Psychol Measure"},{"key":"63_CR9","first-page":"531","volume":"4","author":"ATW Chu","year":"1979","unstructured":"Chu ATW, Kalaba RE, Spingarn K (1979) A comparison of two methods for determining the weight belonging to fuzzy sets. J Optim Theory Appl 4: 531\u2013538","journal-title":"J Optim Theory Appl"},{"key":"63_CR10","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/0377-2217(88)90198-1","volume":"37","author":"WD Cook","year":"1988","unstructured":"Cook WD, Kress M (1988) Deriving weights from pairwise comparison ratio matrices: An axiomatic approach. Eur J Oper Res 37: 355\u2013362","journal-title":"Eur J Oper Res"},{"key":"63_CR11","unstructured":"Condorcet M (1785) Essai sur l\u2019Application de l\u2019Analyse \u00e0 la Probabilit\u00e9 des D\u00e9cisions Rendues \u00e1 la Pluralit\u00e9 des Voix, Paris"},{"key":"63_CR12","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0022-2496(85)90002-1","volume":"29","author":"G Crawford","year":"1985","unstructured":"Crawford G, Williams C (1985) A note on the analysis of subjective judgment matrices. J Math Psychol 29: 387\u2013405","journal-title":"J Math Psychol"},{"key":"63_CR13","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/0022-2496(84)90013-0","volume":"28","author":"P De Jong","year":"1984","unstructured":"De Jong P (1984) A statistical approach to Saaty\u2019s scaling methods for priorities. J Math Psychol 28: 467\u2013478","journal-title":"J Math Psychol"},{"key":"63_CR14","unstructured":"DeGraan JG (1980) Extensions of the multiple criteria analysis method of T.L. Saaty (Technical Report m.f.a. 80-3) Leischendam, The Netherlands: National Institute for Water Supply. Presented at EURO IV, Cambridge, England, July 22-25"},{"key":"63_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/BF01389312","volume":"29","author":"FJ Drexler","year":"1978","unstructured":"Drexler FJ (1978) Eine Methode zur Berechnung s\u00e4mtlicher L\u00f6sungen von Polynomgleichungssystemen. Numer Math 29: 45\u201358","journal-title":"Numer Math"},{"key":"63_CR16","doi-asserted-by":"crossref","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 adjustment for pairwise comparison matrices. Numer Linear Algebra Appl 10: 689\u2013700","journal-title":"Numer Linear Algebra Appl"},{"key":"63_CR17","unstructured":"Fechner GT (1860) Elemente der Psychophysik. Breitkopf und H\u00e4rtel, Leipzig"},{"key":"63_CR18","doi-asserted-by":"crossref","unstructured":"F\u00fcl\u00f6p J (2008) A method for approximating pairwise comparison matrices by consistent matrices. J Global Optim (in print)","DOI":"10.1007\/s10898-008-9303-0"},{"key":"63_CR19","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1006\/jsco.1998.0272","volume":"28","author":"T Gao","year":"1999","unstructured":"Gao T, Li TY, Wang X (1999) Finding isolated zeros of polynomial systems in $${\\mathbb{C}^n}$$ with stable mixed volumes. J Symbolic Comput 28: 187\u2013211","journal-title":"J Symbolic Comput"},{"key":"63_CR20","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF01582106","volume":"16","author":"CB Garcia","year":"1979","unstructured":"Garcia CB, Zangwill WI (1979) Finding all solutions to polynomial systems and other systems of equations. Math Program 16: 159\u2013176","journal-title":"Math Program"},{"key":"63_CR21","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/S0377-2217(02)00755-5","volume":"154","author":"SI Gass","year":"2004","unstructured":"Gass SI, Rapcs\u00e1k T (2004) Singular value decomposition in AHP. Eur J Oper Res 154: 573\u2013584","journal-title":"Eur J Oper Res"},{"key":"63_CR22","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/0377-2217(93)90165-J","volume":"69","author":"B Golany","year":"1993","unstructured":"Golany B, Kress M (1993) A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices. Eur J Oper Res 69: 210\u2013220","journal-title":"Eur J Oper Res"},{"key":"63_CR23","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/0377-2217(94)90153-8","volume":"73","author":"A Hashimoto","year":"1994","unstructured":"Hashimoto A (1994) A note on deriving weights from pairwise comparison ratio matrices. Eur J Oper Res 73: 144\u2013149","journal-title":"Eur J Oper Res"},{"key":"63_CR24","unstructured":"Jensen RE (1983) Comparison of Eigenvector, Least squares, Chi square and Logarithmic least square methods of scaling a reciprocal matrix. Working Paper 153. http:\/\/www.trinity.edu\/rjensen\/127wp\/127wp.htm"},{"key":"63_CR25","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0022-2496(84)90003-8","volume":"28","author":"RE Jensen","year":"1984","unstructured":"Jensen RE (1984) An Alternative Scaling Method for Priorities in Hierarchical Structures. J Math Psychol 28: 317\u2013332","journal-title":"J Math Psychol"},{"key":"63_CR26","first-page":"139","volume":"36","author":"G K\u00e9ri","year":"2005","unstructured":"K\u00e9ri G (2005) Criteria for pairwise comparison matrices (in Hungarian. Krit\u00e9riumok p\u00e1ros \u00f6sszehasonl\u00edt\u00e1s m\u00e1trixokra). Szigma 36: 139\u2013148","journal-title":"Szigma"},{"key":"63_CR27","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1017\/S0962492900002749","volume":"6","author":"TY Li","year":"1997","unstructured":"Li TY (1997) Numerical solution of multivariate polynomial systems by homotopy continuation methods. Acta Numer 6: 399\u2013436","journal-title":"Acta Numer"},{"key":"63_CR28","volume-title":"The analytic hierarchy process","author":"TL Saaty","year":"1980","unstructured":"Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York"},{"key":"63_CR29","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0270-0255(84)90008-3","volume":"5","author":"TL Saaty","year":"1984","unstructured":"Saaty TL, Vargas LG (1984) Comparison of eigenvalues, logarithmic least squares and least squares methods in estimating ratios. Math Model 5: 309\u2013324","journal-title":"Math Model"},{"key":"63_CR30","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1037\/h0071663","volume":"4","author":"EL Thorndike","year":"1920","unstructured":"Thorndike EL (1920) A constant error in psychological ratings. J Appl Psychol 4: 25\u201329","journal-title":"J Appl Psychol"},{"key":"63_CR31","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1037\/h0065439","volume":"21","author":"LL Thurstone","year":"1927","unstructured":"Thurstone LL (1927) The Method of Paired Comparisons for Social Values. J Abnormal Social Psychol 21: 384\u2013400","journal-title":"J Abnormal Social Psychol"},{"key":"63_CR32","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0038-0121(86)90046-7","volume":"20","author":"F Zahedi","year":"1986","unstructured":"Zahedi F (1986) A simulation study of estimation methods in the analytic hierarchy process. Socio-Econ Plan Sci 20: 347\u2013354","journal-title":"Socio-Econ Plan Sci"}],"container-title":["Central European Journal of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-008-0063-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10100-008-0063-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10100-008-0063-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:49:26Z","timestamp":1559123366000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10100-008-0063-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6,19]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["63"],"URL":"https:\/\/doi.org\/10.1007\/s10100-008-0063-1","relation":{},"ISSN":["1435-246X","1613-9178"],"issn-type":[{"value":"1435-246X","type":"print"},{"value":"1613-9178","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6,19]]}}}