{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T17:24:25Z","timestamp":1775582665580,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,11,9]],"date-time":"2014-11-09T00:00:00Z","timestamp":1415491200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2015,7]]},"DOI":"10.1007\/s10898-014-0253-4","type":"journal-article","created":{"date-parts":[[2014,11,14]],"date-time":"2014-11-14T16:29:00Z","timestamp":1415982540000},"page":"529-543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Heuristic rating estimation: geometric approach"],"prefix":"10.1007","volume":"62","author":[{"given":"Konrad","family":"Ku\u0142akowski","sequence":"first","affiliation":[]},{"given":"Katarzyna","family":"Grobler-D\u0119bska","sequence":"additional","affiliation":[]},{"given":"Jaros\u0142aw","family":"W\u0105s","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,11,9]]},"reference":[{"key":"253_CR1","doi-asserted-by":"crossref","unstructured":"Boz\u00f3ki, S., F\u00fcl\u00f6p, J., R\u00f3nyai, L.: On optimal completion of incomplete pairwise comparison matrices. Math. Comput. Model. 52(1\u20132), 318\u2013333 (2010). doi: 10.1016\/j.mcm.2010.02.047","DOI":"10.1016\/j.mcm.2010.02.047"},{"key":"253_CR2","doi-asserted-by":"crossref","unstructured":"Boz\u00f3ki, S., Rapcsak, T.: On Saaty\u2019s and Koczkodaj\u2019s inconsistencies of pairwise comparison matrices. J. Glob. Optim. 42(2), 157\u2013175 (2008)","DOI":"10.1007\/s10898-007-9236-z"},{"key":"253_CR3","doi-asserted-by":"crossref","unstructured":"Brunelli, M., Canal, L., Fedrizzi, M.: Inconsistency indices for pairwise comparison matrices: a numerical study. Ann. Oper. Res. 211, 493\u2013509 (2013). doi: 10.1007\/s10479-013-1329-0","DOI":"10.1007\/s10479-013-1329-0"},{"key":"253_CR4","doi-asserted-by":"crossref","unstructured":"Brunelli, M., Fedrizzi, M.: Axiomatic properties of inconsistency indices. J. Oper. Res. Soc. (2013). doi: 10.1057\/jors.2013.135","DOI":"10.1057\/jors.2013.135"},{"issue":"2","key":"253_CR5","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s00355-011-0598-2","volume":"40","author":"JM Colomer","year":"2011","unstructured":"Colomer, J.M.: Ramon Llull: from \u2018Ars electionis\u2019 to social choice theory. Soc. Choice Welf. 40(2), 317\u2013328 (2011)","journal-title":"Soc. Choice Welf."},{"key":"253_CR6","doi-asserted-by":"crossref","unstructured":"Crawford, G.B.: The geometric mean procedure for estimating the scale of a judgement matrix. Math. Model. 9(3\u20135), 327\u2013334 (1987). doi: 10.1016\/0270-0255(87)90489-1","DOI":"10.1016\/0270-0255(87)90489-1"},{"key":"253_CR7","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1613\/jair.2697","volume":"35","author":"P Faliszewski","year":"2009","unstructured":"Faliszewski, P., Hemaspaandra, E., Hemaspaandra, L.A., Rothe, J.: Llull and Copeland voting computationally resist bribery and constructive control. J. Artif. Intell. Res. (JAIR) 35, 275\u2013341 (2009)","journal-title":"J. Artif. Intell. Res. (JAIR)"},{"key":"253_CR8","first-page":"71","volume":"1","author":"J F\u00fcl\u00f6p","year":"2010","unstructured":"F\u00fcl\u00f6p, J., Koczkodaj, W.W., Szarek, S.J.: A different perspective on a scale for pairwise comparisons. Trans. Comput. Collect. Intell. 1, 71\u201384 (2010)","journal-title":"Trans. Comput. Collect. Intell."},{"issue":"11","key":"253_CR9","first-page":"14,336","volume":"38","author":"A Ishizaka","year":"2011","unstructured":"Ishizaka, A., Labib, A.: Review of the main developments in the analytic hierarchy process. Expert Syst. Appl. 38(11), 14,336\u201314,345 (2011)","journal-title":"Expert Syst. Appl."},{"key":"253_CR10","doi-asserted-by":"crossref","unstructured":"Ishizaka, A., Lusti, M.: How to derive priorities in AHP: a comparative study. Cent. Eur. J. Oper. Res. 14(4), 387\u2013400 (2006). http:\/\/ideas.repec.org\/a\/spr\/cejnor\/v14y2006i4p387-400.html","DOI":"10.1007\/s10100-006-0012-9"},{"issue":"4","key":"253_CR11","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1093\/jigpal\/jzr018","volume":"20","author":"R Janicki","year":"2012","unstructured":"Janicki, R., Zhai, Y.: On a pairwise comparison-based consistent non-numerical ranking. Log. J. IGPL 20(4), 667\u2013676 (2012)","journal-title":"Log. J. IGPL"},{"key":"253_CR12","doi-asserted-by":"crossref","unstructured":"Kacprzyk, J., Zadrozny, S., Fedrizzi, M., Nurmi, H.: On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: a survey and some perspectives. In: Studies in Fuzziness and Soft Computing, Studies in Fuzziness and Soft Computing, vol. 220, pp. 263\u2013295. Springer, Berlin (2008)","DOI":"10.1007\/978-3-540-73723-0_14"},{"issue":"3","key":"253_CR13","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1007\/s11192-014-1258-y","volume":"99","author":"W Koczkodaj","year":"2014","unstructured":"Koczkodaj, W., Ku\u0142akowski, K., Lig\u0119za, A.: On the quality evaluation of scientific entities in Poland supported by consistency-driven pairwise comparisons method. Scientometrics 99(3), 911\u2013926 (2014). doi: 10.1007\/s11192-014-1258-y","journal-title":"Scientometrics"},{"issue":"7","key":"253_CR14","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/0895-7177(93)90059-8","volume":"18","author":"WW Koczkodaj","year":"1993","unstructured":"Koczkodaj, W.W.: A new definition of consistency of pairwise comparisons. Math. Comput. Model. 18(7), 79\u201384 (1993). doi: 10.1016\/0895-7177(93)90059-8","journal-title":"Math. Comput. Model."},{"issue":"3","key":"253_CR15","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/S0898-1221(99)00048-6","volume":"37","author":"WW Koczkodaj","year":"1999","unstructured":"Koczkodaj, W.W., Or\u0142owski, M.: Computing a consistent approximation to a generalized pairwise comparisons matrix. Comput. Math. Appl. 37(3), 79\u201385 (1999)","journal-title":"Comput. Math. Appl."},{"key":"253_CR16","doi-asserted-by":"crossref","unstructured":"Ku\u0142akowski, K.: A heuristic rating estimation algorithm for the pairwise comparisons method. Cent. Eur. J. Oper. Res. 1\u201317 (2013). doi: 10.1007\/s10100-013-0311-x","DOI":"10.1007\/s10100-013-0311-x"},{"key":"253_CR17","doi-asserted-by":"crossref","unstructured":"Ku\u0142akowski, K.: Heuristic rating estimation approach to the pairwise comparisons nethod. Fundam. Inform. (to be appeared) 133, 367\u2013386 (2014). doi: 10.3233\/FI-2014-1081","DOI":"10.3233\/FI-2014-1081"},{"key":"253_CR18","unstructured":"Ku\u0142akowski, K.: Notes on the existence of solutions in the pairwise comparisons method using the heuristic rating estimation approach. CoRR abs\/1402.4064 (2014)"},{"key":"253_CR19","unstructured":"Lotfi, F.H., Fallahnejad, R., Navidi, N.: Ranking efficient units in DEA by using TOPSIS method. Appl. Math. Sci. (2011)"},{"issue":"3","key":"253_CR20","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0165-0114(02)00383-4","volume":"134","author":"L Mikhailov","year":"2003","unstructured":"Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgements. Fuzzy Sets Syst. 134(3), 365\u2013385 (2003)","journal-title":"Fuzzy Sets Syst."},{"issue":"4","key":"253_CR21","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","volume":"7","author":"JA Nelder","year":"1965","unstructured":"Nelder, J.A., Mead, R.: A simplex-method for function minimization. Comput. J. 7(4), 308\u2013313 (1965)","journal-title":"Comput. J."},{"key":"253_CR22","doi-asserted-by":"crossref","unstructured":"Peterson, G.L., Brown, T.C.: Economic valuation by the method of paired comparison, with emphasis on evaluation of the transitivity axiom. Land Econ. 240\u2013261 (1998)","DOI":"10.2307\/3147054"},{"issue":"2","key":"253_CR23","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/0024-3795(77)90073-8","volume":"18","author":"RJ Plemmons","year":"1976","unstructured":"Plemmons, R.J.: M-matrix characterizations. I\u2014nonsingular M-matrices. Linear Algebra Appl. 18(2), 175\u2013188 (1976)","journal-title":"Linear Algebra Appl."},{"key":"253_CR24","volume-title":"Numerical Mathematics","author":"A Quarteroni","year":"2000","unstructured":"Quarteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, Berlin (2000)"},{"key":"253_CR25","doi-asserted-by":"crossref","unstructured":"Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15(3), 234\u2013281 (1977). doi: 10.1016\/0022-2496(77)90033-5","DOI":"10.1016\/0022-2496(77)90033-5"},{"key":"253_CR26","doi-asserted-by":"crossref","unstructured":"Saaty, T.L.: The analytic hierarchy and analytic network processes for the measurement of intangible criteria and for decision-making. In: Multiple Criteria Decision Analysis: State of the Art Surveys, International Series in Operations Research and Management Science, vol. 78, pp. 345\u2013405. Springer, New York (2005). doi: 10.1007\/0-387-23081-5_9","DOI":"10.1007\/0-387-23081-5_9"},{"issue":"02","key":"253_CR27","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1090\/noti944","volume":"60","author":"TL Saaty","year":"2013","unstructured":"Saaty, T.L.: On the measurement of intangibles. A principal eigenvector approach to relative measurement derived from paired comparisons. Not. Am. Math. Soc. 60(02), 192 (2013)","journal-title":"Not. Am. Math. Soc."},{"key":"253_CR28","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1037\/0033-295X.101.2.266","volume":"101","author":"LL Thurstone","year":"1994","unstructured":"Thurstone, L.L.: A law of comparative judgment, reprint of an original work published in 1927. Psychol. Rev. 101, 266\u2013270 (1994)","journal-title":"Psychol. Rev."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0253-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-014-0253-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0253-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T20:39:13Z","timestamp":1598474353000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-014-0253-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,11,9]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,7]]}},"alternative-id":["253"],"URL":"https:\/\/doi.org\/10.1007\/s10898-014-0253-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,11,9]]}}}