Czasopismo
2016
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Vol. 144, nr 3/4
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279--289
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the latter’s components is at least as close to the corresponding element of the pairwise comparison matrix as the one of the former’s components is, and the latter’s approximation is strictly better in at least one position. A pairwise comparison matrix is called simple perturbed if it differs from a consistent pairwise comparison matrix in one element and its reciprocal. One of the classical weighting methods, the eigenvector method is analyzed. It is shown in the paper that the principal right eigenvector of a simple perturbed pairwise comparison matrix is efficient. An open problem is exposed: the search for a necessary and sufficient condition of that the principal right eigenvector is efficient.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
279--289
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
- Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende utca 13-17, 1111 Budapest, Hungary, abele-nagy.kristof@sztaki.mta.hu
- Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Fővám tér 8, 1093 Budapest, Hungary
autor
- Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende utca 13-17, 1111 Budapest, Hungary, bozoki.sandor@sztaki.mta.hu
- Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Fővám tér 8, 1093 Budapest, Hungary
Bibliografia
- [1] Bajwa G, Choo EU, WedleyWC. Effectiveness analysis of deriving priority vectors from reciprocal pairwise comparison matrices. Asia-Pacific Journal of Operational Research. 2008;25(3):279–299. Available from: http://www.worldscientific.com/doi/abs/10.1142/S0217595908001754. doi:10.1142/S0217595908001754.
- [2] Choo EU, Wedley WC. A common framework for deriving preference values from pairwise comparison matrices. Computers & Operations Research. 2004;31(6):893–908. ISSN: 0305-0548. Available from: http://www.sciencedirect.com/science/article/pii/S030505480300042X. doi: http://dx.doi.org/10.1016/S0305-0548(03)00042-X. doi: 10.1016/S0305-0548(03)00042-X.
- [3] Dijkstra TK. On the extraction of weights from pairwise comparison matrices. Central European Journal of Operations Research. 2013;21(1):103–123. ISSN: 1435-246X. Available from: http://link.springer.com/article/10.1007/s10100-011-0212-9. doi: 10.1007/s10100-011-0212-9.
- [4] Golany B, Kress M. A multicriteria evaluation of methods for obtaining weights from ratio-scale matrices. European Journal of Operational Research. 1993;69(2):210–220. ISSN: 0377-2217. Available from: http://www.sciencedirect.com/science/article/pii/037722179390165J. doi: 10.1016/0377-2217(93)90165-J.
- [5] Saaty TL. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology. 1977;15(3):234–281. ISSN: 0022-2496. Available from: http://www.sciencedirect.com/science/article/pii/0022249677900335. doi:10.1016/0022-2496(77)90033-5.
- [6] Zeleny M. Multiple criteria decision making. McGraw-Hill; 1982. ISBN: 0-07-072795-3.
- [7] Blanquero R, Carrizosa E, Conde E. Inferring efficient weights from pairwise comparison matrices. Mathematical Methods of Operations Research. 2006;64(2):271–284. Available from: http://link.springer.com/article/10.1007/s00186-006-0077-1.
- [8] Conde E, Pérez MdlPR. A linear optimization problem to derive relative weights using an interval judgement matrix. European Journal of Operational Research. 2010;201(2):537–544. ISSN: 0377-2217. Available from: http://www.sciencedirect.com/science/article/pii/S0377221709001878. doi:10.1016/j.ejor.2009.03.029.
- [9] Fedrizzi M. Obtaining non-dominated weights from preference relations through norm-induced distances. XXXVII Meeting of the Italian Association for Mathematics Applied to Economic and Social Sciences (AMASES), September 5-7, 2013, Stresa, Italy; Available from: http://www.amases2013.eco.uninsubria.it/site/.
- [10] Bozóki S. Inefficient weights from pairwise comparison matrices with arbitrarily small inconsistency. Optimization. 2014;63(12):1893–1901. ISSN: 0233-1934. Available from: http://www.tandfonline.com/doi/full/10.1080/02331934.2014.903399. doi:10.1080/02331934.2014.903399.
- [11] Bozóki S, Fülöp J, Poesz A. On pairwise comparison matrices that can be made consistent by the modification of a few elements. Central European Journal of Operations Research. 2011;19(2):157–175. ISSN:1613-9178. Available from: http://link.springer.com/article/10.1007%2Fs10100-010-0136-9. doi:10.1007/s10100-010-0136-9.
- [12] Cook WD, Kress M. Deriving weights from pairwise comparison ratio matrices: An axiomatic approach. European Journal of Operational Research. 1988;37(3):355–362. ISSN: 0377-2217. Available from: http://www.sciencedirect.com/science/article/pii/0377221788901981#. doi:10.1016/0377-2217(88)90198-1.
- [13] Brunelli M, Fedrizzi M. Axiomatic properties of inconsistency indices for pairwise comparisons. Journal of the Operational Research Society. 2014;66:1–15. ISSN: 0160-5682. Available from: http://www.palgrave-journals.com/jors/journal/v66/n1/full/jors2013135a.html. doi: 10.1057/jors.2013.135.
- [14] Farkas A. The analysis of the principal eigenvector of pairwise comparison matrices. Acta Polytechnica Hungarica. 2007;4(2):99–115. ISSN: 1785-8860. Available from: http://www.uni-obuda.hu/journal/Farkas_10.pdf.
- [15] Farkas A, Rózsa P, Stubnya E. Transitive matrices and their applications. Linear Algebra and its Applications. 1999;302-303:423–433. ISSN: 0024-3795. Available from: http://www.sciencedirect.com/science/article/pii/S0024379599002086. doi: 10.1016/S0024-3795(99)00208-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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