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New optimization based method for estimating priority weights

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The estimation of priority vectors from pairwise comparison matrices is a core of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (EM). Despite its popularity, various shortcomings of the EM have been described in literature. In this paper a new method for deriving priority vectors is proposed. This method makes use of the idea underlying the EM but in difference to the latter, the new one is optimization based. Important features of this new technique are studied via computer simulations and illustrated by some numerical examples.
Rocznik
Strony
33--44
Opis fizyczny
Bibliogr. 15 poz., tab.
Twórcy
  • Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland
Bibliografia
  • [1] Saaty T.L., Scaling method for priorities in hierarchical structures, J. Math. Psychol. 1977, 15, 3, 234-28.
  • [2] Basak I., Comparison of statistical procedures in analytic hierarchy process using a ranking test, Math. Comp. Model. 1998, 28, 105-118.
  • [3] Budescu D.V., Zwick R., Rapoport A., Comparison of the analytic hierarchy process and the geometric mean procedure for ratio scaling, Appl. Psychol. Meas. 1986, 10, 69-78.
  • [4] Choo E.U., Wedley W.C., A common framework for deriving preference values from pairwise comparison matrices, Comp. Oper. Res. 2004, 31, 893-908.
  • [5] Grzybowski A.Z., Goal Programming Approach for Deriving Priority Vectors - Some New Ideas, Scientific Research of the Institute of Mathematics and Computer Science 2010, 1(9), 17-27.
  • [6] Grzybowski A.Z., Note on a new optimization based approach for estimating priority weights and related consistency index, Expert Systems with Applications 2012, 39, 11699-11708.
  • [7] Kazibudzki P.T., Comparison of analytic hierarchy process and some new optimization procedures for ratio scaling, Scientific Research of the Institute of Mathematics and Computer Science 2011, 1(10), 101-108.
  • [8] Lin C-C., A revised framework for deriving preference values from pairwise comparison matrices, Euro. J. Oper. Res. 2007, 176, 1145-1150.
  • [9] Crawford G., Williams C.A., A note on the analysis of subjective judgment matrices, J. Math. Psychol. 1985, 29, 387-405.
  • [10] Hovanov N.V., Kolari J.W., Sokolov M.V., Deriving weights from general pairwise comparison matrices, Math. Soc. Sci. 2008, 55, 205-220.
  • [11] Lipovetsky S., Tishler A., Interval estimation of priorities in the AHP, Euro. J. Oper. Res. 114, 1997, 153-164.
  • [12] Saaty T.L., Decision making with the AHP Why is the principal eigenvector necessary, Euro. J. Oper. Res. 2003, 145, 85-91.
  • [13] Zahedi F., A simulation study of estimation methods in the analytic hierarchy process, Socio-Econ. Plann. Sci. 1986, 20, 347-354.
  • [14] Koczkodaj W.W., A new definition of consistency of pairwise comparisons, Mathematical and computer modeling 1993, 18(7), 79-84.
  • [15] Saaty T.L., Vargas L.G. Comparison of eigenvalue, logarithmic least square and least square methods in estimating ratio, J. Math. Model. 1984, 5, 309-324.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-372120b1-d214-4179-af9b-11bd75775ed5
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