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Fast Convergence of Distance-based Inconsistency in Pairwise Comparisons

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This study presents theoretical proof and empirical evidence of the reduction algorithm convergence for the distance-based inconsistency in pairwise comparisons. Our empirical research shows that the convergence very quick. It usually takes less than 10 reductions to bring the inconsistency of the pairwise comparisons matrix below the assumed threshold of 1/3 (sufficient for most applications). We believe that this is the first Monte Carlo study demonstrating such results for the convergence speed of inconsistency reduction in pairwise comparisons.
Wydawca
Rocznik
Strony
355--367
Opis fizyczny
Bibliogr. 14 poz., wykr.
Twórcy
  • Computer Science, Laurentian University 935 Ramsey Lake Road, Sudbury ON P3E 2C6, Canada
autor
  • Jagiellonian University Department of Mathematics and Computer Science Prof. St. Łojasiewicza 6, 30-348 Kraków, Poland
autor
  • AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krak´ow, Poland
autor
  • Computer Science, Laurentian University 935 Ramsey Lake Road, Sudbury ON P3E 2C6, Canada
Bibliografia
  • [1] S. Bozoki and T. Rapcsak. On saaty’s and koczkodaj’s inconsistencies of pairwise comparison matrices. Journal of Global Optimization, 42:157–175, 2008.
  • [2] Marie Jean Antoine Nicolas de Caritat Marquis deCondorcet. Essay on the Application of Analysis to the Probability of Majority Decisions. De LiImprimerie Royale,Paris, France, 1785.
  • [3] Zbigniew Duszak and Waldemar W. Koczkodaj. Generalization of a New Definition of Consistency for Pairwise Comparisons. Inf. Process. Lett., 52(5):273–276, 1994.
  • [4] G.T. Fechner. Elemente der Psychophysik. Leipzig: Breitkopf und H¨artel, 2:p. 559, 1860.
  • [5] Shapiro H.N. Gerard, H.B. Determining the Degree of Inconsistency in a Set of Paired Comparisons. Psychometrika, 23(1):p33–46, 1958.
  • [6] A.Z. Grzybowski. Note on a new optimization based approach for estimating priority weights and related consistency index. Expert Systems with Applications, 39(14):11699–11708, 2012.
  • [7] Michael W. Herman and Waldemar W. Koczkodaj. A Monte Carlo study of pairwise comparison Amsterdam. The Netherlands, vol. 57 (1):pp. 25–29, 1996.
  • [8] R.J. Hill. A note on inconsistency in paired comparison judgments. American Sociological Review, 18(5):564–566, 1953.
  • [9] Wlodzimierz Holsztynski and Waldemar W. Koczkodaj. Convergence of Inconsistency Algorithms for the Pairwise Comparisons. Inf. Process. Lett., 59(4):197–202, 1996.
  • [10] M.G. Kendall and B. Babington-Smith. On the method of paired comparisons. biometrika, 31, 324–345. Biometrika, 31(3/4):324–345, 1939.
  • [11] W. Koczkodaj. A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling, (18)7:79–84, 1993.
  • [12] Waldemar W. Koczkodaj and S.J. Szarek. On distance-based inconsistency reduction algorithms for pairwise comparisons. Logic Journal of the IGPL, 18(6):859–869, 2010.
  • [13] W.W. Koczkodaj and R. Szwarc. On axiomatization of inconsistency indicators in pairwise comparisons. Fundamenta Informaticae, 32(4):485–500, 2014.
  • [14] T.L. Saaty. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3):234–281, 1977.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b1ebfecd-ee23-472a-9a01-8ed6a664fe2d
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