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2020 | 30 | nr 2 | 77--89
Tytuł artykułu

Satisfaction of the Condition of Order Preservation : a Simulation Study

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty's consistency index below 0.10), and the more inconsistent matrices (Saaty's consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj's inconsistency index and Saaty's consistency index, respectively, and we provide graphs to illustrate these relationships. (original abstract)
Rocznik
Tom
30
Numer
Strony
77--89
Opis fizyczny
Twórcy
  • Silesian University in Opava, Czech Republic
  • AGH University of Science and Technology, Cracow, Poland
Bibliografia
  • [1] AGUARON J., MORENO-JIMENEZ J.M., The geometric consistency index: Approximated threshold, Eur. J. Oper. Res., 2003, 147 (1), 137-145.
  • [2] BANA E COSTA C.A., VANSNICK J., A critical analysis of the eigenvalue method used to derive priorities in AHP, Eur. J. Oper. Res., 2008, 187 (3), 1422-1428.
  • [3] BARZILAI J., Consistency measures for pairwise comparison matrices, J. Multi-Crit. Dec. Anal., 7 (3), 1998, 123-132.
  • [4] BOZÓKI S., RAPCSÁK T., On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices, J. Global Opt., 2008, 42 (2), 157-175.
  • [5] BRUNELLI M., CANAL L., FEDRIZZI M., Inconsistency indices for pairwise comparison matrices: a numerical study, Ann. Oper. Res., 2013, 211 (1), 493-509.
  • [6] BRUNELLI M., FEDRIZZI M., Axiomatic properties of inconsistency indices for pairwise comparisons, J. Oper. Res. Soc., 2015, 66 (1), 1-15.
  • [7] BRUNELLI M., Studying a set of properties of inconsistency indices for pairwise comparisons, Ann. Oper. Res., 2017, 248 (1-2), 143-161.
  • [8] BRUNELLI M., A survey of inconsistency indices for pairwise comparisons, Int. J. Gen. Syst., 2018, 47 (8), 751-771.
  • [9] CAVALLO B., Functional relations and Spearman correlation between consistency indices, J. Oper. Res. Soc., 2020, 71 (2), 301-311.
  • [10] CAVALLO B., D'APUZZO L., Preservation of preferences intensity of an inconsistent pairwise comparison matrix, Int. J. Appr. Reas., 2020, 116, 33-42.
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  • [12] CRAWFORD G.B., The geometric mean procedure for estimating the scale of a judgement matrix, Math. Model., 1987, 9 (3), 327-334.
  • [13] CSATÓ L., Characterization of an inconsistency ranking for pairwise comparison matrices, Ann. Oper. Res., 2018, 261 (1-2), 155-165.
  • [14] CSATÓ L., PETRÓCZY D.G., Rank monotonicity and the eigenvector method, Manuscript, 2020, ArXiv: 1902.10790.
  • [15] GOLDEN B., WANG Q., An alternate measure of consistency, [In:] B. Golden, E. Wasil, P.T. Harker (Eds.), The Analytic Hierarchy Process, Applications and Studies, Springer-Verlag, Berlin 1989, 68-81.
  • [16] HERMAN M.W., KOCZKODAJ W.W., A Monte Carlo Study of Parwise Comparison, Inf. Proc. Lett., 1996, 57, 25-29.
  • [17] ISHIZAKA A., LUSTI M., How to derive priorities in AHP: a comparative study, Central Eur. J. Oper. Res., 2006, 14 (4), 387-400.
  • [18] KOCZKODAJ W.W., A new definition of consistency of pairwise comparisons, Math. Comp. Model., 1993, 18 (7), 79-84.
  • [19] KULAKOWSKI K., Notes on Order Preservation and Consistency in AHP, Eur. J. Oper. Res., 2015, 245, 333-337.
  • [20] KULAKOWSKI K., MAZUREK J., RAMÍK J., SOLTYS M., When is the condition of preservation met?, Eur. J. Oper. Res., 2019, 277, 248-254.
  • [21] MAZUREK J., Some notes on the properties of inconsistency indices in pairwise comparisons, Oper. Res. Dec., 2018, 1, 27-42.
  • [22] MAZUREK J., RAMÍK J., Some new properties of inconsistent pairwise comparison matrices, Int. J. Appr. Reas., 2019, 113, 119-132.
  • [23] SAATY T.L., A scaling method for priorities in hierarchical structures, J. Math. Psych., 1977, 15 (3), 234-281.
  • [24] SAATY T.L., Analytic Hierarchy Process, McGraw-Hill, New York 1980.
  • [25] https://data.mendeley.com/datasets/kskpwfcf9z/1
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171603307

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