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Some notes on the properties of inconsistency indices in pairwise comparisons

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Języki publikacji
EN
Abstrakty
EN
Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies have focused on the means of expressing and measuring this inconsistency, and several inconsistency indices have been proposed as an alternative to Saaty’s inconsistency index, CI, and consistency ratio, CR, for reciprocal pairwise comparison matrices. The aims of this paper are threefold: firstly, a row inconsistency index (RIC) is proposed and the properties of this index are examined. Secondly, a comparison of selected inconsistency indices for a corner pairwise comparison matrix is provided. Last, but not least, another axiom about the upper bound on the value of an inconsistency index is postulated, and a set of selected inconsistency indices is examined with respect to this axiom. Numerical examples complete the paper.
Rocznik
Strony
27--42
Opis fizyczny
Bibliogr. 30 poz., rys.
Twórcy
autor
  • School of Business Administration in Karvina, Silesian University in Opava, Czech Republic
Bibliografia
  • [1] AGUARÓN J., MORENO-JIMENEZ J.M., The geometric consistency index. Approximated threshold, Eur. J. Oper. Res., 2003, 147 (1), 137–145.
  • [2] ALONSO J.A., LAMATA M.T., Consistency in the analytic hierarchy process. A new approach, Int. J. Uncertainty, Fuzz. Knowl. Syst., 2006, 14 (4), 445–459.
  • [3] 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.
  • [4] BARZILAI J., Consistency measures for pairwise comparison matrices, J. Multi-Crit. Dec. Anal., 1998, 7 (3), 123–132.
  • [5] BRUNELLI M., CANAL L., FEDRIZZI M., Inconsistency indices for pairwise comparison matrices. A numerical study, Res. 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, Res. Oper. Res., 2017, 248 (1–2), 143–161.
  • [8] CAVALLO B., D’APUZZO L., A general unified framework for pairwise comparison matrices in multicriterial methods, 2009, Int. J. Intell. Syst., 24 (4), 377–398.
  • [9] CHANDRAN B., GOLDEN B., WASIL E., Linear programming models for estimating weights in the analytic hierarchy process, J. Comp. Oper. Res., 2005, 32 (9), 2235–2254.
  • [10] CSATÓ L., Characterization of an inconsistency measure for pairwise comparison matrices, 2016, arXiv:1610.07388v2.
  • [11] DYER J.S., Remarks on the analytic hierarchy process, Manage. Sci., 1990, 36 (3), 249–258.
  • [12] 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, Berlin 1989, 68–81.
  • [13] ISHIZAKA A., LUSTI M., How to derive priorities in AHP: a comparative study, Central Eur. J. Oper. Res., 2006, 14 (4), 387–400.
  • [14] KOCZKODAJ W., A new definition of consistency of pairwise comparisons, Math. Comp. Model., 1993, 18 (7), 79–84.
  • [15] KOCZKODAJ W., SZYBOWSKI J., The limit of inconsistency reduction in pairwise comparisons, Int. J. Appl. Math. Comp. Sci., 2016, 26 (3), 721–729.
  • [16] KOCZKODAJ W., SZWARC R., On axiomatization of inconsistency indicators for pairwise comparisons, Fund. Inform., 2014, 132 (4), 485–500.
  • [17] KOCZKODAJ W., MAGNOT J.-P., MAZUREK J., PETERS J.F., RAKSHANI H., SOLTYS M., STRZALKA D., SZYBOWSKI J., TOZZI A., On normalization of inconsistency indicators in pairwise comparisons, Int. J. Appr. Reas., 2017, 86, 73–79.
  • [18] KOU G., LIN C., A cosine maximization method for the priority vector derivation in AHP, Eur. J. Oper. Res., 2014, 235, 225–232.
  • [19] KULAKOWSKI K., Notes on order preservation and consistency in AHP, Eur. J. Oper. Res., 2015, 245, 333–337.
  • [20] MILLER G., The magical number seven, plus or minus two. Some limits on our capacity for processing information, Psych. Rev., 1956, 63 (2), 81–97.
  • [21] PELÁEZ J.I., LAMATA M.T., A new measure of inconsistency for positive reciprocal matrices, Comp. Math. Appl., 2003, 46 (12), 1839–1845.
  • [22] RAMÍK J., Pairwise comparison matrix with fuzzy elements on alo-groups, Inf. Sci., 2015, 297, 236–253.
  • [23] RAMÍK J., KORVÍNY P., Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean, Fuzzy Sets Syst., 2010, 161, 1604–1613.
  • [24] SAATY T.L., A scaling method for priorities in hierarchical structures, J. Math. Psych., 1977, 15, 234–281.
  • [25] SAATY T.L., Analytic Hierarchy Process, McGraw-Hill, New York 1980.
  • [26] SAATY T.L., Decision making. The analytic hierarchy and network processes (AHP/ANP), J. Syst. Sci. Syst. Eng., 2004, 13 (1), 1–34.
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Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d18b25d0-5c97-4bbf-8ea4-ae16aae6409d
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