Redefinition of triad’s inconsistency and its impact on the consistency measurement of pairwise comparison matrix

• Autorzy: Kazibudzki P.

Identyfikatory

DOI

10.17512/jamcm.2016.1.07

• Języki publikacji: EN

Abstrakty

EN

There is a theory which meets a prescription of the efficient and effective multicriteria decision making support system called the Analytic Hierarchy Process (AHP). It seems to be the most widely used approach in the world today, as well as the most validated methodology for decision making. The consistency measurement of human judgments appears to be the crucial problem in this concept. This research paper redefines the idea of the triad’s consistency within the pairwise comparison matrix (PCM) and proposes a few seminal indices for PCM consistency measurement. The quality of new propositions is then studied with application of computer simulations coded and run in Wolfram Mathematica 9.0.

Słowa kluczowe

EN

AHP; analytic hierarchy process (AHP); pairwise comparisons; consistency; judgments; Monte Carlo simulation

PL

AHP; Analytic Hierarchy Process; porównanie parami; konsystencja; symulacje Monte Carlo

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 1
• Strony: 71--78
• Opis fizyczny: Bibliogr. 14 poz., rys., tab.

Twórcy

autor

Kazibudzki P.

• Institute of Management and Marketing, Jan Dlugosz University in Czestochowa Częstochowa, Poland

Bibliografia

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• [6] Crawford G., Williams C.A., A note on the analysis of subjective judgment matrices, J. Math. Psychol. 1985, 29, 387-405.
• [7] Choo E.U., Wedley W.C., A common framework for deriving preference values from pairwise comparison matrices, Comp. Oper. Res. 2004, 31, 893-908.
• [8] 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.
• [9] Grzybowski A.Z., Note on a new optimization based approach for estimating priority weights and related consistency index, Expert Syst. Appl. 2012, 39, 11699-11708.
• [10] Grzybowski A.Z., New optimization-based method for estimating priority weights, Journal of Applied Mathematics and Computational Mechanics 2013, 12(1), 33-44.
• [11] Koczkodaj W.W., A new definition of consistency of pairwise comparisons, Mathematical and Computer Modeling 1993, 18(7), 79-84.
• [12] Winsberg E.B., Science in the Age of Computer Simulations, The University of Chicago Press, Chicago 2010.
• [13] Grzybowski A., Domański Z., A sequential algorithm for modeling random movements of chain-like structures, Scientific Research of the Institute of Mathematics and Computer Science 2011, 10(1), 5-10.
• [14] Grzybowski A.Z., New results on inconsistency indices and their relationship with the quality of priority vector estimation, Expert Syst. Appl. 2016, 43, 197-212.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.