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Relationship between priority ratios disturbances and priority estimation errors

Starczewski T.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 3

143--154

This article is devoted to some problems connected with multicriteria decision analysis. We consider the relationship between the pairwise comparison matrix (PCM) and a priority vector (PV) obtained on the basis of this matrix. The PCM elements are the decision makers’ judgments about priority ratios i.e. the ratios of weights contained in the PV. It is known, that in the case of consistent matrix, we can obtain the exact value of related PV. However, the real-world practice shows that the decision maker does not create a perfectly consistent PCM, and thus usually in such a matrix the judgment’s errors occur. In our paper we use Monte Carlo simulation to study the relationship between various possible distributions of these errors and the distributions of the errors in estimates of the true PV. In these simulation we apply some initial families distribution and some different parameters. We obtain interesting results which show very slight influence families distribution on final PV errors. Our paper show that much bigger influence on simulation result have adopted parameters than selection distribution family.

Efficacy Analysis of Ratios from Pairwise Comparisons

Wedley W. C., Choo E. U., Wijnmalen D. J. D.

Fundamenta Informaticae

2016

Vol. 146, nr 3

321--338

The true pairwise comparison matrix is simulated and used as a benchmark for evaluating different priority vectors derived from a decision maker’s pairwise comparison matrix. The accuracy of the decision maker’s comparisons are progressively improved until they emulate the true values. Using four different distance measures to evaluate five different methods of deriving priorities, the geometric mean, normalized column mean, and right eigenvector techniques are more accurate. All methods exhibit rare reversals in accuracy as the comparison values approach the true values.

New optimization based method for estimating priority weights

Grzybowski A. Z.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 1

33--44

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.