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2 Fundamenta Informaticae

2 2016

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Mathematical Support for the Geometric Mean when Deriving a Consistent Matrix from a Pairwise Ratio Matrix

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

Fundamenta Informaticae

2016

Vol. 144, nr 3/4

263--278

A ratio pairwise comparison matrix estimates another matrix of true ratios between objects. From the pairwise comparison matrix, various methods are used to derive a priority vector and associated consistent matrix that also estimates the matrix of true ratios. The distance from the consistent matrix and the true matrix measures the accuracy of a method. The geometric mean is shown to be the only method with error below a basic threshold while being invariant to any reordering and rescaling of columns. Besides being simple to calculate, the geometric mean has excellent performance and many desirable properties.

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.