A simple formula to find the closest consistent matrix to a reciprocal matrix |
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Institution: | 1. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain;2. FluIng-Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Spain |
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Abstract: | Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benítez et al., 2011 10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. |
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Keywords: | Analytic hierarchy process Decision-making Linearization |
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