A simple formula to find the closest consistent matrix to a reciprocal matrix

作者：Benitez J; Izquierdo J^*; Perez Garcia R; Ramos Martinez E

来源：Applied Mathematical Modelling, 2014, 38(15-16): 3968-3974.

DOI：10.1016/j.apm.2014.01.007

• Analytic hierarchy process
• Decision-making
• Linearization

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 (Benitez 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.

• 出版日期2014-8-1