期刊
APPLIED MATHEMATICAL MODELLING
卷 38, 期 15-16, 页码 3968-3974出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2014.01.007
关键词
Analytic hierarchy process; Decision-making; Linearization
资金
- IDAWAS, Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain) [DPI2009-11591]
- Conselleria d'Educacio of the Generalitat Valenciana [ACOMP/2010/146]
- Spanish project [MTM2010-18539]
- Universitat Politecnica de Valencia, Spain
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. (C) 2014 Elsevier Inc. All rights reserved.
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