Gustavo B. Alvarez, Rafael G. de Almeida, Cecilia T. Hernández, Patrícia A. P. de Sousa
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引用次数: 3
Abstract
The Analytic Hierarchy Process (AHP) is a decision making method, which has as its greatest criticism the rank reversal effect. Here a new mathematical analysis of this method is performed, and three new results are highlighted. First, the method is formulated as a linear system of equations, where it is possible to assign a geometric interpretation, determine the number of possible solutions, and perform an sensitivity analysis based on the condition number of the matrix. Second, the causes of rank reversal can be encompassed by two mathematical aspects related to the properties of the matrix of AHP: high condition number and deficient rank. When the matrix is deficient rank, it is possible to obtain a condensed formulation of the AHP with a new full rank matrix. This guarantees greater stability to the method. Third, some mathematical results can be used as a robustness test for the matrix of AHP.
期刊介绍：
The Journal of Multi-Criteria Decision Analysis was launched in 1992, and from the outset has aimed to be the repository of choice for papers covering all aspects of MCDA/MCDM. The journal provides an international forum for the presentation and discussion of all aspects of research, application and evaluation of multi-criteria decision analysis, and publishes material from a variety of disciplines and all schools of thought. Papers addressing mathematical, theoretical, and behavioural aspects are welcome, as are case studies, applications and evaluation of techniques and methodologies.
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