The analytic hierarchy process: Does adjusting a pairwise comparison matrix to improve the consistency ratio help?

Finan, James S.; Hurley, W. J.

doi:10.1016/s0305-0548(96)00090-1

Cited by 79 publications

(27 citation statements)

References 13 publications

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“…They used simulation to show that AHP models using their suggestion do not suffer from inaccuracy due to data loss. Finan and Hurley [45] used simulation to prove that further reduction of inconsistency in matrices already considered consistent is still beneficial to the overall decision analysis in AHP.…”

Section: Use Of Simulation In Hdm/ahp Researchmentioning

confidence: 99%

Consistency Analysis for Judgment Quantification in Hierarchical Decision Model

Abbas¹

2000

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The objective of this research is to establish consistency thresholds linked to alpha () levels for HDM's (Hierarchical Decision Model) judgment quantification method.Measuring consistency in order to control it is a crucial and inseparable part of any AHP/HDM experiment. The researchers on the subject recommend establishing thresholds that are statistically based on hypothesis testing, and are linked to the number of decision variables and  level. Such thresholds provide the means with which to evaluate the soundness and validity of an AHP/HDM decision. The linkage of thresholds to  levels allows the decision makers to set an appropriate inconsistency tolerance compatible with the situation at hand. The measurements of judgments are unreliable in the absence of an inconsistency measure that includes acceptable limits.All of this is essential to the credibility of the entire decision making process and hence is extremely useful for practitioners and researchers alike. This research includes distribution fitting for the inconsistencies. It is a valuable and interesting part of the research results and adds usefulness, practicality and insight. The superb fits obtained give confidence that all the statistical inferences based on the fitted distributions accurately reflect the HDM's inconsistency measure.

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Section: Use Of Simulation In Hdm/ahp Researchmentioning

confidence: 99%

Consistency Analysis for Judgment Quantification in Hierarchical Decision Model

Abbas¹

2000

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“…The main problem is the possible lack of consistency in comparison matrices, as comparative judgments are subjective since they are issued by experts and/or other actors in the decision process. These matrices should accommodate a chosen scale (see [12,22,18,23], including, of course, the work by Saaty). Consequently, it is predictable -even reasonable-that the issued global opinion body lacks a minimum consistency, which is essential for the prioritization to be meaningful, reliable, and consequently, conducive to a sound decision.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, it is predictable -even reasonable-that the issued global opinion body lacks a minimum consistency, which is essential for the prioritization to be meaningful, reliable, and consequently, conducive to a sound decision. The literature contains numerous mechanisms to improve consistency, [11,21,8,1,20,9,13,3,4,6] among many others, and any attempt to improve consistency results in a better quality decision [18]. Among the methods to improve consistency, we present in Section 3 the linearization method introduced by the authors [4] on which the main contribution of this article is built.…”

Section: Introductionmentioning

confidence: 99%

Consistent completion of incomplete judgments in decision making using AHP

Benítez

Delgado-Galván

Izquierdo

et al. 2015

Journal of Computational and Applied Mathematics

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Abstract. Decision making (DM) processes are becoming increasingly complex. The reasons are manifold. DM usually involves many aspects; some are purely technical, while others are subjective and derived from social, political, and environmental factors, among others. As a result, they involve items that are not easily comparable under the same units of measurement. Problems are made even more complex by the fact that current governance processes tend to involve all the stakeholders in the DM process.In this paper we consider the AHP methodology (analytic hierarchy process), which is used to build consistent aggregate results from data provided by decision makers. As some of the actors involved may not be completely familiar with all the criteria under consideration, it is common that the body of opinion, expressed in terms of pairwise comparison, is incomplete. To overcome this weakness, we propose a framework that enables users to provide data on their preferences in a partial and/or incomplete way and at different times. This article is an advance towards a dynamic model of AHP. The authors have addressed the problem of adding a new criterion or deleting obsolete criteria. Here, we address the consistent completion of a reciprocal matrix as a mechanism to obtain a consistent body of opinion issued in an incomplete manner by a specific actor. This feature is incorporated into a process of linearization previously introduced by the authors, which is concisely presented. Finally, we provide an application for leakage control in a water supply company. The adoption of suitable control leakage policies in water supply is a problem of enormous interest in the water industry, particularly in urban hydraulics.

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“…Achieving consistency in AHP has become an important issue and different methods have been proposed in the literature [1,2,3,6,7,8,9,10,11,12,13,14]. In this paper, we focus on the linearization process [10] not as method to directly obtain the priority vector, but as a method that provides a closed form for achieving complete consistency.…”

Section: Introductionmentioning

confidence: 99%

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

Benítez

Izquierdo

Pérez-García

et al. 2014

Applied Mathematical Modelling

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ElsevierBenítez López, J.; Izquierdo Sebastián, J.; Pérez García, R.; Ramos Martinez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling. 38(15-16):3968-3974. doi:10.1016Modelling. 38(15-16):3968-3974. doi:10. /j.apm.2014 A simple formula to nd the closest consistent matrix to a reciprocal matrix J. Benítez * , J. Izquierdo † , R. Pérez-García † , E. Ramos-Martínez † Abstract: Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decisionmaking based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benítez et al., Achieving matrix consistency in AHP through linearization, Applied Mathematical Modelling 35 (2011) 4449-4457), 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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The analytic hierarchy process: Does adjusting a pairwise comparison matrix to improve the consistency ratio help?

Cited by 79 publications

References 13 publications

Consistency Analysis for Judgment Quantification in Hierarchical Decision Model

Consistency Analysis for Judgment Quantification in Hierarchical Decision Model

Consistent completion of incomplete judgments in decision making using AHP

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

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