Consistency Indices in Analytic Hierarchy Process: A Review

This paper serves as an introduction to the Analytic Hierarchy Process -A multicriteria decision making approach in which factors are arranged in a hierarchic structure. The principles and the philosophy of the theory are summarized giving general background information of the type of measurement utilized, its properties and applications.

Decisions involve many intangibles that need to be traded off. To do that, they have to be measured along side tangibles whose measurements must also be evaluated as to, how well, they serve the objectives of the decision maker. The Analytic Hierarchy Process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgements of experts to derive priority scales. It is these scales that measure intangibles in relative terms. The comparisons are made using a scale of absolute judgements that represents, how much more, one element dominates another with respect to a given attribute. The judgements may be inconsistent, and how to measure inconsistency and improve the judgements, when possible to obtain better consistency is a concern of the AHP. The derived priority scales are synthesised by multiplying them by the priority of their parent nodes and adding for all such nodes. An illustration is included.

2018

This paper examines the pattern of development of the AHP research. The Analytic Hierarchy Process (AHP) was introduced by T.L. Saaty, is an effective tool for dealing with complex decision making, and may aid the decision maker to set priorities and make the best decision. The analytic hierarchy process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgments of experts to derive priority scales, these scales that measure intangibles in relative terms. The ratio scales are derived from the principal Eigen vectors and the consistency index is derived from the principal Eigen value.

Mathematical and Computer Modelling, 1993

Despite the many books and jonmal articles that have appeared about the Analytic Hierarchy Process (AHP), some important misconceptions about AHP remain. This paper discusses issues which underlie these misconceptions, including the cause and significance of "rank reversal," situations allowing or preventing rank reversals, the constraint of a 9 point scale, the roles of redundancy, intransitivities, and inconsistencies, the accommodation of objectivity and uncertainty, the similarities of AHP and Multi Attribute Utility Theory (MAUT), and opportunities to combine MCDM methodologies in real world decisions.

Procedia Economics and Finance, 2014

The Analytic Hierarchy Process (AHP) is widely used method in multiple-attribute decision making. In the recent literature many authors used different judgment scales which influenced the results and decisions. In this paper the author reviews and discusses effects of utilization of various judgment scales on priority estimation in AHP. There has been studies that have been concerned with the comparison of judgment scales but there were no studies concerned with consistency measures that are needed. The goal of this paper is to compare and discuss the application of various judgment scales on the results in particular practical example that has been used in previous paper by Saaty (2003). Thus the focus of the paper is to analyze the impact of using different judgment scales on the resulting priorities and consistency to default scale as proposed by Saaty. Results suggest that judgment scales have a profound impact on criteria priorities but not on ranking of criteria. However, the consistency varies among applied judgment scales. Authors calculated the values of random index needed for calculation of the consistency index in AHP for all concerned scales. Based on them the consistency index was computed and compared. Both consistent and inconsistent Saaty matrices were used for comparison.

European Journal of Operational Research, 1991

The uncertainty in the relative weights of a pairwise comparison matrix in the Analytic Hierarchy Process (AHP) is caused by the uncertainty in our decision judgements and in many cases can not be avoided. In this paper, it is explicitly shown how such uncertainties can be incorporated within the framework of AHP and how the resulting uncertainties in the relative priorities of the decision alternatives can be computed. The required algorithm and the computational procedures are also developed and illustrated with examples. Uncertainty is introduced as a fundamental concept independent of the concept of consistency with a view to extend the AHP as a decision analysis procedure.

2001

The objective of this study is to find the scale of the Analytic Hierarchy Process (AHP) appropriate for representing decision maker's perception. Specifically, two scales, linear scale and power scale, employed in the pair-wise comparison of the AHP are evaluated. The results offer some evidence that the power scale is preferable to the linear scale as the judgment scale.

The analytic hierarchy process (AHP) is a decision-making procedure widely used in management for establishing priorities in multicriteria decision problems. Underlying the AHP is the theory of ratio-scale measures developed in psychophysics since the middle of the last century. It is, however, well known that classical ratio-scaling approaches have several problems. We reconsider the AHP in the light of the modern theory of measurement based on the so-called separable representations recently axiomatized in mathematical psychology. We provide various theoretical and empirical results on the extent to which the AHP can be considered a reliable decision-making procedure in terms of the modern theory of subjective measurement.

2008 5th International Conference on the European Electricity Market, 2008

This paper presents the application of Paraconsistent Logic to the decision-making multi-criteria method AHP -Analytic Hierarchy Process. The model uses pairwise comparison matrixes and multiple specialists' evaluations, to calculate the degree of inconsistency of each analyzed alternative. With this tool, decision-makers can acquire greater confidence in decisions based on feeling, subjective parameters or intuitions.