Interactive consistency correction in the analytic hierarchy process to preserve ranks
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Interactive consistency correction in the analytic hierarchy process to preserve ranks Alessio Ishizaka1
· Sajid Siraj2
Received: 18 November 2019 / Accepted: 14 October 2020 © Associazione per la Matematica Applicata alle Scienze Economiche e Sociali (AMASES) 2020
Abstract The analytic hierarchy process is a widely used multi-criteria decision-making method that involves the construction of pairwise comparison matrices. To infer a decision, a consistent or near-consistent matrix is desired, and therefore, several methods have been developed to control or improve the overall consistency of the matrix. However, controlling the overall consistency does not necessarily prevent having strong local inconsistencies. Local inconsistencies are local distortions which can lead to rank reversal when a new alternative is added or deleted. To address this problem, we propose an algorithm for controlling the inconsistency during the construction of the pairwise comparison matrix. The proposed algorithm assists decision makers whilst entering their judgments and does not allow strong local inconsistencies. This algorithm is based on the transitivity rule and has been verified through statistical simulations. Appropriate thresholds of acceptable evaluations have been inferred from these simulations. We demonstrate that the proposed algorithm is a helpful decision aid to decision makers when entering pairwise comparison judgments. Keywords Decision making · Multi-criteria · AHP · Rank reversal · Consistency ratio JEL Classification C440
1 Introduction The analytic hierarchy process (AHP) is a structured method to help people in making complex yet important decisions. It provides a comprehensive and rational framework
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Alessio Ishizaka [email protected] Sajid Siraj [email protected]
1
NEOMA Business School, 1 rue du Maréchal Juin, BP 215, 76130 Mont-Saint-Aignan Cedex, France
2
Leeds University Business School, University of Leeds, Leeds LS2 9JT, UK
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A. Ishizaka, S. Siraj
to structure a problem, represent and quantify its elements, relate those elements to the overall goals and finally evaluate and prioritise the available alternatives (Ishizaka and 2011a; Saaty 1980). The AHP method has been extensively used for making strategic decisions in the presence of conflicting criteria (Sipahi and Timor 2010; Subramanian and Ramanathan 2012). It has also been used for performance measurement and efficiency analysis, either as a standalone method (Ishizaka and López 2019; Ishizaka and Labib 2011b) or in combination with data envelopment analysis (DEA) (Tone 2017; Veni et al. 2012; Keskin and Köksal 2019). Besides the fact that it has been widely applied, it has been widely criticised in the academic community for the rank reversal problem. A rank reversal occurs whenever the relative ranking of two alternatives in the global ranking is reversed when a new alternative is added or removed. In fact, the rank reversal can be produced by two distinct and independent causes: the normalisation of the weights and str
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