Abstract
The Best-Worst Method (BWM) uses ratios of the relative importance of criteria in pairs based on the assessment done by decision-makers. When a decision-maker provides the pairwise comparisons in BWM, checking the acceptable inconsistency, to ensure the rationality of the assessments, is an important step. Although both the original and the extended versions of BWM have proposed several consistency measurements, there are some deficiencies, including: (i) the lack of a mechanism to provide immediate feedback to the decision-maker regarding the consistency of the pairwise comparisons being provided, (ii) the inability to consider the ordinal consistency into account, and (iii) the lack of consistency thresholds to determine the reliability of the results. To deal with these problems, this study starts by proposing a cardinal consistency measurement to provide immediate feedback, called the input-based consistency measurement, after which an ordinal consistency measurement is proposed to check the coherence of the order of the results (weights) against the order of the pairwise comparisons provided by the decision-maker. Finally, a method is proposed to balance cardinal consistency ratio under ordinal-consistent and ordinal-inconsistent conditions, to determine the thresholds for the proposed and the original consistency ratios.
Highlights
The Best Worst Method (BWM), which is a Multi-Criteria Decision Making (MCDM) method that was recently developed by Rezaei [37], uses ratios of the relative importance of criteria in pairwise comparisons provided by a decision-maker (DM), based on two evaluation vectors: the Best criterion against the Other criteria, and the Other criteria against the Worst criterion
Inspired by Amenta et al [3,4], we develop a method for determining the thresholds for BWM, which is based on the cardinal consistency measurement and the definition of ordinal consistency
We addressed the consistency issue in BWM
Summary
The Best Worst Method (BWM), which is a Multi-Criteria Decision Making (MCDM) method that was recently developed by Rezaei [37], uses ratios of the relative importance of criteria in pairwise comparisons provided by a decision-maker (DM), based on two evaluation vectors: the Best criterion against the Other criteria, and the Other criteria against the Worst criterion. The contribution of this study is threefold: (i) Developing a mechanism designed to provide a DM with immediate feedback regarding his/her consistency status and making the elicitation process more effective To this end, we propose an input-based consistency measurement, which is simple to use and has several desirable properties; (ii) Developing an ordinal consistency ratio that shows a DM’s violation level involving ordinal consistency and complements the cardinal consistency measurement. We propose an input-based consistency measurement, which is simple to use and has several desirable properties; (ii) Developing an ordinal consistency ratio that shows a DM’s violation level involving ordinal consistency and complements the cardinal consistency measurement With this ratio, a DM can revise his/her judgments to meet the ordinal consistency condition, which is a minimum requirement for a logical and rational DM; (iii) The most significant contribution of this study is to establish thresholds for the consistency ratios (the proposed consistency ratio and the original consistency ratio) used in BWM.
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