Developing random indices and consistency ratios for inconsistency methods in pairwise comparison

Abstract

Consistency indexes are used to determine the consistency of pairwise comparison evaluations used in decision-making methods, especially the Analytical Hierarchical Process (AHP). Consistency ratios are used as an important tool for decision makers in deciding the consistency of pairwise comparisons by defining threshold values for consistency indices. Among the 14 consistency calculation methods defined by the literature review, the threshold value is defined as 0,1 only in Saaty's consistency ratio (CR) and for Crawford and Williams's geometric consistency ratio (GCR). In this study, random indices are calculated for Takeda and Golden-Wang consistency methods and consistency ratios similar to CR and GCR methods are defined based on these random indexes. The threshold value is set as 0.1 for these consistency ratios, which are compatible with Saaty's CR values. GWCR and MCCR consistency ratio calculation formulas are developed for Golden -Wang (GW) and Takeda (MC) consistency methods, respectively. Correlation and compatible rates are measured between the GWCR and MCCR consistency rates and the CR consistency values. The validity of the Golden-Wang and Takeda consistency ratio equations, which show high agreement and correlation with CR, is demonstrated. Thus, decision makers who use Golden -Wang and Takeda consistency methods in the consistency values of pairwise comparison matrices (HRC) are able to make a more accurate and faster evaluation at the 0.1 consistency threshold.