REDUCE—A Tool Supporting Inconsistencies Reduction in the Decision-Making Process

Abstract

This paper presents REDUCE, a free online tool designed to support decision-making processes by addressing inconsistency in multiplicative pairwise comparison (PC) matrices, a key element of many multi-criteria decision-making (MCDM) methods, including the analytic hierarchy process (AHP). AHP relies on pairwise comparisons to assign weights to decision criteria or alternatives, but human-generated PC matrices often exhibit inconsistencies. Consistency is evaluated using Saaty’s consistency ratio ( CR ), where a value below 0.10 is considered acceptable. Higher inconsistency levels necessitate matrix corrections, which are challenging if the original expert is unavailable or revision constraints exist. REDUCE autonomously reduces inconsistency in PC matrices using two different algorithms that require no expert intervention. The tool accommodates different PC matrices, enabling users to specify the desired CR threshold (e.g., CR≤0.10) and select the algorithm for adjustment. It ensures the resulting matrix is consistent while preserving the original preference structure to the greatest extent possible. Additionally, REDUCE calculates weights for the compared entities, making it a valuable tool for applications of AHP and related methodologies. Quantitative evaluations demonstrate that REDUCE can improve matrices with high inconsistency (e.g., CR=0.25) to acceptable levels (e.g., CR=0.08) while retaining up to 95% of the original preference integrity, depending on the chosen algorithm. By addressing the accessibility gap for small and medium enterprises (SMEs) that lack resources for costly decision-making software or expert consultants, REDUCE facilitates broader adoption of MCDM tools. This work highlights the potential of REDUCE to enhance decision-making reliability and accessibility in resource-constrained environments.