Towards minimization of overall inconsistency involved in criteria weights for improved decision making

Abstract In multi-criteria decision making (MCDM), the role of criteria weights is highly significant, as any inconsistency associated with their weights leads to a wrong evaluation and non-optimal selection. This work proposes a novel subjective method for determining optimal criteria weights. Further, a new non-linear measure termed as ‘Error Index’ is proposed to quantify overall inconsistency in a full pairwise comparison matrix, which takes care of both the global and the local characteristics of the inconsistent matrix. Since the error index accounts for the error due to local weights as well that due to the deviation in eigenvalue, it is considered more indicative of inconsistency in a comparison matrix than the frequently employed consistency ratio index. The ‘Error Index’ was used to formulate a non-linear constrained optimization model, which was later solved using Particle Swarm Optimization (PSO), due to its faster convergence and simpler computation as compared to Genetic Algorithm, Ant Colony and, Firefly optimizations. For the sake of simulation, a user-friendly solver named ‘Criteria Weight Estimation using Non-Linear Programming (CWENLiP)’ is also developed. Several numerical problems are solved to illustrate the procedure and explore the potential applications of the proposed method. The results of robustness check, statistical significance test and, comparative analysis revealed that the proposed method is more robust and efficient. Hence, the Error Index based inconsistency quantification, combined with user-friendly CWENLiP solver, may be considered a more reliable method of estimating criteria weights, thereby leading to accurate ranking results and improved decision making, especially for problems encompassing large sets of criteria.