Simulation-Based Evaluation of Criteria Rank-Weighting Methods in Multi-Criteria Decision-Making

Abstract

This paper presents a simulation study to assess the performance of the five known methods for converting ranks of several criteria into weights in multi-criteria decision-making. The five methods assessed for converting criteria ranks into weights are: rank- sum (RS) weights, rank reciprocal (RR) weights, rank order centroid (ROC) weights, geometric weights (GW), and variable-slope linear (VSL) weights. The methods are compared in terms of weight estimation accuracy considering different numbers of criteria and decision makers’ (MS) preference structures. Alternative preference structures are represented by different probability distributions of randomly generated criteria weights, namely the uniform, normal, and exponential distributions. Results of the simulation experiments indicate that no single method is consistently superior to all others. On average, RS is best for uniform weights, VSL is best for normal weights, and ROC is best for exponential weights. However, for any multi-criteria decision-making (MCDM) problem, the best method for converting criteria ranks into weights depends on both the number of criteria and the weight distribution.