Novel coefficients for improved robustness in multi-criteria decision analysis

Abstract

In multi-criteria decision-making (MCDM), decision-makers face increasing complexity and the need for enhanced tools to facilitate informed and well-aligned decision outcomes. A critical challenge in MCDM is the determination of criteria weights, which significantly influence the final ranking of alternatives. While recent approaches aim to eliminate the need for explicit weight assignment, certain decision contexts necessitate their inclusion. This study introduces two novel coefficients, Rank Stability (RS) and Balance Point (BP), designed to provide deeper insights into the decision problem and its solution properties. Rank Stability quantifies the robustness of a solution against perturbations, while Balance Point evaluates the conditioning of the solution within the problem’s structure. The decision problem is defined by a set of alternatives and criteria, where modifications to alternatives require a reassessment of the decision model. To examine the properties of these coefficients, this study employs simulation experiments utilizing the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods, alongside case-based analyses demonstrating their practical applications. Additionally, extreme cases of RS and BP values are explored to enhance interpretability for decision-makers. A real-world decision problem is further analyzed to illustrate the applicability of these coefficients and introduce a novel framework for comparing MCDM methodologies. This approach facilitates a more systematic and comprehensive assessment of MCDM methods, contributing to the advancement of decision-support tools.