Smoothed Power-Weakness Ratio (sPWR): a new informative system for multi-criteria decision making

Nowadays, the large number of measurable variables has considerably increased the complexity of data. In the framework of the decision-making process, this leads to the need of adequate tools to set priorities and rank the available options. Ordering is one of the possible ways to analyse multivariate data, which provides an overview of the relationships among the elements of a system. The Multi-Criteria Decision Making (MCDM) encompasses a broad set of methods designed to set priority-based lists of alternatives based on multiple criteria, which support decision problems. Among the most widely adopted techniques, TOPSIS, dominance-based approaches, the Analytic Hierarchy Process (AHP), and Copeland scores represent some of the classical methodologies in both theoretical research and applied decision analysis. Among the dominance-based approaches, an effective MCDM method is the Power-Weakness Ratio (PWR), which generates a tournament table (i.e., the pairwise comparison matrix) from a data matrix with a varying number of samples (i.e., alternatives to be compared) and variables (i.e., the criteria for pairwise comparisons), weighted according to their relative importance in determining the final ranking. In this study, a variant of the classical Power-Weakness Ratio is presented, significantly modifying the way the tournament table is obtained. The method, called smoothed Power-Weakness Ratio (sPWR), takes into account the dominance degree of the alternatives in each pairwise comparison exploiting the differences between the criterion values. The rationale behind the method is described by the aid of an illustrative example on a simple benchmark dataset with known reference ranking of the samples. The main advantage of the new method over PWR is that its tournament table is much more informative and sensitive to the original data values than the classical pairwise comparison matrix. A multivariate comparison with other classical MCDM methods, performed on several diverse datasets, demonstrated that the results obtained by sPWR were quite similar to those obtained by Copeland Score and TOPSIS with range scaling. However, sPWR showed a higher tendency toward generating full rankings with an enhanced ability to remove ties in the pairwise comparisons.