TOPSIS is a multi-criteria decision-making technique based on distance minimization, which allows ranking the compared alternatives according to their distances from ideal and anti-ideal solutions. Usually, the technique measures distances in Euclidean norm, assuming that the considered attributes are independent. However, in practice, this rarely happens, so the technique needs to be adapted to the new situation. Using Mahalanobis distance to include correlations between attributes expressed as Z-scores, this paper proposes an extension of Z-TOPSIS that captures the dependencies between them, but unlike Euclidean distance, does not require data normalization. The results obtained with the new proposal are compared with the three most commonly used Minkowski norms for distance calculation: Manhattan distance; Euclidean distance; and Tchebycheff distance. In addition, simulation methods are used to analyze the relationship between the Z-TOPSIS results obtained with Euclidean distance and those obtained with Mahalanobis distance.