Notes on Dependent Attributes in TOPSIS

TOPSIS is a multicriteria decision making technique based on the minimization of geometric distances that allows the ordering of compared alternatives in accordance with their distances from the ideal and anti-ideal solutions. The technique, that usually measures distances in the Euclidean norm, implicitly supposes that the contemplated attributes are independent. However, as this rarely occurs in practice, it is necessary to adapt the technique to the new situation. Using the Mahalanobis distance to incorporate the correlations among the attributes, this paper proposes a TOPSIS extension that captures the dependencies among them, but, in contrast to the Euclidean distance, does not require the normalization of the data. Results obtained by the new proposal have been compared by means of the three Minkowski norms most commonly employed for the calculation of distance: (i) the Manhattan distance (p=1); (ii) the Euclidean distance (p=2); and (iii) the Tchebycheff distance (p=∞). Furthermore, simulation techniques are used to analyse the connection between the TOPSIS results traditionally obtained with the Euclidean distance and those obtained with the Mahalanobis distance.