A new synthesis procedure for TOPSIS based on AHP

Vega et al. [1] analyzed the influence of the attributes’ dependence when ranking a set of alternatives in a multicriteria decision making problem with TOPSIS. They also proposed the use of the Mahalanobis distance to incorporate the correlations among the attributes in TOPSIS. Even in those situations for which dependence among attributes is very slight, the results obtained for the Mahalanobis distance are significantly different from those obtained with the Euclidean distance, traditionally used in TOPSIS, and also from results obtained using any other distance of the Minkowsky family. This raises serious doubts regarding the selection of the distance that should be employed in each case. To deal with the problem of the attributes’ dependence and the question of the selection of the most appropriate distance measure, this paper proposes to use a new method for synthesizing the distances to the ideal and the anti-ideal in TOPSIS. The new procedure is based on the Analytic Hierarchy Process and is able to capture the relative importance of both distances in the context given by the measure that is considered; it also provides rankings, which are closer to the distances employed in TOPSIS, regardless of the dependence among the attributes. The new technique has been applied to the illustrative example employed in Vega et al. [1].