Robust Mahalanobis Distance based TOPSIS to Evaluate the Economic Development of Provinces

Abstract

In this paper, 81 Turkish provinces with different development levels were ranked using the TOPSIS method. To evaluate the ranking with TOPSIS, we presented an improvement to Mahalanobis distances, by considering a robust MM estimator of the covariance matrix to deal with the presence of outliers in the dataset. Additionally, the homogenous subsets, which were obtained from the robust Mahalanobis distance-based TOPSIS were compared with robust cluster analysis. According to our findings, robust TOPSIS-M scores reflect the inter-class differences in economic developments of provinces spanning from the extremely low to the extremely high level of economic developments. Considering indicators of economic development, which are often used in the literature, İstanbul ranked first, Ankara second, and İzmir third according to the Robust TOPSIS-M method. Moreover, with the Robust Cluster analysis, these provinces were diagnosed as outliers and it was seen that obtained clusters were compatible with the ranking of Robust TOPSIS-M.