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A Mathematical programming evaluation approach for multiple criteria sorting problems

Civelek, Merve
Multiple criteria sorting problem is to assign alternatives, evaluated according to multiple criteria, into predefined preference ordered classes. In this study, a new distance metric based sorting method is developed to solve multiple criteria sorting problems without specifying class thresholds between preference-ordered classes. The aim of the proposed method is to assign each alternative to one class or a set of possible adjacent classes considering the distance to class centroids. In the proposed method, two cases are considered. In the first case, centroids of the classes are estimated using the whole data set. In the second case, class centroids are estimated using only the training data set. Distance of alternatives to the centroids are used as criteria aggregation function. A mathematical model is formulated to determine the weights of the criteria. Assignment is performed according to the weighted distance of each alternative to each class centroids. The proposed method is applied to five data sets with four different distance norms and several performance measures are calculated. The results show that centroid information is not so important to obtain better performances. The performance of the proposed method is compared with PDIS method and UTADIS method. The computational studies show that with relatively large data sets the proposed method performed better than the other methods.