# A multiple criteria sorting approach based on distance functions

2011
Çelik, Bilge
Sorting is the problem of assignment of alternatives into predefined ordinal classes according to multiple criteria. A new distance function based solution approach is developed for sorting problems in this study. The distance to the ideal point is used as the criteria disaggregation function to determine the values of alternatives. These values are used to sort them into the predefined classes. The distance function is provided in general distance norm. The criteria disaggregation function is determined according to the sample preference set provided by decision maker. Two mathematical models are used in order to determine the optimal values and assign classes. The method also proposes an approach for handling alternative opt imal solutions, which are widely seen in sorting problems. Probabilities of belonging to each class for an alternative are calculated using the alternative optimal solutions and provided as the outputs of the model. Decision maker assigns the alternatives into classes according to these probabilities. The method is applied to five data sets and results are provided for different performance measures. Different distance norms are tried for each data set and their performances are evaluated for each data set. The probabilistic approach is also applied to UTADIS. The performance of the distance based model and modified UTADIS are compared with the previous sorting methods such as UTADIS and classification tree. The developed method has new aspects such as using distances to ideal point for sorting purpose and providing probabilities of belonging to classes. The handling of alternative optimal solutions within the method instead of a post-optimality analysis is another new and c ritical aspect of the study.

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Citation Formats
B. Çelik, “A multiple criteria sorting approach based on distance functions,” M.S. - Master of Science, Middle East Technical University, 2011. 