A probabilistic multiple criteria sorting approach based on distance functions

• A new distance-based sorting method is proposed for multicriteria sorting problems.
• Several distance norms for aggregation are compared for different data sets.
• Distance to ideal point is shown to be a good indicator for class identification.
• Optimistic and pessimistic positions are determined for each class.
• Optimistic and pessimistic probabilities are calculated for each alternative.

In this paper, a new probabilistic distance based sorting (PDIS) method is developed for multiple criteria sorting problems. The distance to the ideal point is used as a criteria disaggregation function to determine the values of alternatives. These values are used to sort alternatives into the predefined classes. The method also calculates probabilities that each alternative belong to the predefined classes in order to handle alternative optimal solutions. It is applied to five data sets and its performance is compared with two well-known methods from literature. Computational experiments show that the PDIS method performs better than the other methods.