An ordered clustering algorithm based on K-means and the PROMETHEE method

The multi-criteria decision aid (MCDA) has been a fast growing area of operational research and management science during the past two decades. The clustering problem is one of the well-known MCDA problems, in which the K-means clustering algorithm is one of the most popular clustering algorithms. However, the existing versions of the K-means clustering algorithm are only used for partitioning the data into several clusters which don't have priority relations. In this paper, we propose a complete ordered clustering algorithm called the ordered K-means clustering algorithm, which considers the preference degree between any two alternatives. Different from the K-means clustering algorithm, we apply the relative net flow of PROMETHEE to measure the closeness of alternatives. In this case, the ordered K-means clustering algorithm can capture the different importance degrees of criteria. At last, we employ the proposed algorithm to solve a practical ordered clustering problem concerning the human development indexes. Then a comparison analysis with an existing approach is conducted to demonstrate the advantages of the ordered K-means clustering algorithm.