An ordered clustering algorithm based on fuzzy c-means and PROMETHEE

The ordered clustering problem in the context of multicriteria decision aid has been increasingly examined in management science and operational research during the past few years. However, the existing clustering algorithms may not provide an exact suggestion for a partition number for decision makers by using the diagram method. In addition, these methods may be not appropriate for real-life problems under big data environments due to their high computational complexities. Therefore, we propose a new clustering algorithm called the ordered fuzzy c-means clustering algorithm (OFCM) to overcome the abovementioned deficiencies. Different from the classical fuzzy c-means clustering algorithm, we use the net outranking flow of PROMETHEE and validity measures for clustering to establish a new objective function, whose properties are mathematically justified as well. Finally, we employ OFCM to solve a practical ordered clustering problem concerning the human development indexes. A comparison analysis with existing approaches is also conducted to validate the efficiency of OFCM.