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

  • Chengzu Bai
  • Ren Zhang
  • Longxia Qian
  • Lijun Liu
  • Yaning Wu
Original Article


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.


Multicriteria decision aid Ordered cluster Fuzzy c-means clustering PROMETHEE method 



This paper was supported by the National Natural Science Foundation of China (No. 51609254) and the Specific Fund (CQZ-2014001) for the Industrial Site in the City of Tangshan.

Supplementary material

13042_2018_824_MOESM1_ESM.docx (355 kb)
Supplementary material 1 (DOCX 354 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Center of Ocean Environment Numerical Simulation, College of Meteorology and OceanographyNational University of Defense and TechnologyNanjingChina
  2. 2.Collaborative Innovation Center on Forecast Meteorological Disaster Warning and AssessmentNanjing University of Information Science and TechnologyNanjingChina
  3. 3.Meteorologic Bureau of Air Force StaffBeijingChina
  4. 4.Research Center of Software Engineering, Institute of Information SystemPLA University of Science and TechnologyNanjingChina

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