An ordered clustering algorithm based on fuzzy c-means and PROMETHEE
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ORIGINAL ARTICLE
An ordered clustering algorithm based on fuzzy c-means and PROMETHEE Chengzu Bai1,2 · Ren Zhang1,2 · Longxia Qian1,2 · Lijun Liu3 · Yaning Wu4 Received: 4 June 2017 / Accepted: 8 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract 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. Keywords Multicriteria decision aid · Ordered cluster · Fuzzy c-means clustering · PROMETHEE method
1 Introduction Supervised classification, i.e., assigning alternatives to predefined classes, is a classic problem encountered in multicriteria decision aid (MCDA). To be more specific, this topic has received tremendous attention from fields such as clinical problem [31], marketing [22], medicine [15], production systems [21], economic and financial management [34], Electronic supplementary material The online version of this article (https://doi.org/10.1007/s13042-018-0824-7) contains supplementary material, which is available to authorized users. * Ren Zhang [email protected] 1
Research Center of Ocean Environment Numerical Simulation, College of Meteorology and Oceanography, National University of Defense and Technology, Shuanglong Road, Nanjing 211101, China
2
Collaborative Innovation Center on Forecast Meteorological Disaster Warning and Assessment, Nanjing University of Information Science and Technology, Nanjing, China
3
Meteorologic Bureau of Air Force Staff, Beijing, China
4
Research Center of Software Engineering, Institute of Information System, PLA University of Science and Technology, Nanjing, China
etc. [20, 26, 29, 33]. Moreover, in the context of MCDA, a number of scholars have developed novel and excellent approaches such as ELECTRE-SORT [13], ELECTRE TRI [27], Flowsort [18], PAIRCLASS [10], PROAFTN [1], UTADIS [32], etc. Generally, these methods assume the classes are defined a priori by a set of alternatives and their central or limit profiles. The challenge with the supervised classification is that the groups sometimes are unknown a
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