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A Clustering Algorithm for Triangular Fuzzy Normal Random Variables

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Abstract

In view of the fact that most clustering algorithms cannot solve the clustering problem about samples with uncertain information, according to the theory of fuzzy sets and probability, we define the fuzzy-probability binary measure space and triangular fuzzy normal random variables firstly, and then combine the advantages of k-means algorithm, such as simple principle, few parameters, fast convergence rate, good clustering effect and good scalability, etc., a clustering algorithm is proposed for samples containing multiple triangular fuzzy normal random variables, which we call TFNRV-k-means algorithm. The algorithm uses our proposed Euclidean random comprehensive absolute distance (ERCAD for short) as a measurement, under the fuzzy measure, the lower bound, the principal value and the upper bound of the triangular fuzzy normal random variables are iterated, respectively, by means, and then the cluster center is updated until it becomes stable and unchanged. Then we analyze the time complexity of the proposed algorithm, and test the algorithm under different sample sets by random simulation experiments. We get the highest clustering accuracy of 99.00% and the maximum Kappa coefficient of 0.9850, and draw the conclusion that TFNRV-k-means clustering algorithm has good clustering effect. Finally, we summarize the content of the article, list the advantages and disadvantages of TFNRV-k-means clustering algorithm, and propose corresponding improvement methods, which provide ideas for further research on TFNRV-k-means in the future.

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Author information

Author notes

  1. Ye Li, Yiyan Chen and Qun Li contributed equally to this work and should be considered co-first authors.

Authors and Affiliations

  1. University of Chinese Academy of Social Sciences (Graduate School), Beijing, 102488, China

    Ye Li

  2. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

    Yiyan Chen

  3. Institute of Quantitative & Technical Economics, Chinese Academy of Social Sciences, Beijing, 100732, China

    Qun Li

Authors
  1. Ye Li
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  2. Yiyan Chen
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  3. Qun Li
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Corresponding author

Correspondence to Yiyan Chen.

Appendix

Appendix

See Tables 5, 6, 7, 8, 9, 10, 11, 12, 13.

Table 5 Experimental condition for the first set of random simulation
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Table 6 Experimental condition for the second set of random simulation
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Table 7 Experimental condition for the third set of random simulation
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Table 8 Experimental condition for the fourth set of random simulation
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Table 9 Experimental condition for the fifth set of random simulation
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Table 10 Experimental condition for the sixth set of random simulation
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Table 11 Experimental condition for the seventh set of random simulation
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Table 12 Experimental condition for the eighth set of random simulation
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Table 13 Experimental condition for the ninth set of random simulation
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Li, Y., Chen, Y. & Li, Q. A Clustering Algorithm for Triangular Fuzzy Normal Random Variables. Int. J. Fuzzy Syst. 22, 2083–2100 (2020). https://doi.org/10.1007/s40815-020-00933-7

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  • DOI: https://doi.org/10.1007/s40815-020-00933-7

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