HFC: Data clustering based on hesitant fuzzy decision making

Document Type : Research Paper

Authors

1 Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

3 Department of Computing Science, Ume\aa University, Ume\aa , Sweden

Abstract

In a clustering task, choosing a proper clustering algorithm and obtaining qualified clusters are crucial issues. Sometimes, a clustering algorithm is chosen based on the data distribution, but data distributions are not known beforehand in real world problems. In this case, we hesitate which clustering algorithm to choose. In this paper, this hesitation is modeled by a hesitant fuzzy multi criteria decision making problem {\small (HFMCDM)} in which some clustering algorithms play the role of experts. Here, we consider fuzzy {\footnotesize C}-means {\small (FCM)} and agglomerative clustering algorithms as representative of two popular categories of clustering algorithms partitioning and hierarchical clustering methods, respectively.
Then, we propose a new clustering procedure based on hesitant fuzzy decision making approaches {\small (HFC)} to decide which of the {\small FCM} family or hierarchical clustering algorithms is suitable for our data. This procedure ascertains a good clustering algorithm using neutrosophic {\small FCM} ({\small NFCM}) through a two phases process. The {\small HFC} procedure not only makes a true decision about applying partitioning clustering algorithms, but also improves the performance of {\small FCM} and evolutionary kernel intuitionistic fuzzy c-means clustering algorithm ({\small EKIFCM}) with construction hesitant fuzzy partition {\small (HFP)} conveniently. Experimental results show that the clustering procedure is applicable and practical. According to {\small HFC} procedure, it should be mentioned that it is possible to replace the other clustering algorithms that belong to any partitioning and hierarchical clustering methods. Also, we can consider other categories of clustering algorithms.

Keywords

References

[1] L. Aliahmadipour, A. Taghavi, E. Eslami, An introduction to hesitant fuzzy data clustering, 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS), Zahedan, Iran, (2015), 1-4.
[2] L. Aliahmadipour, V. Torra, E. Eslami, On hesitant fuzzy clustering and clustering of hesitant fuzzy data, In Fuzzy Sets, Rough Sets, Multisets and Clustering, Springer, Cham, 157-168.
[3] L. Aliahmadipour, V. Torra, E. Eslami, M. Eftekhari, A definition for hesitant fuzzy partitions, International Journal of Computational Intelligent System, 9 (2016), 497-505.
[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[5] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms, Plenum Press, New York, (1981), 191-203.
[6] T. Chaira, A novel intuitionistic fuzzy C-means clustering algorithm and its application to medical images, Applied Soft Computing, 11 (2011), 1711-1717.
[7] Y. H. Chang, C. H. Yeh, Y. W. Chang, A new method selection approach for fuzzy group multicriteria decision making, Applied Soft Computing, 13 (2013), 2179-2187.
[8] T. Y. Chen, H. P. Wang, Y. Y. Lu, A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective, Expert Systems and Application, 38 (2011), 7647-7658.
[9] S. L. Chiu, Fuzzy model identification based on cluster estimation, Journal of Intelligent and Fuzzy System, 2 (1994), 267-278.
[10] J. Demsar, Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research, 7 (2006), 1-30.
[11] R. Duwairi, M. Abu-Rahmeh, A novel approach for initializing the spherical K-means clustering algorithm, Simulation Modelling Practice and Theory, 54 (2015), 49-63.
[12] M. Eftekhari, A. Mehrpooya, F. Saberi-Movahed, V. Torra, How fuzzy concepts contribute to machine learning, Studies in Fuzziness and Soft Computing, Springer, 416, (2022).
[13] M. Erisoglu, N. Calis, S. Sakallioglu, A new algorithm for initial cluster centers in k-means algorithm, Pattern Recognition Letters, 32 (2011), 1701-1705.
[14] B. S. Everitt, S. Landau, M. Leese, Cluster analysis, U. K.: Arnold, London, 2001.
[15] B. Farhadinia, A series of score functions for hesitant fuzzy sets, Information Sciences, 277 (2014), 102-110.
[16] M. Filipponea, F. Camastrab, F. Masulli, S. Rovetta, Asurvey of kernel and spectral methods for clustering, Pattern Recognition, 41 (2008), 176-190.
[17] A. Frank, A. Asuncion, UCI machine learning repository, University of California, School of Information and Computer Science, Irvine, CA, USA, 2010, http://archive.ics.uci.edu/ml.
[18] I. Gath, A. Geva, Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (1989), 773-781.
[19] D. Graves, W. Pedrycz, Kernel-based fuzzy clustering and fuzzy clustering: A comparative experimental study, Fuzzy Sets and Systems, 161 (2010), 522-543.
[20] Y. Guo, A. Sengur, NECM: Neutrosophic evidential c-means clustering algorithm, Neural Computing and Application, 26 (2014), 561-571.
[21] D. E. Gustafson, W. Kessel, Fuzzy clustering with a fuzzy covariance matrix, In: Proceedings of IEEE Conference on Decision Control, San Diego, (1979), 761-766.
[22] J. Han, M. Kamber, Data mining: Concepts and techniques, Morgan Kaufmann Publishers is an Imprint of Elsevier, 2009.
[23] A. Hatami-Marbini, M. Tavana, M. Moradi, F. Kangi, A fuzzy group electre method for safety and health assessment in hazardous waste recycling facilities, Safety Science, 51 (2013), 414-426.
[24] A. K. Jain, Data clustering: 50 years beyond k-means, Pattern Recognition Letters, 31 (2010), 651-666.
[25] L. Kaufman, P. J. Rousseeuw, Finding groups in data: An introduction to cluster analysis, John Wiley Sons, 1990.
[26] S. A. Mingoti, J. O. Lima, Comparing SOM neural network with fuzzy c-means, K-means and traditional hierarchical clustering algorithms, European Journal of Operational Research, 174 (2006), 1742-1759.
[27] W. Pedrycz, Allocation of information granularity in optimization and decision-making models: Towards building the foundations of granular computing, European Journal of Operational Research, 232 (2014), 137-145.
[28] A. H. Pilevar, M. Sukumar, GCHL: Agrid-clustering algorithm for high-dimensional very large spatial data bases, Pattern Recognition Letters, 26 (2005), 999-1010.
[29] E. Rashedi, A. Mirzaei, A hierarchical clusterer ensemble method based on boosting theory, Knowledge-Based Systems, 45 (2013), 83-93.
[30] B. Rezaee, A cluster validity index for fuzzy clustering, Fuzzy Sets and Systems, 161 (2010), 3014-3025.
[31] R. M. Rodriguez, L. Martinez, V. Torra, Z. S. Xu, F. Herrera, Hesitant fuzzy sets: State of the art and future directions, International Journal of Intelligent Systems, 29 (2014), 495-524.
[32] M. Sato, Y. Sato, Fuzzy clustering model for fuzzy data, Fuzzy Systems, International Joint Conference of the Fourth, (1995), 2123-2128.
[33] School of computing university of Eastern Finland P.O.Box 111 FIN-80101 Joensuu Finland, http://cs.joensuu.fi/sipu/datasets.
[34] S. Theodoridis, K. Koutroumbas, Pattern recognition, Elsevier, 2009.
[35] V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems, 25 (2010), 529-539.
[36] V. Torra, On the selection of m for fuzzy c-means, Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, (2015), 1571-1577.
[37] V. Torra, S. Miyamoto, A definition for I-fuzzy partition, Soft Computing, 15 (2011), 363-369.
[38] V. Torra, Y. Narukawa, On hesitant fuzzy sets and decision, IEEE International Conference on Fuzzy Systems, (2009), 1378-1382.
[39] J. Valente de Oliveira, W. Pedrycz, Advances in fuzzy clustering and its applications, Wiley, 2007.
[40] Y. K. Varshney, P. K. Muhuri, Q. M. Danish Lohani, PIFHC: The probabilistic intuitionistic fuzzy hierarchical clustering algorithm, Applied Soft Computing, 120 (2022), 108584.
[41] M. M. Xia, Z. S. Xu, Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning, 52 (2011), 395-407.
[42] M. M. Xia, Z. S. Xu, N. Chen, Some hesitant fuzzy aggregation operators with their application in group decision making, Group Decision and Negotiation, 22 (2011), 259-279.
[43] H. J. Xing, M. H. Ha, Further improvements in feature-weighted fuzzy C-means, Information Sciences, 267 (2014), 1-15.
[44] Z. S. Xu, Intuitionistic fuzzy aggregation and clustering, Studies in Fuzziness and Soft Computing, Springer, 279 (2012), 1-284.
[45] Z. Xu, Hesitant fuzzy sets theory, Studies in Fuzziness and Soft Computing, 314 (2014), 474 pages.
[46] Z. S. Xu, M. M. Xia, Distance and similarity measures for hesitant fuzzy sets, Information Sciences, 181 (2011), 2128-2138.
[47] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[48] D. Q. Zhang, S. C. Chen, Clustering incomplete data using kernel-based fuzzy C-means algorithm, Neural Processing Letters, 18 (2003), 155-162.
[49] Y. Zhao, G. Karypis, Evaluation of hierarchical clustering algorithms for document datasets, in Proceeding of 11th International Conference on Information and Knowledge Management, McLean, Virginia, USA, (2002), 515-524.
Iranian Journal of Fuzzy Systems
Volume 19, Issue 5
September and October 2022
Pages 167-181

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