A parametric method for fuzzy data clustering

Document Type : Original Article

Authors

Chamran University of Ahvaz

Abstract

Given that the current era is the era of information explosion, so the clustering of existing data and information is inevitable that must be done. Since in many cases we encounter widespread uncertainties in the available data, the best way to use clustering techniques is to combine them with fuzzy mathematics. Researchers have developed a variety of clustering algorithms for data clustering, some of which have fuzzy versions. The basic idea in fuzzy clustering is to assume that each cluster is a set of elements, then by changing the definition of element membership in this set from a state where an element can only be a member of a cluster, to a state where each element can To rank different memberships within several clusters, provide more realistic categories. The fuzzy mean c clustering algorithm (FCM) is the most common fuzzy clustering method. Various forms of FCM have been proposed so far. In this paper, based on FCM algorithm and similarity criterion, an efficient and robust clustering method for fuzzy data is proposed. This is the method. The similarity criterion proposed in this paper is based on α-sections and gives the decision maker the ability to make decisions at different levels. At the end, two numerical examples and a practical example are presented to show the efficiency of the proposed method.

Keywords

References

[1] Jafari, H., and M. J. Ebadi. “Malliavin calculus in statistical inference: CramerRao lower bound for fuzzy random variables.”, Journal of Decisions and Operations Research, 5(2) (2020): 124-132.
 
[2] Farahani, H., and M. J. Ebadi, “Finding Fuzzy Inverse Matrix Using Wu’s Method”, Journal of Mahani Mathematical Research Center, 10(1) (2021), 37- 52.
 
[3] Farahani, H., M. J. Ebadi, and H. Jafari. ”Finding Inverse of a Fuzzy Matrix using Eigenvalue Method.”, International Journal of Innovative Technology and Exploring Engineering, 9(2) (2019): 3030-3037.
 
[4] Ebadi, M. J., and M. S. Shiri Shahraki. ”Determination of scale elasticity in the existence of non-discretionary factors in performance analysis.” Knowledge Based Systems 23.5 (2010): 434-439.
 
[5] Ebadi, M. J., Hosseini, M.M., Karbassi, S.M.: An efficient one-layer recurrent neural network for solving a class of nonsmooth pseudoconvex optimization problems. Journal of Theoretical and Applied Information Technology 96.7 (2018).
 
[6] R.O. Duda, P.E. Hart, (1973). Pattern ClassiIcation and Scene Analysis, Wiley, New York.
 
[7] Na, S., Xumin, L., & Yong, G. (2010, April). Research on k-means clustering algorithm: An improved k-means clustering algorithm. In Intelligent Information Technology and Security Informatics (IITSI), 2010 Third International Symposium on (pp. 63-67). IEEE.
 
 [8] Srinivas, M., & Mohan, C. K. (2010, July). Efficient clustering approach using incremental and hierarchical clustering methods. In Neural Networks (IJCNN), The 2010 International Joint Conference on (pp. 1-7). IEEE.
 
[9] Kim, Y., Shim, K., Kim, M. S., & Lee, J. S. (2014). DBCURE-MR: an efficient density-based clustering algorithm for large data using MapReduce. Information Systems, 42, 15-35.
 
[10] Lee, J., & Lee, D. (2005). An improved cluster labeling method for support vector clustering. IEEE Transactions on pattern analysis and machine intelligence, 27(3), 461-464.
 
[11] Liu, B., Wan, C., & Wang, L. (2006). An efficient semi-unsupervised gene selection method via spectral biclustering. IEEE Transactions on nanobioscience, 5(2), 110-114.
 
[12] Pedrycz, W., & Rai, P. (2008). Collaborative clustering with the use of Fuzzy C-Means and its quantification. Fuzzy Sets and Systems, 159(18), 2399-2427.
 
[13] Staiano, A., Tagliaferri, R., & Pedrycz, W. (2006). Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering. Neurocomputing, 69(13), 1570-1581.
 
[14] Ji, Z. X., Sun, Q. S., & Xia, D. S. (2011). A modified possibilistic fuzzy cmeans clustering algorithm for bias field estimation and segmentation of brain MR image. Computerized Medical Imaging and Graphics, 35(5), 383-397.
 
[15] Ding, Y., & Fu, X. (2016). Kernel-based fuzzy c-means clustering algorithm based on genetic algorithm. Neurocomputing, 188, 233-238.
 
[16] Song, Q., Yang, X., Soh, Y. C., & Wang, Z. M. (2010). An information-theoretic fuzzy C-spherical shells clustering algorithm. Fuzzy Sets and Systems, 161(13), 1755-1773.
 
 [17] Li, K., & Li, P. (2014). Fuzzy clustering with generalized entropy based on neural network. In Unifying Electrical Engineering and Electronics Engineering (pp. 2085-2091). Springer, New York, NY.
 
[18] Sridhar, V., & Murty, M. N. (1991). A knowledge-based clustering algorithm. Pattern recognition letters, 12(9), 511-517.
 
[19] Dovžan, D., & Škrjanc, I. (2011). Recursive fuzzy c-means clustering for recursive fuzzy identification of time-varying processes. ISA transactions, 50(2), 159-169.
 
[20] Ji, Z. X., Sun, Q. S., & Xia, D. S. (2011). A modified possibilistic fuzzy cmeans clustering algorithm for bias field estimation and segmentation of brain MR image. Computerized Medical Imaging and Graphics, 35(5), 383-397.
 
[21] Alpaydin, E. (2014). Introduction to machine learning. MIT press.
 
[22] Webb, A, (2002). Statistical Pattern Recognition. Wiley, New Jersey.
 
[23] Borlea, I. D., Precup, R. E., Borlea, A. B., & Iercan, D. (2021). A unified form of fuzzy C-means and K-means algorithms and its partitional implementation. Knowledge-Based Systems, 214, 106731.
 
[24] Surono, S., & Putri, R. D. A. (2021). Optimization of fuzzy c-means clustering algorithm with combination of minkowski and chebyshev distance using principal component analysis. International Journal of Fuzzy Systems, 23(1), 139-144.
 
[25] Kaushal, M., & Lohani, Q. M. (2022). Generalized intuitionistic fuzzy c-means clustering algorithm using an adaptive intuitionistic fuzzification technique. Granular Computing, 7(1), 183-195.
 
 [26] Abdellahoum, H., Mokhtari, N., Brahimi, A., & Boukra, A. (2021). CSFCM: An improved fuzzy C-Means image segmentation algorithm using a cooperative approach. Expert Systems with Applications, 166, 114063.
 
[27] Zimmermann, (1995) H. J. Fuzzy set theory and its Application, kluwer Academic publishers, Boston / Derdecht / London.
 
[28] Ma, M., Friedman, M., and Kandel, A. (1999). A new fuzzy arithmetic, fuzzy sets and systems, vol. 108, no. 1, pp. 83-90.
 
[29] Dunn, J. C. (1973). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters.
 
[30] Bezdek JC (1981) Models for pattern recognition. In: In: Pattern recognition with fuzzy objective function algorithms, 1-13. US: Springer.
 
[31] Castro‐Company, F., & Tirado, P. (2014). On Yager and Hamacher t‐Norms and Fuzzy Metric Spaces. International Journal of Intelligent Systems, 29(12), 1173- 1180.
 
[32] Zhang, D., Ji, M., Yang, J., Zhang, Y., & Xie, F. (2014). A novel cluster validity index for fuzzy clustering based on bipartite modularity. Fuzzy Sets and Systems, 253, 122-137.
 
[33] Bezdek, J. C. (1973). Cluster validity with fuzzy sets.
 
[34] Bezdek, J. C. (1974). Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1(1), 57-71.
 
[35] Windham, M. P. (1982). Cluster validity for the fuzzy C-means clustering algorithm. IEEE transactions on pattern analysis and machine intelligence, (4), 357-363.
 
[36] Fukuyama, Y. (1989). A new method of choosing the number of clusters for the fuzzy c-mean method. In Proc. 5th Fuzzy Syst. Symp., 1989 (pp. 247-250).
 
[37] Xie, X. L., & Beni, G. (1991). A validity measure for fuzzy clustering. IEEE Transactions on pattern analysis and machine intelligence, 13(8), 841-847.
 
[38] Rezaee, B. (2010). A cluster validity index for fuzzy clustering. Fuzzy Sets and Systems, 161(23), 3014-3025.
 
[39] Yang, M. S., Hung, W. L., & Cheng, F. C. (2006). Mixed-variable fuzzy clustering approach to part family and machine cell formation for GT applications. International Journal of Production Economics, 103(1), 185-198.
 
[40] Hathaway, R. J., Bezdek, J. C., & Pedrycz, W. (1996). A parametric model for fusing heterogeneous fuzzy data. IEEE transactions on Fuzzy Systems, 4(3), 270- 281.
 
[41] Effati, S., Yazdi, H. S., & Sharahi, A. J. (2013). Fuzzy clustering algorithm for fuzzy data based on α-cuts. Journal of Intelligent & Fuzzy Systems, 24(3), 511- 519.
 
[42] Coppi, R., D’Urso, P., & Giordani, P. (2012). Fuzzy and possibilistic clustering for fuzzy data. Computational Statistics & Data Analysis, 56(4), 915-927
 
Fuzzy Systems and its Applications
Volume 5, Issue 2 - Serial Number 11
January 2023
Pages 93-119

Files

History

  • Receive Date: 13 July 2022
  • Revise Date: 20 August 2022
  • Accept Date: 11 January 2023

Share

How to cite

Statistics