Grouping fuzzy granular structures based on k-means and fuzzy c-means clustering algorithms in information granulation

Document Type : Research Paper

Authors

1 Beijing University of Posts and Telecommunications

2 School of Science Beijing University of Posts and Telecommunications Beijing 100876, China

Abstract

Fuzzy information granulation theory is based on the way humans granulate and reason about information, and it is essential to the remarkable ability of people to act logically in ambiguous and uncertain situations. In the study of fuzzy information granulation, instead of discussing single fuzzy granules, it is common to consider a fuzzy granular structure arising from a set of fuzzy information granules. Different approaches and perspectives may generate different fuzzy granular structures in the same universe by dividing the object into a number of meaningful fuzzy information granules. However, a specific task usually requires only a selection of representative fuzzy granular structures. Therefore, the main aim of this paper is to group fuzzy granular structures efficiently and accurately. To this end, we first introduce the distances between two fuzzy granular structures and illustrate the relevant properties. Subsequently, k-means and fuzzy c-means clustering algorithms are designed for clustering fuzzy granular structures, and their convergence is demonstrated. In this way, similar fuzzy granular structures can be grouped into the same class. In addition, two evaluation indicators, dispersion and separation, are constructed to evaluate the effect of clustering fuzzy granular structures. Experiments on 12 publicly available datasets demonstrate the feasibility and effectiveness of the proposed algorithms.

Keywords

Main Subjects

References

[1] J. C. Bezdek, R. Ehrlich, W. Full, FCM: The fuzzy c-means clustering algorithm, Computers and Geosciences, 10(2-3) (1984), 191-203.
[2] T. Calinski, J. A. Harabasz, A dendrite method for cluster analysis, Communications in Statistics-Theory and Methods, 3(1) (1974), 1-27.
[3] J. H. Dai, H. W. Tian, Entropy measures and granularity measures for set-valued information systems, Information Sciences, 240 (2013), 72-82.
[4] D. L. Davies, D. W. Bouldin, A cluster separation measure, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (1979), 224-227.
[5] Z. Deng, J. Y. Wang, New distance measure for Fermatean fuzzy sets and its application, International Journal of Intelligent Systems, 37 (2022), 1903-1930.
[6] J. C. Dunn, A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, Journal of Cybernetics, (1973), 32-57.
[7] A. W. Edwards, L. L. Cavalli-Sforza, A method for cluster analysis, Biometrics, (1965), 362-375.
[8] L. G. Fei, H. Wang, L. Chen, Y. Deng, A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators, Iranian Journal of Fuzzy Systems, 16(3) (2019), 113-126.
[9] B. Gohain, R. Chutia, P. Dutta, S. Gogoi, Two new similarity measures for intuitionistic fuzzy sets and its various applications, International Journal of Intelligent Systems, 37(9) (2022), 5557-5596.
[10] J. A. Hartigan, W. A. Wong, Algorithm AS 136: A k-means clustering algorithm, Journal of The Royal Statistical Society, Series c (applied statistics), 28(1) (1979), 100-108.
[11] T. C. Havens, J. C. Bezdek, C. Leckie, L. O. Hall, M. Palaniswami, Fuzzy c-means algorithms for very large data, IEEE Transactions on Fuzzy Systems, 20(6) (2012), 1130-1146. 
[12] M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences, 112 (1998), 39-49.
[13] U. Kuzelewska, Advantages of information granulation in clustering algorithms, International Conference on Agents and Arti cial Intelligence, Springer, Berlin, Heidelberg, (2011), 131-145.
[14] Z. W. Li, X. F. Liu, J. H. Dai, J. L. Chen, H. Fujita, Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system, Knowledge-Based Systems, 196 (2020), 105791.
[15] Z. W. Li, Z. H. Wang, Y. Song, C. F. Wen, Information structures in a fuzzy set-valued information system based on granular computing, International Journal of Approximate Reasoning, 134 (2021), 72-94.
[16] J. Y. Liang, Z. Z. Shi, The information entropy, rough entropy and knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(1) (2004), 37-46.
[17] J. Y. Liang, Z. Z. Shi, D. Li, M. J. Wierman, Information entropy, rough entropy and knowledge granulation in incomplete information systems, International Journal of General Systems, 35(6) (2006), 641-654.
[18] T. Y. Lin, Granular computing on binary relations I: Data mining and neighborhood systems, Rough Sets in Knowledge Discovery, 1(1) (1979), 3-18.
[19] T. Y. Lin, Granular computing on binary relations II: Rough set representations and belief functions, Rough Sets in Knowledge Discovery, (1998), 122-140.
[20] T. Y. Lin, Granular computing: Fuzzy logic and rough sets, Computing with Words in Information/Intelligent Systems 1, Physica, Heidelberg, (1999), 183-200.
[21] K. Y. Liu, X. B. Yang, H. L. Yu, H. Fujita, X. J. Chen, D. Liu, Supervised information granulation strategy for attribute reduction, International Journal of Machine Learning and Cybernetics, 11(9) (2020), 2149-2163.
[22] R. L. Liu, H. L. Yang, L. J. Zhang, Information structures in a fuzzy  -covering information system, Journal of Intelligent and Fuzzy Systems, 40(6) (2021), 11691-11716.
[23] J. MacQueen, Classi cation and analysis of multivariate observations, Proceedings of the Fifth Berkeley Sympo-sium on Mathematical Statistics and Probability, (1967), 281-297.
[24] Z. Pawlak, Rough sets: Theoretical aspects of reasoning about data, Springer Science and Business Media, (1991), 3-5.
[25] W. Pedrycz, Granular computing: An introduction, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), (2001), 1349-1354.
[26] B. Prabir, N. P. Mukherjee, Fuzzy relations and fuzzy groups, Information Sciences, 36(3) (1985), 267-282.
[27] Y. H. Qian, H. H. Cheng, J. T. Wang, J. Y. Liang, W. Pedrycz, C. Y. Dang, Grouping granular structures in human granulation intelligence, Information Sciences, 382 (2017), 150-169.
[28] Y. H. Qian, Y. B. Li, J. Y. Liang, G. P. Lin, C. Y. Dang, Fuzzy granular structure distance, IEEE Transactions on Fuzzy Systems, 23(6) (2015), 2245-2259.
[29] Y. H. Qian, J. Y. Liang, W. Z. Wu, G. Q. Zhang, Information granularity in fuzzy binary GrC model, IEEE Transactions on Fuzzy Systems, 19 (2011), 253-264.
[30] P. J. Rousseeuw, Silhouettes: A graphical aid to the interpretation and validation of cluster analysis, Journal of Computational and Applied Mathematics, 20 (1987), 53-65.
[31] C. Z. Wang, Y. Huang, M. W. Shao, D. G. Chen, Uncertainty measures for general fuzzy relations, Fuzzy Sets and Systems, 360 (2019), 82-96.
[32] N. X. Xie, Z. W. Li, W. Z. Wu, G. Q. Zhang, Fuzzy information granular structures: A further investigation, International Journal of Approximate Reasoning, 114 (2019), 127-150.
[33] J. Yang, G. Y. Wang, Q. H. Zhang, Knowledge distance measure in multigranulation spaces of fuzzy equivalence relations, Information Sciences, 448 (2018), 18-35.
[34] T. Yang, X. R. Zhong, G. M. Lang, Y. H. Qian, J. H. Dai, Granular matrix: A new approach for granular structure reduction and redundancy evaluation, IEEE Transactions on Fuzzy Systems, 28(12) (2020), 3133-3144.
[35] Y. Y. Yao, Information granulation and rough set approximation, International Journal of Intelligent Systems, 16(1) (2001), 87-104.
[36] Y. Y. Yao, Three-way decision and granular computing, International Journal of Approximate Reasoning, 103 (2018), 107-123.
[37] M. X. Yao, Granularity measures and complexity measures of partition-based granular structures, Knowledge-Based Systems, 163 (2019), 885-897.
[38] J. Yu, General c-means clustering model, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(8) (2005), 1197-1211.
[39] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353.
[40] L. A. Zadeh, Fuzzy sets and information granularity, Advances in Fuzzy Set Theory and Applications, 11 (1979), 3-18.
[41] L. A. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems, 90(2) (1997), 111-127.
[42] L. A. Zadeh, Fuzzy logic=computing with words, Computing with Words in Information/Intelligent Systems 1, Physica, Heidelberg, (1999), 3-23.
[43] H. Y. Zhang, S. Y. Yang, Uncertainty analysis of hierarchical granular structures for multi-granulation typical hesitant fuzzy approximation space, Iranian Journal of Fuzzy Systems, 17(4) (2020), 69-84.
[44] P. Zhu, An improved axiomatic de nition of information granulation, Fundamenta Informaticae, 120(1) (2012), 93-109.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 5
September and October 2023
Pages 9-31

Files

Share

How to cite

Statistics