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Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering for Noisy Data

Pham Huy Thong1,2,3, Florentin Smarandache4, Phung The Huan5, Tran Manh Tuan6, Tran Thi Ngan6,*, Vu Duc Thai5, Nguyen Long Giang2, Le Hoang Son3

1 Graduate University of Science and Technology, Vietnam Academy of Science and Technology, Hanoi, 100000, Vietnam
2 Institute of Information Technology, Vietnam Academy of Science and Technology, Hanoi, 100000, Vietnam
3 VNU Information Technology Institute, Vietnam National University, Hanoi, 100000, Vietnam
4 Department of Mathematics, University of New Mexico, Gallup, 87301, New Mexico, USA
5 University of Information and Communication Technology, Thai Nguyen University, Thai Nguyen, 250000, Vietnam
6 Faculty of Computer Science and Engineering, Thuyloi University, Hanoi, 100000, Vietnam

* Corresponding Author: Tran Thi Ngan. Email:

Computer Systems Science and Engineering 2023, 46(2), 1981-1997.


Clustering is a crucial method for deciphering data structure and producing new information. Due to its significance in revealing fundamental connections between the human brain and events, it is essential to utilize clustering for cognitive research. Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties. Noisy data can lead to incorrect object recognition and inference. This research aims to innovate a novel clustering approach, named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering (PNTS3FCM), to solve the clustering problem with noisy data using neutral and refusal degrees in the definition of Picture Fuzzy Set (PFS) and Neutrosophic Set (NS). Our contribution is to propose a new optimization model with four essential components: clustering, outlier removal, safe semi-supervised fuzzy clustering and partitioning with labeled and unlabeled data. The effectiveness and flexibility of the proposed technique are estimated and compared with the state-of-art methods, standard Picture fuzzy clustering (FC-PFS) and Confidence-weighted safe semi-supervised clustering (CS3FCM) on benchmark UCI datasets. The experimental results show that our method is better at least 10/15 datasets than the compared methods in terms of clustering quality and computational time.


Cite This Article

P. H. Thong, F. Smarandache, P. T. Huan, T. M. Tuan, T. T. Ngan et al., "Picture-neutrosophic trusted safe semi-supervised fuzzy clustering for noisy data," Computer Systems Science and Engineering, vol. 46, no.2, pp. 1981–1997, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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