Intuitionistic fuzzy any relation clustering algorithm based on similarity matrix integration with intuitionistic fuzzy C-means and differential evolution optimization

Öz

Data clustering, as a cornerstone technique in machine learning and data mining, plays a pivotal role in partitioning unlabeled datasets into distinct clusters based on inherent similarities. This study proposes the Intuitionistic Fuzzy Any Relation Clustering Algorithm (IF-ARCA) algorithm, a novel hybrid method that integrates the intuitionistic fuzzy C-means (IFCM) algorithm with the Any Relation Clustering Algorithm (ARCA). The IF-ARCA algorithm employs intuitionistic fuzzy similarity matrices (IFSM) constructed using cosine similarity (COS) and fuzzy metrics (FM), alongside dissimilarity and hesitation matrices, to enhance clustering precision. To address the inherent challenges of computational complexity and manual parameter tuning in traditional methods, the algorithm incorporates Differential Evolution (DE) optimization for automatic parameter adjustment, significantly improving performance in high-dimensional datasets. Experimental validation on UCI benchmark datasets demonstrates the superior efficacy of IF-ARCA in terms of clustering accuracy and scalability. The effectiveness of the proposed algorithm is rigorously evaluated using metrics such as F1 score, accuracy, precision, and recall, highlighting its potential for handling complex and ambiguous data.

Anahtar Kelimeler

• Intuitionistic fuzzy C-means
• Differential evolution
• Similarity matrices
• Data clustering

Intuitionistic fuzzy any relation clustering algorithm based on similarity matrix integration with intuitionistic fuzzy C-means and differential evolution optimization

Öz

Veri kümeleme, makine öğrenimi ve veri madenciliğinin temel tekniklerinden biri olarak, etiketlenmemiş veri kümelerini içsel benzerliklerine göre farklı kümelere ayırmada kritik bir rol oynar. Bu çalışma, sezgisel bulanık C-means (IFCM) algoritması ile Any Relation Clustering Algorithm (ARCA) yönteminin entegrasyonunu içeren yeni bir melez yöntem olan Sezgisel Bulanık Herhangi-İlişki Kümeleme Algoritması’nı (IF-ARCA) önermektedir. IF-ARCA, kosinüs benzerliği ve bulanık ölçütlerle oluşturulan sezgisel bulanık benzerlik matrislerinin (IFSM) yanı sıra ayrışma ve tereddüt matrislerini kullanarak kümeleme hassasiyetini artırır. Geleneksel yöntemlerdeki yüksek hesaplama karmaşıklığı ve manuel parametre ayarlama zorluklarını gidermek amacıyla algoritma, parametreleri otomatik olarak ayarlayan Diferansiyel Evrim (DE) optimizasyonunu içerir; bu sayede yüksek boyutlu veri kümelerinde performansı önemli ölçüde iyileştirir. UCI benchmark veri kümeleri üzerindeki deneysel doğrulamalar, IF-ARCA’nın kümeleme doğruluğu ve ölçeklenebilirlik açısından üstün etkinliğini göstermektedir. Önerilen algoritmanın başarısı, F1 skoru, doğruluk, keskinlik (precision) ve geri çağırma (recall) gibi ölçütlerle titizlikle değerlendirilmiş olup, karmaşık ve belirsiz verileri işleme potansiyelini vurgulamaktadır.

Anahtar Kelimeler

• Sezgisel bulanık C-ortalamalar
• Diferansiyel evrim
• Benzerlik matrisleri
• Veri kümeleme

Kaynakça

1. [1] Jain AK. “Data clustering: 50 years beyond K-means”. Pattern Recognition Letters, 31(8), 651-666, 2010.
2. [2] Gan G, Ma C, Wu J. Data Clustering: Theory, Algorithms, and Applications. 2nd ed. Philadelphia, USA, Siam, 2020.
3. [3] Bezdek JC, Ehrlich R, Full W. “FCM: The fuzzy c-means clustering algorithm”. Computers & Geoscience, 10(2-3), 191-203, 1984.
4. [4] Ruspini EH, Bezdek JC, Keller JM. “Fuzzy clustering: A historical perspective”. IEEE Computational Intelligence Magazine, 14(1), 45-55, 2019.
5. [5] Alışkan İ, Ünsal S. “Farklı çıkarım yöntemlerine sahip bulanık mantık denetleyicileri kullanarak kalıcı mıknatıslı senkron motorun hız denetimi”. Pamukkale University Journal of Engineering Sciences, 24(2), 185-191, 2016.
6. [6] Tongbram S, Shimray BA. Singh LS, Dhanachandra N. “A novel image segmentation approach using fcm and whale optimization algorithm”. Journal of Ambient Intelligence and Humanized Computing, 2021.
7. [7] Sharma R, Vashisht V, Singh U. “EEFCM-DE: Energy-efficient clustering based on fuzzy C means and differential evolution algorithm in WSNs”. IET Communications. 13(8), 996-1007, 2019.
8. [8] Katarya R, Verma OP. “Recommender system with grey wolf optimizer and FCM”. Neural Computing and Applications, 30(5), 1679-1687, 2018.

9. [9] Corsini P, Lazzerini B, Marcelloni F. “A Fuzzy relational custering algorithm based on a dissimilarity measure extracted from data”. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(1), 775-781, 2004.
10. [10] Corsini P, Lazzerini B, Marcelloni F. “A new fuzzy relational clustering algorithm based on the fuzzy C-means algorithm”. Soft Computing, 9(6), 439-447, 2005.
11. [11] Atanassov K.T. Intuitionistic Fuzzy Sets. In Intuitionistic Fuzzy Sets: Theory and Applications (pp. 1-137). Heidelberg: Physica-Verlag HD, 1999.
12. [12] Xu Z, Wu J. “Intuitionistic fuzzy C-means clustering algorithms”. Journal of Systems Engineering and Electronics, 21(4), 580-590, 2010.
13. [13] Chaira T. “A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images”. Applied Soft Computing Journal, 11(2), 1711-1717, 2011.
14. [14] Kumar D, Verma H, Mehra A, Agrawal RK. “A modified intuitionistic fuzzy c-means clustering approach to segment human brain MRI image”. Multimedia Tools and Applications, 78(10), 12663-12687, 2019.
15. [15] Thao NX, Ali M, Smarandache F. “An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis”. Journal of Intelligent & Fuzzy Systems, 36(1), 189-198, 2019.
16. [16] Hou WH, Wang YT, Wang, JQ, Cheng PF, Li L. “Intuitionistic fuzzy c-means clustering algorithm based on a novel weighted proximity measure and genetic algorithm”. International Journal of Machine Learning and Cybernetics. 12(3), 859-875, 2021.
17. [17] Ren C, Song Z, Meng Z. “Differential Evolution with fitness-difference based parameter control and hypervolume diversity indicator for numerical optimization”. Engineering Applications of Artificial Intelligence, 133, 108081, 2024.
18. [18] Xia P, Zhang L, Li F. “Learning similarity with cosine similarity ensemble”. Information Science, 307, 39-52, 2015.
19. [19] Kramosil I, Michalek J. “Fuzzy Metrics and Statistical Metric Spaces”. Kybernetika. 11(5), 336-344, 1975.
20. [20] George A, Veeramani P. “On some results in fuzzy metric spaces”. Fuzzy Sets and Systems. 64(3), 395-399, 1994.
21. [21] Gregori V, Morillas S, Sapena A. “Examples of fuzzy metrics and applications”. Fuzzy Sets Systems. 170(1), 95-111, 2011.
22. [22] Shankar B, Murugan K, Obulesu A, Shadrach FDS, Anitha R. MRI image segmentation using bat optimization algorithm with fuzzy C means clustering”. Journal of Medical Imaging Health information, 11(3), 661-666, 2020.
23. [23] Soppari K, Chandra NS. “Development of improved whale optimization based FCM clustering for image watermarking”. Computer Science Review, 37, 100287, 2020.
24. [24] Storn R, Price K. “Differential evolution a simple and efficient heuristic for global optimization over continuous spaces”. Journal of Global Optimization, 11(4), 341-359, 1997.
25. [25] University of California, Irvine. “UCI Machine Learning Repository”. https://archive.ics.uci.edu (15.05.2025).
26. [26] Saladi, S., Yepuganti, K., Chinthaginjala, R., Kim, T. H., & Ahmad, S. “A unique unsupervised enhanced intuitionistic fuzzy C-means for MR brain tissue segmentation”. Scientific Reports, 14(1), 29804, 2024.
27. [27] Kaur A, Kumar Y, Sidhu J. “Exploring meta-heuristics for partitional clustering: Methods, metrics, datasets, and challenges”. Artificial Intelligence Review, 57(10), 287, 2024.
28. [28] Priya MP, Roopa CK, Harish BS. “Modified Intuitionistic Fuzzy Clustering Method (MIFCM) for Microarray Image Spot Segmentation”, Procedia Computer Science, 235, 878-888, 2024.
29. [29] Xie Y, Yang J, Luo Y, Zhang X, Luo J. “Constructing intuitionistic neighborhood based on intuitionistic fuzzy sets for three-way clustering”. International Journal of Approximate Reasoning, 186, 109512, 2025.
30. [30] Alcantud JCR, Stojanović N, Djurović L, Laković M. “Decision-making and clustering algorithms based on the scored-energy of hesitant fuzzy soft sets”. International Journal of Fuzzy Systems, 28, 492–506, 2026.
31. [31] Kutlu F, Ayaz İ, Garg H. “Integrating fuzzy metrics and negation operator in FCM algorithm via genetic algorithm for MRI image segmentation”. Neural Computing & Applications, 36, 17057-17077, 2024.
32. [32] Kutlu F, Göleli K, Castillo O. “Enhanced classification in IF-ARCA and IF-KNN with fuzzy metrics and cosine similarity through dual stage optimization using Harris Hawks algorithm”. Signal, Image & Video Processing, 19(3), 1162, 2025.
33. [33] Sethia, K., Singh, J., & Gosain, A. “An effective imputation approach for handling missing data using intuitionistic fuzzy clustering algorithms”. Discover Computing, 28(1), 133, 2025.
34. [34] Koçoğlu FÖ, Esnaf Ş. “Fuzzy clustering-based hybrid model proposal on location selection for disaster stations”. Journal of Industrial and Management Optimization, 21(11), 6632–6656, 2025.
35. [35] Alharbe NR. “Fuzzy clustering based scheduling algorithm for minimizing the tasks completion time in cloud computing environment”. Scientific Reports, 15(1), 19505, 2025.