Robust hesitant fuzzy partitional clustering algorithms and their applications in decision making

Hesitant fuzzy sets (HFSs) are a powerful tool to describe uncertain and vague information, whose relationship can be analyzed and mined by clustering algorithms. The partitional idea is widely used in clustering analysis for real-number data but little for hesitant fuzzy data. After pointing out the weakness of the existing partitional clustering algorithms between HFSs, we modify the existing partitional clustering algorithms and propose four new algorithms with two types under hesitant fuzzy environment. One type, including the hesitant fuzzy K-medians (HFKME) and the hesitant fuzzy C-medians (HFCME) algorithms, is based on median but not mean. The other type, including the improved hesitant fuzzy K-means (IHFKM) and the improved hesitant fuzzy C-means (IFHCM) algorithms, is on the basis of a new and more robust distance measure which will be developed by HFSs. We find that these four new clustering algorithms are more robust than the existing ones and have better performance under the noise environment. After that, we compare our proposed partitional clustering algorithms with each other and also compare them with the existing methods, and then apply them to multi-attribute decision making and cluster analysis. Numerical results show that HFCME has better performance than HFKME, and IHFCM is better than IHFKM.