An orthogonal clustering method under hesitant fuzzy environment

Abstract

In this paper, we investigate the cluster techniques of hesitant fuzzy information. Consider that the distance measure is one of the most widely used tools in clustering analysis, we first point out the weakness of the existing distance measures for hesitant fuzzy sets (HFSs), and then put forward a novel distance measure for HFSs, which involves a new hesitation degree. Moreover, we construct the distance matrix and choose different values of λ so as to obtain the λ - cutting matrix, each column of which is treated as a vector. After that, an orthogonal clustering method is developed for HFSs. The main idea of this clustering method is that the orthogonal vectors in the distance matrix should be clustered into the same group, and according to the different values of λ, the procedure will repeat again and again until all the cases are considered. Finally, two numerical examples are given to demonstrate the effectiveness of our algorithm.