Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets

As a novel and powerful tool, the notion of probabilistic linguistic term sets (PLTSs) can efficiently model this kind of qualitative assessment information utilizing several possible linguistic terms associated with probabilities or weights over alternatives. Considering that there are no investigation and research on the correlation coefficient and clustering analysis for the concept of PLTSs. Therefore, some correlation coefficient formulas are put forward to measure the relationship between two PLTSs and then they are utilized to develop two novel clustering algorithms to group PLTSs in this paper. We first define some correlation coefficient formulas and their weighted forms to measure the relationship between PLTSs. Then, we extend a fuzzy clustering algorithm for PLTSs and also propose a novel orthogonal clustering algorithm for PLTSs. Finally, we provide a practical example, which performs cluster analysis on the levels of general higher education in different regions of China, to test and verify the usability of our proposed clustering algorithm.