Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets

Abstract

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. K E Y W O R D S cluster analysis, correlation coefficient, hesitant fuzzy sets, hesitant linguistic term sets, probabilistic linguistic term sets Int J Intell Syst. 2018;33:2402-2424. wileyonlinelibrary.com/journal/int 2402 |

Linguisticq‐rung orthopair fuzzy sets and their interactional partitioned Heronian mean aggregation operators

“…It refers to a process, which ranks all the alternatives according to the evaluation information from the decision‐makers (DMs) and then selects the best one, happens frequently in our daily . The multiattribute group decision‐making (MAGDM) refers to a process that calls a group of DMs to assess the alternatives concerning each attribute and then makes choice from all the alternatives . In the early stage of social development, people usually use real numbers to offer their evaluation information .…”

A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment

“…However, the value of the correlation coefficient proposed by Mao et al [12] lies in [0,1], and is thus not consistent with the correlation coefficient in statistics that lies in [−1,1]. Lin et al [33] then introduced a new correlation coefficient on the basis of the mean and variance of the PLTSs, which conforms to the correlation coefficient in statistics that lies in [−1,1]. However, this correlation coefficient actually measures the correlated relationship between the PLTS vectors, and it is a partial correlation coefficient of the mean type.…”

“…Moreover, the method proposed by Lin et al [33] cannot be applied to calculate the correlation coefficient between LP 1 and LP 2 as given in this example. The reason is that this form of correlation coefficient given developed by Lin et al [33] actually reflects the correlated relationship between two PLTS vectors rather than two PLTSs because all elements in each PLTS are simply aggregated a single value by the formula (l) . Therefore, it is impossible to calculate the correlation coefficient between two values.…”

“…Thus, it fails to describe the negative correlated relationship between PLTSs. In definition 8, although the correlation coefficient defined by Lin et al [33] is bounded in [−1,1], the mean and variance of PLTSs used in the correlation coefficient are not the true sense of the PLTS mean and the PLTS variance as they ignore the importance of each element in the PLTS, which actually reflects the correlated relationship between two PLTS vectors rather than two PLTSs. It is only a mean type of correlation coefficient.…”

“…Therefore, the best alternative is x 2 . The computational process and results utilizing the weighted PLTS correlation coefficient defined in [33] are illustrated as follows:…”