An Orthogonal Fuzzy Clustering Algorithm Based On Probabilistic Linguistic Term Sets

Fuzzy linguistics is mainly used to solve the problems of decision making and clustering analysis.This thesis focuses on the clustering techniques based on hesitant fuzzy information in fuzzy linguistics.Traditional clustering techniques are divided into hard divisions and soft divisions,the studies on them have become relatively mature.While it's in recent years,clustering techniques based on hesitant fuzzy information become a hot topic for many scholars,in hence,it still have many deficiencies.For example,the linguistic model used to describe fuzzy data sets is relatively old and cannot accurately describe uncertain information,the lack of weight information lacks countermeasures on multiple standard fuzzy clustering problems affects the accuracy of fuzzy clustering effects and the existing fuzzy clustering algorithms are too complex and inefficient.Therefore,this article mainly focuses on solving the above deficiencies,and the main works are shown as follows:(1)As for the problem of accurate description of uncertain information,this thesis selects probabilistic linguistic term sets(PLTSs)to solve it.Because PLTSs not only allow evaluators to provide multiple linguistic terms,but also allow for a hesitance.It greatly tolerates uncertainty.In order to provide better clustering tools,this thesis also deduced and proved PLTSs' correlation coefficient formulas,the upper and lower bounds of the correlation coefficient and the hesitance.(2)For the lack of weight information,this thesis proposes a standard weight determination algorithm,considering the impact of the main and objective weights on the clustering.This algorithm mainly includes the three steps of calculating the objective weights produced by the differences of the data itself,standardizing the subjective weights,and combining the subjective and objective weights according to the proportions to obtain the final weight vector.And it can solve the problems under completely known,partially known,and completely unknown conditions.(3)In view of the complexity and low efficiency of the clustering process,this thesis combines with the latest research work to propose an orthogonal fuzzy clustering algorithm based on PLTSs,which has simple process and high efficiency.The main steps involved in the algorithm are as follows:First,the weighted correlation coefficient matrix is calculated by combining the standard weight determination algorithm and the weighted correlation coefficient formula proposed in this thesis;secondly,the equivalent matrix of the correlation coefficient matrix is calculated;then,the confidence level is determined according to the equivalent matrix and then obtain the cutting matrix;Finally,the column vectors inside the cutting matrix are orthogonal or not determine whether the corresponding samples can be placed in the same category,by which,we obtain the final clustering result.At the end of the thesis,the experimental comparison and K-means clustering algorithm verify the accuracy and efficiency of the proposed algorithm.