Research On Clustering Algorithm Based On T-spherical Fuzzy Set

Clustering analysis is a method in unsupervised learning and an important research direction in the field of data mining.In recent years,clustering analysis is booming and has been successfully applied to pattern recognition,image processing,medical diagnosis and many other fields.Clustering problems in the real world are mostly fuzzy and uncertain.In order to better describe the evaluation information given by decision makers in complex environments,a variety of information expression forms have emerged.Scholars have proposed fuzzy sets(FS),intuitionistic fuzzy sets(IFS),image fuzzy sets(PFS),spherical fuzzy sets(SFS)and other theories.However,the representation range of these fuzzy set information is limited.At this time,Tspherical fuzzy set theory(TSFS)was born.T-spherical fuzzy sets can describe the complex decision information between things in detail.Based on the previous scholars ’ research,this paper further studies the T-spherical fuzzy clustering analysis method,and applies these methods to practice.The main work of this paper is as follows :(1)In this paper,a new T-spherical fuzzy Jaccard similarity is proposed in the T-spherical fuzzy environment,and a T-spherical fuzzy spectral clustering algorithm is given on this basis.Finally,the effectiveness of the proposed algorithm is verified by an example,and it is compared with the existing T-spherical fuzzy clustering algorithm.(2)A T-spherical fuzzy clustering algorithm based on set-valued statistics is proposed.The information of initial classification opinions of experts is integrated based on set-valued statistics to obtain T-spherical fuzzy similarity matrix.On this basis,a T-spherical fuzzy clustering method based on set-valued statistics is proposed.Finally,the feasibility of the method is verified by an example.(3)A T-spherical fuzzy clustering algorithm based on fuzzy C-means(FCM)algorithm is proposed.Based on FCM algorithm,T-spherical fuzzy C-means(TSFCM)algorithm is proposed by introducing Tsallis entropy into the objective function.Gaussian,salt and pepper and mixed noise are added to the fuzzy C-means(FCM)algorithm,intuitionistic fuzzy C-means(IFCM)algorithm,image fuzzy C-means(FCPFS)algorithm and the proposed T-spherical fuzzy C-means(TSFCM)algorithm to simulate the mri image,which verifies the effectiveness and noise immunity of the proposed algorithm.(4)A T-spherical fuzzy clustering algorithm based on correlation coefficient is proposed.Firstly,a new correlation coefficient of TSFS is constructed,and the properties of the newly defined correlation coefficient are discussed.Then it is extended to T-spherical fuzzy clustering algorithm and applied to practical problems.Finally,the proposed algorithm is compared with the existing algorithms,the defects of the existing algorithms are pointed out,and the advantages of the new algorithm are discussed.