The Research On Multiple Attribute Group Decision Making Methods Based On T-spherical Fuzzy Numbers

As an important branch of modern decision-making theory,the approaches of multiple attribute decision-making have been widely used in many fields such as economy,management,military,and engineering.With the rapid development of economy and society,more and more realistic decision-making issues such as pattern recognition,supplier selection,medical diagnosis,and investment project selection need to rely on expert decision-making.The fuzzy and complex decision-making information and environment make the multiple attribute group decision-making problem full of uncertainty.So in order to better and more conveniently describe the evaluation information given by decision makers in this complex environment,various forms of information expression have appeared.Therefore,scholars have successively proposed fuzzy set theories such as fuzzy set,intuitionistic fuzzy set,picture fuzzy set,Pythagorean fuzzy set,neutrosophic fuzzy set and Q-rung orthopair fuzzy sets.However,the range of information expression of these fuzzy sets is limited,and in some cases,the information cannot be expressed completely.Therefore,the theory of T-spherical fuzzy sets came into being.The complex decision-making information among things can be expressed in detail by T-spherical fuzzy sets.On the basis of previous studies,multiple attribute group decision-making methods under the environment of T-spherical fuzzy sets have been systematically studied in this paper,and these decision-making methods have been applied to practice.The main work of this paper is as follows:(1)We propose the generalized Hamming distance,the generalized Euclidean distance,and the generalized Chen's distance of T-spherical fuzzy sets,and discusses the relationship between them.And we prove the common properties they satisfy.Then,based on the Jensen-Shannon divergence measure,the divergence measure of T-spherical fuzzy sets is proposed,which is the TSFSJS distance measure proposed below.Finally,the proposed TSFSJS distance measure is applied to pattern recognition;(2)We propose nine similarity measures of T-spherical fuzzy sets,including cosine similarity measures,cosine function-based similarity measures and cotangent function-based similarity measures,and prove the relevant properties of these similarity measures.Then,we discuss the application of the proposed similarity measures in supplier selection;(3)Based on the dice similarity measure,the dice similarity measures of type I,type II of T-spherical fuzzy sets are proposed.Then the generalized dice similarity measures of T-spherical fuzzy sets are proposed.Finally,the proposed generalized dice similarity measures are applied to medical diagnosis,and the advantages of the proposed method are analyzed;(4)Based on Dombi operators,the following operators of T-spherical fuzzy sets are proposed: Dombi weighted average operator,Dombi order weighted average operator,Dombi hrbrid weighted average operator,Dombi weighted geometric operator,Dombi order weighted geometric operator and Dombi hybrid weighted geometric operator are proposed.Then,TOPSIS method based on the T-spherical fuzzy Dombi aggregation operator is proposed,and the decision-making steps of the proposed method are introduced in detail.Finally,the proposed multiple attribute group decision-making method is applied to the investment project selection problem.