The Extension Of Cubic Set And Their Application

Since Zadeh put forward the theory of fuzzy sets,the theory of fuzzy sets has developed rapidly.Cubic set is one of the extended sets of fuzzy sets.On the basis of the existing literature,this paper studies and extends the cubic set theory,striving to improve the theory and provide solutions to some practical problems.In this paper,complex cubic sets,probabilistic cubic hesitant fuzzy sets and cubic dual hesitant fuzzy sets are proposed and the properties of these new sets are studied.On this basis,some new multi-attribute decision making methods are proposed.The main research contents and specific work of this paper are as follows:The first chapter is the introduction.This chapter introduces the practical significance of studying the cube set theory,and the research status of cube set at home and abroad.It also introduces the definition of cube set and related operations as the theoretical basis of this paper.In the second chapter,based on cubic set and complex fuzzy set,the concept of complex cubic set is proposed,and the distance measure of complex cubic set is defined according to the existing literature,and it is applied to contour recognition.In the third chapter,based on the cubic set and probabilistic hesitant fuzzy set,the probabilistic cubic hesitant fuzzy set is proposed.According to the existing literature,the scoring function and aggregation operator of probabilistic cubic hesitant fuzzy set are defined and applied to multi-attribute decision making problems.In the fourth chapter,based on cubic sets and dual hesitant fuzzy sets,a cubic dual hesitant fuzzy set is proposed.According to the existing literature,the weighted average operator and score function of cubic dual hesitant fuzzy sets are defined and applied to multi-attribute decision making problems.The fifth chapter is conclusion and prospect.This chapter summarizes the main work and innovation of the full text,and prospects the future research work.