The Correlation Coefficients Of Several Extended Fuzzy Soft Sets And Their Application In Multi-attribute Decision Making

As an extension of fuzzy set,fuzzy soft set can effectively express uncertain and vague information which combines fuzzy set theory with soft set theory.In recent years,many scholars have studied fuzzy soft sets,such as intuitionistic fuzzy soft set,hesitant fuzzy soft set,dual hesitant fuzzy soft sets,and so on.These theories are widely used in decision-making,prediction,measure theory and data analysis.Based on the existing literature,according to the attribute characteristics of extended fuzzy soft sets,the correlation coefficients are constructed and the corresponding weighted correlation coefficients are put forward.Finally,the correlation coefficients are proved to be applicable to the multi-attribute decision making problem by some examples,which could show their feasibility and effectiveness.Intuitionistic fuzzy soft set,hesitant fuzzy soft set and dual hesitant fuzzy soft set are the main research objects of this paper.The main research contents and specific work are as follows:The first chapter includes the background of this paper and the historical background and current status of the extended fuzzy soft sets.The chapter two is about correlation coefficient of intuitionistic fuzzy soft set.Based on the properties of intuitionistic fuzzy soft sets and the correlation coefficient of intuitionistic fuzzy sets,the correlation coefficients of intuitionistic fuzzy soft set and the corresponding calculation rules are presented in this chapter.On this basis,we further discuss the weighted correlation coefficient of intuitionistic fuzzy soft sets.Finally,we propose a multi-attribute decision-making method and apply it to an example.The chapter three introduced the correlation coefficient of hesitant fuzzy soft set.According to the idea of the correlation coefficient between variables in statistics,the concept of the correlation coefficient of the hesitant fuzzy soft set is put forward based on the numerical characteristics of mathematical statistics,and its correlation properties are studied.Then,considering the inconsistency of attribute weights,theweighted correlation coefficient is given and its correlation properties are studied.Finally,an example is used to compare the proposed correlation coefficient with the existing correlation coefficient theory in order to prove its practicability and validity.The chapter four is about the correlation coefficient of dual hesitant fuzzy soft set.In this chapter,the correlation coefficients of dual hesitant fuzzy soft set are presented,and the corresponding weighted correlation coefficients are given.Then,a multi-attribute decision-making method is proposed based on the correlation coefficients of dual hesitant fuzzy soft set.Finally,we use the investment problem to illustrate the practicability of the decision-making method.