The Extension Of Fuzzy Preference Relation And Its Application In Decision Making

Decision-making problems have always received enthusiastic attention from scholars because of their close correlation with human life.In recent years,as an effective tool to deal with uncertain decision-making problem,fuzzy theory has been widely concerned and studied by scholars.However,with the increasingly complex social environment,more and more decision-making problems are difficult for a single decision-maker to make decisions in a timely and explicit manner.Therefore,various fuzzy sets and fuzzy preference relations reflecting the uncertainty of decision-maker's thinking have been proposed successively and widely applied in various fields.In this paper,the fuzzy preference relation(FPR)and fuzzy set are extended for the complex decision problems in various environments.On the one hand,it can make up for the limitation of existing fuzzy theory in dealing with complex decision-making problems;on the other hand,it has important theoretical value and practical significance to enrich and promote the development and application of uncertain decision-making theory.The specific research work is as follows:The first chapter gives the background and significance of this paper,introduces the research status and related preparatory knowledge of fuzzy set and FPR,and summarizes the research work and main innovation points of this paper.In chapter two,a new method for decision making using intuitionistic fuzzy preference relations is given on the basis of considering the mutual influence between decision makers.At the same time,a case study is given and compared with the existing methods.The third chapter proposes the probabilistic hesitant fuzzy linguistic preference relation,gives its consistency definition and its consistency improvement method,and proves its excellent properties by applying it to the investment decision problem.Chapter 4 further proposes the probabilistic linguistic dual hesitant fuzzy preference relation,defines its equivalent consistency with the interval fuzzy preference relation,gives the concrete method of using it for decision-making,and demonstrates the effectiveness and superiority of the method with numerical examples.In chapter 5,on the basis of the first two chapters,the author puts forward the probabilistic uncertain linguistic intuitionistic fuzzy preference relation(PULIFPR),discusses its application in group decision making(GDM),and proves its superiority by comparative analysis.Chapter 6 is the conclusion and outlook.