The Convergence Of Fuzzy Variable Sequences

Probability theory can be used to study random phenomena and random events.However,only using probability theory can not effectively solve the problem with fuzziness in reality,which brings difficulties to the development of many fields.Thus,it is of great importance to study credibility theory.Credibility theory is a new axiomatic system method for dealing with fuzzy events.Convergence is an important part of credibility theory.Considering the importance of the convergence of fuzzy variable sequences in practical problems,this dissertation introduces two kinds of special fuzzy variable sequences,proposes the concepts of statistical convergence of fuzzy variable sequences based on the existing convergences of fuzzy variable sequences,and derives the relationships among these convergences based on credibility theory.The main contents are as follows:(1)Extend the definition of the classical Cauchy sequence to credibility theory,redefining several new fuzzy variable sequences,including Cauchy sequence a.s.and Cauchy sequence in credibility,and further study the convergences of these fuzzy variable sequences.(2)Research the convergences of fuzzy variable sequences under the action of a convex function and a continuous function,by using the properties of convex and continuous functions,and then derive the relationships among them.(3)Propose the concepts of statistical convergence of fuzzy variable sequences,and explore the relationships among these convergences.