Random Fuzzy Variable Sequence Convergence

The notion of random fuzzy variable was first introduced by Baoding Liu in 2002. Arandom fuzzy variable is a function from a credibility space to the set of random variables.From then on, more and more researchers have paid attention to random fuzzy theoryand gotten many results on the theory. For example, Yuanguo Zhu and Baoding Liu hadproposed the concepts of random fuzzy variable's critical values, expected value, moments,and so on. Moreover they have studied the properties of these concepts. At the sametime, random fuzzy simulation has played an important role to solve the models of randomfuzzy programming. But the studies on the convergence of random fuzzy variables areless. Zhu and Liu [25] and Zhu and Liu [26]are included in those studies.In 2006 the concept of new chance space and hybrid variable was introduced byBaoding Liu. New chance space inherits the mathematical foundations of both proba-bility and credibility theory, and a hybrid variable is measurable function from a chancespace to the set of real numbers. Random variable, fuzzy variable, fuzzy random variableand random fuzzy variable are instances of hybrid variable. In order to measure hybridvariable, a concept of chance measure was introduced by Li and Liu. It can also measurefuzzy random variable.Above all, this paper inherits the mathematical foundations of both random fuzzytheory and new chance theory. It is to introduce some new convergence concepts forsequence of random fuzzy variables such as uniform convergence, almost uniform conver-gence, convergence in chance, convergence in distibution(chance measure is new chanceto measure hybrid events). The relations among these types of convergence are alsodiscussed.