Mixed Variable Series A Certain Convergence Of Concepts

Kwakernaak first introduced the notion of fuzzy random variable in 1978. The notion of random fuzzy variable was first introduced by Baoding Liu in 2002. A fuzzy random variable is a function from a probability space to the set of fuzzy variables. A random 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 theory and gotten many results on the theory. For example, Yuanguo Zhu and Baoding Liu had proposed the concepts of random fuzzy variable's critical values, expected value, moments, and so on.In 2006 the concept of new chance space and hybrid variable was introduced by Baoding Liu. New chance space inherits the mathematical foundations of both probability and credibility theory, and a hybrid variable is measurable function from a chance space to the set of real numbers. In order to measure hybrid variable, a concept of chance measure was introduced by Li and Liu. And we have gotten many results on the theory. Zhu is included in those studies. But the studies on the convergence of the series of hybrid variables are still less.In this paper, we shall introduce concept of series of hybrid variables and present concept of convergence of series. Besides, we shall introduce concept of global weak independence for hybrid variables and show that convergence almost surely and convergence in chance are equivalent for series of globally weak independent hybrid variables. And we introduce some new convergence concepts for sequence of hybrid variables such as uniform convergence, almost uniform convergence. At last we discuss the relations among these types of convergence.