Some Properties Of Random Fuzzy Variable Characteristic Function

The notion of random fuzzy variable was first introduced by Baoding Liu in 2002.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 chance distribution,critical values, expected value,moments,and so on.Moreover they have studied the properties of these concepts.At the same time,random fuzzy simulation has played an important role to solve the models of random fuzzy programming.But the studies on the random fuzzy variables of characteristic function are less.Based on the chance distribution,we have studied many mathematical properties of random fuzzy variable,and so on.But sometimes we find that using chance distribution to study the mathematical properties of random fuzzy variable is not convenient.In order to study random fuzzy variable well,we introduce the new concept of characteristic function so that we can study the mathematical properties of random fuzzy variable well.Above all,this paper inherits the mathematical foundations of both random fuzzy theory and probability theory.A new concept of characteristic function for random fuzzy variable is introduced and some properties of characteristic function are obtained.It is proven that characteristic function for random fuzzy variableφ(t₁,t₂)is differentiable in t₁ and t₂,respectively,and partial derivatives ofφ(t₁,t₂)are continuous.Furthermore, the Taylor's expansion ofφ(t₁,t₂)is given and the relation between chance distribution and characteristic function such as inversion formula is obtained.