The Convergence Of Fuzzy Random Variables

Based on fuzzy random theory, this thesis discusses the issue of the convergence for sequence of fuzzy random variables. First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.The major new results can be summarized as follows:· Some new convergence concepts for sequence of fuzzy random variables are presented;· The relations among some types of convergence are studied;· Some algorithms about fuzzy random simulations are designed.