Some inequalities and limit theorems for fuzzy random variables adopted with alpha-values of fuzzy numbers

摘要

In this paper, some essential stochastic inequalities and several convergence theorems were investigated for fuzzy random variables. The classical counterpart relationship between the proposed convergence theorems was also discussed in the fuzzy environment. The main advantage of the proposed method is its minimal requirements for such limit theorems and inequalities compared to the conventional methods used in the fuzzy environments. The previous methods mostly rely on the lower and upper bounds of the alpha-cuts of fuzzy random variables, while the proposed method utilizes a unified quantity called alpha-value.