Equilibrium Mean Value of Random Fuzzy Variable and Its Convergence Properties

The equilibrium measure is a natural extension of both probability and credibility measures. The convergence modes of random fuzzy variables with respect to equilibrium measure is an important issue for research. In this paper, we first introduce several convergence concepts for sequences of random fuzzy variables, including convergence in equilibrium measure and convergence in equilibrium distribution. Then we deal with the properties of the convergence modes of random fuzzy variables. The equilibrium mean value of random fuzzy variable with respect to equilibrium measure is also defined by nonlinear integral. For sequence of integrable random fuzzy variables, we deal with the important monotone convergence theorems as well as dominated convergence theorems. The convergent results obtained in this paper have potential applications in the approximation scheme of equilibrium optimization models. c ©2013 World Academic Press, UK. All rights reserved.