CONVERGENCE OF SEQUENCES OF FUZZY RANDOM-VARIABLES AND ITS APPLICATION

This paper defines two types of generalized metrics in the set of all fuzzy random variables on a probability space. Several different kinds of convergence for sequences of fuzzy random variables with respect t o the generalized metrics are introduced (e.g. everywhere convergence, almost everywhere convergence, almost uniform convergence, convergenc e in probability measure, etc.). The relations of these kinds of conve rgence are also investigated. Moreover, this paper proves some converg ence theorems for sequences of integrals of fuzzy random variables (e. g. monotone convergence theorems, Lebesgue dominated convergence theor ems, etc.) under different convergence senses.