On the convergence of fuzzy martingales

Abstract

The purpose of this paper is to prove the convergence theorem for fuzzy martingales without assuming that their values are Lipschitz or continuous fuzzy numbers on R n . This approach allows us to deduce many results on convergence of fuzzy numbers and fuzzy random variables from the relevant results on real numbers and real-valued random variables that appear as their support functions. Based on the concept of fuzzy downward martingale and applications of convergence theorem of fuzzy martingales, the strong law of large numbers for fuzzy random variables is proved, here the convergence is in the uniform metric but not the separable metric on fuzzy number space.