On Chung's type law of large numbers for fuzzy random variables

Let {Xn|n⩾1} be a sequence of independent fuzzy random variables and {an|n⩾1} a sequence of positive real numbers converging to ∞. In this paper we show that, under the assumption ∑n=1∞Eφ(∥Xn∥ρp)/φ(an)<∞ with some restrictions on φ, Sn/an→0˜ a.s. if and only if Sn/an→0˜ in probability if and only if Sn/an→0˜ in L1 where Sn=∑i=1nXi. This will generalize earlier results of strong law of large numbers for random elements in a Banach space (Choi and Sung (1988). Bull. Austral. Math. Soc. 37, 93-100).