Convergence in the I-fuzzy real line

Infinite sums and sequences in the fuzzy real line R(I) have been investigated by Wang. In this paper, a necessary and sufficient condition for a sequence in R(I) to be convergent is given in terms of α-cut set. It is proved that fuzzy convergence of sequences in R(I) is equivalent to weak convergence. As an application, convergence of sequences of fuzzy numbers in the sense of Chang and Zadeh is discussed.