Abstract
The sequence X = { X k } of fuzzy numbers is statistically convergent to the fuzzy number X 0 provided that for each ϵ ≺ 0 lim l n { the number ofk⩽n:d(X k,X 0)⩾ϵ}=0 . In this paper we study a related concept of convergence in which the set { k: k⩽ n} is replaced by { k: k r−1 ≺ k ⩽ k r } for some lacunary sequence { k r }. Also we introduce the concept of lacunary statistically Cauchy sequence and show that it is equivalent to the lacunary statistical convergence. In addition, the inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers are given.
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