Lacunary statistical convergence of sequences of fuzzy numbers

Abstract

The sequence X = {X-k} of fuzzy numbers is statistically convergent to the fuzzy number X-0 provided that for each epsilon > 0 lim 1/n{the number of k less than or equal to n:(d) over bar(X-k, X-0) greater than or equal to epsilon} = 0. In this paper we study a related concept of convergence in which the set {k: k less than or equal to n} is replaced by {k: k(r-1) < k less than or equal to 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. (C) 1998 Published by Elsevier Science B.V. All rights reserved.