LACUNARY STATISTICAL CONVERGENCE OF SEQUENCES OF FUZZY NUMBERS

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 n umber 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 replac ed by {k: k(r-1) < k less than or equal to k(r)} for some lacunary seq uence {k(r)}. Also we introduce the concept of lacunary statistically Cauchy sequence and show that it is equivalent to the lacunary statist ical convergence. in addition, the inclusion relations between the set s of statistically convergent and lacunary statistically convergent se quences of fuzzy numbers are given. (C) 1998 Published by Elsevier Sci ence B.V. All rights reserved.