Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy Numbers

Abstract

In this article we present the following definition which is natural combination of the definition for asymptotically equivalent and lacunary statistical convergence of fuzzy numbers. Let theta = (k(r)) be a lacunary sequence. The two sequnces X = (X-k) and Y = (Y-k) of fuzzy numbers are said to be asymptotically lacunary statistical equivalent to multiple L provided that for every epsilon > 0 lim(r) 1/h(r) vertical bar{k is an element of I-r : (d) over bar (X-k/Y-k, L) >= epsilon}vertical bar = 0.