On Lacunary Statistical Limit and Cluster Points of Sequences of Fuzzy Numbers

For any lacunary sequence \theta = (k_{r}), we define the concepts of S_{\theta}-limit point and S_{\theta}-cluster point of a sequence of fuzzy numbers X = (X_{k}). We introduce the new sets  \Lambda^{F}_{S_{\theta}}(X), \Gamma^{F}_{S_{\theta}}(X) and prove some inclusion relaions between these and the sets \Lambda^{F}_{S}(X), \Gamma^{F}_{S}(X) introduced in ~\cite{Ayt:Slpsfn} by Aytar [S. Aytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci. ۱۶۵ (۲۰۰۴) ۱۲۹-۱۳۸]. Later, we find restriction on the lacunary sequence  \theta = (k_{r}) for which the sets \Lambda^{F}_{S_{\theta}}(X) and \Gamma^{F}_{S_{\theta}}(X) respectively coincides with the sets \Lambda^{F}_{S}(X) and \Gamma^{F}_{S}(X).

کلیدواژه ها:

Statistical convergence ، Lacunary sequences ، Statistical limit points ، Statistical cluster points ، Fuzzy number sequences