On Lacunary Statistical Limit and Cluster Points of Sequences of Fuzzy Numbers
نویسندگان
1 Department of Mathematics, Haryana College of Technology and Management, Kaithal-136027, Haryana, India
2 Department of Mathematics, Haryana College of Technology and Management, Kaithal-136027, Haryana, India
3 School of Mathematics and Computer Application, Thapar Universtiy, Patiala, Punjab, India
doi
10.22111/ijfs.2013.1315چکیده
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. 165 (2004) 129-138]. 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 $\Gamma^{F}_{S}(X)$.
