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On Lacunary Statistical Limit and Cluster Points of Sequences of Fuzzy Numbers | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 5، دوره 10، شماره 6، اسفند 2013، صفحه 53-62 اصل مقاله (373.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2013.1315 | ||
| نویسندگان | ||
Pankaj Kumar1؛ Satvinder Singh Bhatia2؛ Vijay Kumar  1
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| 1Department of Mathematics, Haryana College of Technology and Management, Kaithal-136027, Haryana, India | ||
| 2School of Mathematics and Computer Application, Thapar Universtiy, Patiala, Punjab, India | ||
| چکیده | ||
| 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 $\Gamma^{F}_{S}(X)$. | ||
| کلیدواژه‌ها | ||
| Statistical convergence؛ Lacunary sequences؛ Statistical limit points؛ Statistical cluster points؛ Fuzzy number sequences | ||
| مراجع | ||
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