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

Document Type: Research Paper

Authors

1 Department of Mathematics, Haryana College of Technology and Management, Kaithal-136027, Haryana, India

2 School of Mathematics and Computer Application, Thapar Universtiy, Patiala, Punjab, India

Abstract

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 $\Gamma^{F}_{S}(X)$.

Keywords


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