In this paper, we present the notions of statistically convergent sequence for fuzzy variables, statistically Cauchy sequence in credibility space, and present a kind of statistical completeness for credibility space. Furthermore, the conditions of statistical convergence almost surely (a.s.), statistical convergence in credibility, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) of fuzzy variable sequences are examined. We have proved relations between these notions.

The purpose of this article is to investigate lacunary ideal convergence of sequences in neutrosophic normed space (NNS). Also, an original notion, named lacunary convergence of sequence in NNS, is defined. Also, lacunary $% \mathcal{I}$-limit points and lacunary $\mathcal{I}$-cluster points of sequences in NNS have been examined. Furthermore, lacunary Cauchy and lacunary $\mathcal{I}$-Cauchy sequences in NNS are introduced and some properties of these notions are studied.

The main goal of this article is to present the notion of Fibonacci I-convergence of sequences on intuitionistic fuzzy normed linear space. To accomplish this goal, we mainly investigate some fundamental properties of the newly introduced notion. Then, we examine the Fibonacci I-Cauchy sequences and Fibonacci I completeness in the construction of an intuitionistic fuzzy normed linear space. Some intuitionistic fuzzy Fibonacci ideal convergent spaces have been established. Further, we prove on some algebraic and topological features of these convergent sequence spaces.

The aim of this article is to investigate the neutrosophic Nörlund ℐ-statistically convergent sequence space. We present some neutrosophic normed spaces (NNSs) in Nörlund convergent spaces. In addition, we also examine various topological and algebraic properties of these convergent sequence spaces. Theorems are proved in light of the NNS theory approach. Results are obtained via different perspectives and new examples are produced to justify the counterparts and show the existence of the introduced notions. The results established in this research work supply an exhaustive foundation in NNS and make a significant contribution to the theoretical development of NNS in the literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementation of neutrosophic Nörlund ℐ-statistically convergent sequences in NNS, based upon the standard definition.

In this paper, we define four types of convergence of a sequence of random variables, namely, $\mathcal{I}$-statistical convergence of order $ \alpha $, $\mathcal{I}$-lacunary statistical convergence of order $\alpha $, strongly $\mathcal{I}$-lacunary convergence of order $\alpha $ and strongly $ \mathcal{I}$-Cesaro summability of order $\alpha $ in probability where $ 0<\alpha <1$. We establish the connection between these notions.