• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.433-440
• /
• 2021

In this study, we defined the notions of invariant convergence and invariant Cauchy sequences in fuzzy normed spaces. Also, we investigated some properties of invariant convergence and relations between invariant convergence and invariant Cauchy sequences in fuzzy normed spaces.

• Honam Mathematical Journal
• /
• v.42 no.1
• /
• pp.161-173
• /
• 2020

We introduce statistically localized sequences in 2-normed spaces and give some main properties of statistically localized sequences. Also, we prove that a sequence is statistically Cauchy sequence if and only if its statistical barrier is equal to zero. Moreover, we define the uniformly statistically localized sequences on 2-normed spaces and investigate its relationship with statistically Cauchy sequences.

• Korean Journal of Mathematics
• /
• v.5 no.1
• /
• pp.1-8
• /
• 1997

In this note, we study on fuzzy uniform convergences of sequences of fuzzy numbers, and sequences of fuzzy functions.

• Korean Journal of Mathematics
• /
• v.29 no.3
• /
• pp.621-629
• /
• 2021

The idea of C^*-algebra valued metric spaces was given by Ma, Jiang and Sun. In this paper we have studied the ideas of I-Cauchy and I^*-Cauchy sequences and their properties in such spaces and also we give the idea of C^*-algebra valued normed spaces.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.18 no.2
• /
• pp.268-271
• /
• 2008

In this paper, we introduce the notions of a fuzzy convergence of sequences, fuzzy Cauchy sequence and the related fuzzy completeness on a fuzzy normed linear space. And we investigate some properties relative to fuzzy normed linear spaces. In particular, we prove an equivalent conditions that a fuzzy norm defined on a ordinary normed linear space is fuzzy complete.

• Honam Mathematical Journal
• /
• v.46 no.3
• /
• pp.378-392
• /
• 2024

In this paper, we study the notion of I-convergence of double sequences in neutrosophic 2-normed spaces which is more generalized version of statistical convergence of double sequences. Also we define I₂-Cauchy sequence and discuss on I₂-completeness with regards to neutrosophic 2-norm.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.1
• /
• pp.143-147
• /
• 2007

With a new ordinary norm as an analogy of Krishna and Sarma[5] and Bag and Samanta[1], we will characterize the notions of the convergence of the sequences of fuzzy points, the fuzzy, ${\alpha}$-Cauchy sequence and fuzzy completeness.

• Korean Journal of Mathematics
• /
• v.31 no.3
• /
• pp.349-361
• /
• 2023

In this article, we construct lacunary ∆^m-statistical convergence for triple sequences within the context of intuitionistic fuzzy n-normed spaces (IFnNS). For lacunary ∆^m-statistical convergence of triple sequence in IFnNS, we demonstrate numerous results. For this innovative notion of convergence, we further built lacunary ∆^m-statistical Cauchy sequences and offered the Cauchy convergence criterion.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.1017-1025
• /
• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.

• International Journal of Contents
• /
• v.6 no.3
• /
• pp.5-9
• /
• 2010

To manage large database system with video, effective video indexing and retrieval are required. A large number of video retrieval algorithms have been presented for frame-wise user query or video content query, whereas a few video identification algorithms have been proposed for video sequence query. In this paper, we propose an effective video identification algorithm for video sequence query that employs the Cauchy function of histograms between successive frames and the modified Hausdorff distance. To effectively match the video sequences with a low computational load, we make use of the key frames extracted by the cumulative Cauchy function and compare the set of key frames using the modified Hausdorff distance. Experimental results with several color video sequences show that the proposed algorithm for video identification yields remarkably higher performance than conventional algorithms such as Euclidean metric, and directed divergence methods.