• 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.

• Journal of applied mathematics & informatics
• /
• v.41 no.3
• /
• pp.541-552
• /
• 2023

In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

• 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.

• 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.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.179-185
• /
• 2008

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

• 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.

• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.391-399
• /
• 2010

In this paper, we introduce the notions of the fuzzy statistical convergence of sequences, the fuzzy statistical Cauchy sequence on a fuzzy normed linear space. And we investigate some properties of the related completeness.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.195-203
• /
• 2000

In this paper, the concept of strongly p-Cesaro summability of sequences of fuzzy numbers is introduced. The relationship between statistical convergence and strongly p-Cesaro summability is discussed.