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<p>The primary objective of this paper is to explore various forms of deferred convergence for triple sequences of fuzzy variables (<i>FV</i>), incorporating the concepts of ideal convergence and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>-density. We also establish a number of instances to illustrate our definitions. In this study, we also present important findings that reveal the connections between these definitions. The if and only if condition for the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>-deferred <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {I}_{3}\)</EquationSource> </InlineEquation>-statistically pre-Cauchy (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(p\mathfrak {Ca}\)</EquationSource> </InlineEquation>) triple sequence of <i>FV</i> is also examined.</p><p><i>Significance of the work in broad context:</i> Summability theory and the convergence of sequences have numerous applications in mathematical analysis. However, the exploration of sequence convergence in credibility space is still in its early stages with limited progress. This paper contributes to the field by introducing the concept of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mu \)</EquationSource> </InlineEquation>-deferred <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\mathcal {I}_{3}\)</EquationSource> </InlineEquation>-statistical convergence for sequences in credibility space. This novel approach opens up a new direction for researchers in the field.</p>

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An Investigation on µ-Deferred Triple Ideal Statistically Convergent Sequences in Credibility Space

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Binod Chandra Tripathy,
  • Ömer Kişi,
  • Mehmet Gürdal

摘要

The primary objective of this paper is to explore various forms of deferred convergence for triple sequences of fuzzy variables (FV), incorporating the concepts of ideal convergence and \(\mu \) -density. We also establish a number of instances to illustrate our definitions. In this study, we also present important findings that reveal the connections between these definitions. The if and only if condition for the \(\mu \) -deferred \(\mathcal {I}_{3}\) -statistically pre-Cauchy ( \(p\mathfrak {Ca}\) ) triple sequence of FV is also examined.

Significance of the work in broad context: Summability theory and the convergence of sequences have numerous applications in mathematical analysis. However, the exploration of sequence convergence in credibility space is still in its early stages with limited progress. This paper contributes to the field by introducing the concept of \(\mu \) -deferred \(\mathcal {I}_{3}\) -statistical convergence for sequences in credibility space. This novel approach opens up a new direction for researchers in the field.