On the almost everywhere statistical convergence of sequences of fuzzy numbers

Talo Ö.

Filomat, vol.33, no.9, pp.2683-2693, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 9
  • Publication Date: 2019
  • Doi Number: 10.2298/fil1909683t
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2683-2693
  • Keywords: Almost everywhere statistical convergence, Sequence of fuzzy numbers, Statistical limit inferior, Statistical limit superior
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, we define the concept of almost everywhere statistical convergence of a sequence of fuzzy numbers and prove that a sequence of fuzzy numbers is almost everywhere statistically convergent if and only if its statistical limit inferior and limit superior are equal. To achieve this result, new representations for statistical limit inferior and limit superior of a sequence of fuzzy numbers are obtained and we show that some properties of statistical limit inferior and limit superior can be easily derived from these representations.