Statistical convergence of sequences of fuzzy numbers and sequences of alpha-cuts

AYTAR S. , PEHLİVAN S.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, vol.37, no.2, pp.231-237, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1080/03081070701251075
  • Title of Journal : INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Page Numbers: pp.231-237
  • Keywords: sequences of fuzzy numbers, statistical convergence, uniform statistical convergence, levelwise convergence, natural density, METRIC-SPACES

Abstract

In this short paper, we show that the statistical convergence of a sequence of fuzzy numbers with respect to the supremum metric is equivalent to the uniform statistical convergence of the sequences of functions which are defined via the endpoints of -cuts of the same fuzzy numbers sequence. We introduce the concept of levelwise statistical convergence and present the analogous relation between levelwise statistical convergence of a sequence of fuzzy numbers and pointwise statistical convergence of the sequences of endpoint functions.