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

AYTAR S. , PEHLİVAN S.

INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, cilt.37, ss.231-237, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 37 Konu: 2
  • Basım Tarihi: 2008
  • Doi Numarası: 10.1080/03081070701251075
  • Dergi Adı: INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
  • Sayfa Sayıları: ss.231-237

Özet

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.