Statistical convergence of sequences of fuzzy numbers and sequences of α−cuts

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 α-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.