An extension of Lowen's uniformity to the fuzzy soft sets

Abstract

In this paper, first we define the notion of a saturated fuzzy soft filter. Based on this, we introduce the notion of a fuzzy soft uniformity as a generalization of uniformity in the sense of Lowen. Also, we show how a fuzzy soft topology is derived from a fuzzy soft uniformity. Then, we give a new kind of fuzzy soft neighborhood system and investigate the relationship with a fuzzy soft uniformity. Finally, we show that a fuzzy soft uniformly continuous mapping is a fuzzy soft continuous.