Soft semi-linear uniform spaces and their perceptual application

Abstract

In this paper, we use the soft set theory and the concept of semi-linear uniform spaces to introduce the notion of soft semi-linear uniform spaces with its generalization, briefly soft-GSLUS. We investigate some properties of soft topology that induced by soft-GSLUS. Also, we use the members of soft-GSLUS to define a soft proximity space and a soft filter then we establish the relationships between them. Finally, we give the perceptual application of soft semi-linear uniform structures by employing the natural transformation of a soft semi-linear uniform space to a soft proximity.