On S-quasi-fuzzy proximity spaces

Abstract

In 1992, a new definition for a fuzzy topological space was given by introducing the concept of a gradation of openness (Chattopadhyay et al., 1992). In 1996, we gave a new definition for a fuzzy proximity space by introducing the concept of a gradation of proximity (Ghanim et al., 1996). In this paper we introduce the concept of a gradation of S-quasi-proximity. We show that each gradation of S-quasi-proximity induces two gradations of openness. Some relations between a gradation of S-quasi-proximity and its induced gradations of openness are also investigated.