On S-quasi-fuzzy proximity spaces

The category of pointwise S-proximity spaces

“…Definition 2.18 (Ghanim et al [6]). A binary relation ⊆ I X × I X is said to be an S-quasi-proximity on a nonempty set X if and only if it satisfies the following conditions:…”

“…There have been all kinds of studies about the theory of quasi-proximity and proximity in fuzzy set theory (see [2][3][4][5][6][9][10][11]13,14], etc.). Moreover the concept of S-quasi-proximity in [8] was also generalized to [0, 1]-fuzzy set theory by Ghanim et al [6].…”

“…Moreover the concept of S-quasi-proximity in [8] was also generalized to [0, 1]-fuzzy set theory by Ghanim et al [6]. But the definition of S-quasi-proximity in [6] relies on the order-reversing involution in [0, 1], hence it cannot be generalized to K-fuzzy set theory, where basis lattice K has no order-reversing involution.…”

“…When K = {0, 1}, pointwise S-quasi-proximity is exactly equivalent to S-quasi-proximity in [8]. But the concept of pointwise Squasi-proximity is different from the definition of S-quasi-proximity in [6].…”

L-Fuzzy Topological Spaces and L-Fuzzy Quasi-Proximity Spaces

“…In the framework of L-topology, many authors generalized the crisp proximity to L-fuzzy setting. For example, in [5], Ghanim et al introduced the concept of S-quasi-proximities on [0, 1] X and in [12], Shi studied S-quasi-proximities on L X and pointwise S-quasi-proximities. Katsaras [8] introduced quasi-proximity in [0,1]-fuzzy set theory.…”