Gradations of uniformity and gradations of proximity

On L-fuzzy proximity spaces

“…principal fuzzifying proximity) on X in a sense [33]. (2) We easily show that every L-fuzzy proximity space is a Samanta's fuzzy proximity space [25] and Ghanism's fuzzy proximity space [10].…”

L-fuzzifying preproximity spaces and L-fuzzifying preuniform spaces

“…Höhle introduced the concept of L-fuzzifying topological spaces [1]. The notions of proximity and uniformity were studied in a fuzzy setting [2][3][4][5][6][7][8][9][10], in an L-fuzzy setting [11,12] and in a fuzzifying setting [13,14]. The way-below relation '' '' was introduced by Scott and others [15].…”

On Bipolar Fuzzy Gradation of Openness

“…This concept of gradation has been used widely instead of direct fuzzification of some mathematical structures mainly in the field of topology by many researchers. Samanta [14] and Ghanim et al [15] introduced gradation of uniformity and gradation of proximity, Thakur et al [16] studied gradation of continuity, and Mondal et al ([11,[17][18][19]) introduced intuitionistic gradation and L-fuzzy gradation.…”