Characterizations of M-fuzzifying topological operators and its applications

This paper mainly discuss eight kinds of equivalent characterizations of an M-fuzzifying topological closure operator cl: 2X ? MX, an M-fuzzifying topological interior operator int: 2X ? MX, and an M-fuzzifying topological derived operator der: 2X ? MX, in which M is a completely distributive De Morgan algebra. As its applications, we give the fuzzy constructions of M-fuzzifying topological operators cld, intd, derd induced by an M-fuzzifying pseudo metric d in the sense of Morsi?s fuzzy metric and prove that the continuity between M-fuzzifying topological operator spaces and M-fuzzifying pseudo metric spaces is maintained. Finally, we show that the M-fuzzifying topological T induced by d is exactly the M-fuzzifying topological induced by cld, intd and derd. Namely, Td = Tcld = Tintd = Tderd.