Abstract
In this paper, (2, M)-double fuzzifying topology as a generalized (2, M)-fuzzifying topology introduced by Hohle [7] is introduced. The relations between (2, M)-double fuzzy topology and (2, M)-double fuzzifying topology are studied. Also, we provided the definition of (2, M)-double fuzzifying preproximity structure. Not only that we studied the properties of these new notions, but we have also generated (2, M)-double fuzzifying topology from (2, M)-double fuzzifying preproximity. Finally, we introduced (2, M)-double fuzzifying preproximially continuous mapping which it used in more properties.