(2,M)-double fuzzifying topology is a generalization of (2,M)- fuzzifying topology and classical topology. Motivated by the study of (2,M)- fuzzifying topology introduced by Höhle for fuzzifying topology. The main motivation behind this paper is introduce (2,M)-double fuzzifying topology as tight definition and a generalization of (2,M)- fuzzifying topology. Also, study structural properties of (2,M)-double fuzzifying continuous mapping, (2,M)- double fuzzifying quotient mapping, (2,M)-double fuzzifying operator, (2;M)- double fuzzifying totally continuous mapping and define an (2,M)-double fuzzifying Interior (closure) operator. The respective examples of these notions are investigated and the related properties are discussed. On the other hand, a characterization of (2,M)-fuzzifying topology by (2,M)-fuzzifying neighborhood system, where M is a completely distributive, was given in Höhle (2). We extended this defination and others to (2,M)-double fuzzifying topology. As an application of our results, we get characterizations of a (2,M)- double fuzzifying topology by these new notions. These characterizations do not exist in literature before this work. These concepts will help in verifying the existing characterizations and will be useful in achieving new and generalized results in future works.
