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In this paper, we define and investigate the notions of \(L\)-separation axioms in \(L\)-fuzzifying supra-topology. Also, some of their characterizations and a systematic discussion on the relationship among these notions is gave in \(L\)-fuzzifying supra-topology where \(L\) is a complete residuated lattice. Sometimes we need more conditions on \(L\) such as the completely distributive law or that the "\(\wedge\)" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results (see [2, 13]) are generalized and new consequences are obtained.
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