Abstract
In this work, an extension of almost separation axioms is introduced in lattice valued theory. Such a generalized almost separation axioms is a structure of ( i; j)-regular open set of its lattice-valued satisfying axioms. It uses two lattices one complete residuated lattice, and another strictly two-sided commutative quantale. It is a logical generalization of the notions of almost separation axioms. In our de fi nition of generalized fuzzifying separation axioms, each notions can be regarded as relations between the one another to some degree.