In this paper, by relaxing the triangular condition in a non-Archimedean fuzzy metric space further, a notion of an a-non-Archimedean fuzzy metric space is introduced and some of its properties are investigated. Existence of fixed point results of - contraction self map in a complete a-non-Archimedean fuzzy space is proved.

fuzzy metric space, non-Archimedean fuzzy metric space, a-non-Archimedean fuzzy metric space, -mapping, -contraction sequence.