In this article we define a norm on a near-ring in order to present the idea of fuzzy normed near-rings for the first time and study some of its interesting properties. We prove the validity of certain results related to this structure. We also construct the ideals and study its behavior by establishing valuable conclusions.

Index Terms: : Near-ring; Fuzzification; Normed Near-ring; R-subgroup; Idempotent t-Norm