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Abstract
Abstract We consider a special class of fuzzy metric neighbourhood spaces, where the fuzzy distance is induced by a fuzzy pseudo-norm. This class is contained in Lowen's well known category FNS of Fuzzy Neighbourhood Spaces. We define the fuzzy limit of a sequence, a fuzzy Cauchy sequence and fuzzy convergence in fuzzy metric neighbourhood spaces. We prove that the set of all nonnegative fuzzy real numbers R ∗ (I) under the N-Euclidean metric (the standard fuzzy real line for FNS) is complete, but that the smallest fuzzy neighbourhood real algebra M(I) including R ∗ (I) is not complete. We also characterize the fuzzy Cauchy sequences in M(I) in terms of their corresponding (real) sequences of α-cuts.
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