A note on intuitionistic fuzzy metric spaces

Abstract

Recently, J.H. Park [J.H. Park, Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals 2004;22:1039-46] introduced and studied a notion of intuitionistic fuzzy metric space by using the idea of intuitionistic fuzzy set due to Atanassov. In this note we show that for each intuitionistic fuzzy metric space (X, M, N, *, ◇), the topology generated by the intuitionistic fuzzy metric (M, N) coincides with the topology generated by the fuzzy metric M, and hence, the study of the space (X, M, N, *, ◇) reduces to the study of the fuzzy metric space (X, M, *); so that, Park's results follow directly from well-known theorems in fuzzy metric spaces. © 2005 Elsevier Ltd. All rights reserved.