A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric

In this note, we point out some errors to Lemma 4 in Grzegorzewski [Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric, Fuzzy Sets and Systems 148, 319-328] by counterexamples. We find that the inequalities of Euclidean distances and normalized Euclidean distances for intuitionistic fuzzy sets are not valid. (C) 2007 Elsevier B.V. All rights reserved.