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

Authors:
Ting-Yu Chen
Affiliations:
Department of Business Administration, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

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.