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

Ting Yu Chen

doi:10.1016/j.fss.2007.04.024

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

Ting Yu Chen^*

^*Corresponding author for this work

Graduate Institute of Mangement

Research output: Contribution to journal › Journal Article › peer-review

101 Scopus citations

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.

Original language	English
Pages (from-to)	2523-2525
Number of pages	3
Journal	Fuzzy Sets and Systems
Volume	158
Issue number	22
DOIs	https://doi.org/10.1016/j.fss.2007.04.024
State	Published - 16 11 2007

Keywords

Euclidean distance
Intuitionistic fuzzy set

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10.1016/j.fss.2007.04.024

Cite this

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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.",

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AB - 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.

KW - Euclidean distance

KW - Intuitionistic fuzzy set

UR - https://www.scopus.com/pages/publications/34548479697

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DO - 10.1016/j.fss.2007.04.024

M3 - 文章

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JO - Fuzzy Sets and Systems

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ER -

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

Abstract

Keywords

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