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Minimal sets for the Hausdorff measure of noncompactness and related coefficients

✍ Scribed by Elisabetta Maluta; Stanisław Prus

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
480 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

It is proved that every bounded infinite set in a weakly compactly determined Banach space contains a subset minimal for the Hausdorff measure of noncompactness whose measure is the same as the measure of the whole set. Various coefficients related to minimal sets are also studied.

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✍ Wenyi Zeng; Hongxing Li 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 130 KB

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures,