Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure
The goal of this paper is to introduce two new concepts ∗-fuzzy premeasure and outer ∗-fuzzy measure, and to further prove some properties, such as Caratheodory’s Theorem, as well as the unique extension of ∗-fuzzy premeasure. This theorem is remarkable for it allows one to construct a ∗-fuzzy measu...
| Published in: | Axioms |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-05-01
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| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/11/5/240 |
| Summary: | The goal of this paper is to introduce two new concepts ∗-fuzzy premeasure and outer ∗-fuzzy measure, and to further prove some properties, such as Caratheodory’s Theorem, as well as the unique extension of ∗-fuzzy premeasure. This theorem is remarkable for it allows one to construct a ∗-fuzzy measure by first defining it on a small algebra of sets, where its ∗-additivity could be easy to verify, and then this theorem guarantees its extension to a sigma-algebra. |
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| ISSN: | 2075-1680 |