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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/5/240 |
| _version_ | 1827670356528201728 |
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| author | Radko Mesiar Chenkuan Li Abbas Ghaffari Reza Saadati |
| author_facet | Radko Mesiar Chenkuan Li Abbas Ghaffari Reza Saadati |
| author_sort | Radko Mesiar |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:20:57Z |
| format | Article |
| id | doaj.art-e675fb3eac334d7f93cf1e84fa44b6ef |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T03:20:57Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e675fb3eac334d7f93cf1e84fa44b6ef2023-11-23T10:04:32ZengMDPI AGAxioms2075-16802022-05-0111524010.3390/axioms11050240Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy MeasureRadko Mesiar0Chenkuan Li1Abbas Ghaffari2Reza Saadati3Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, SlovakiaDepartment of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, CanadaSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, IranSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, IranThe 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.https://www.mdpi.com/2075-1680/11/5/240∗-outer fuzzy measuret-norm∗-fuzzy premeasureCaratheodory’s theorem |
| spellingShingle | Radko Mesiar Chenkuan Li Abbas Ghaffari Reza Saadati Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure Axioms ∗-outer fuzzy measure t-norm ∗-fuzzy premeasure Caratheodory’s theorem |
| title | Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure |
| title_full | Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure |
| title_fullStr | Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure |
| title_full_unstemmed | Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure |
| title_short | Fuzzy Caratheodory’s Theorem and Outer ∗-Fuzzy Measure |
| title_sort | fuzzy caratheodory s theorem and outer ∗ fuzzy measure |
| topic | ∗-outer fuzzy measure t-norm ∗-fuzzy premeasure Caratheodory’s theorem |
| url | https://www.mdpi.com/2075-1680/11/5/240 |
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