Best Approximation Results for Fuzzy-Number-Valued Continuous Functions
In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the ex...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/192 |
| _version_ | 1797622384606314496 |
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| author | Juan J. Font Sergio Macario |
| author_facet | Juan J. Font Sergio Macario |
| author_sort | Juan J. Font |
| collection | DOAJ |
| description | In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem. |
| first_indexed | 2024-03-11T09:10:34Z |
| format | Article |
| id | doaj.art-f0ca91704a6a4d668f17e55c7a425855 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:10:34Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-f0ca91704a6a4d668f17e55c7a4258552023-11-16T19:06:34ZengMDPI AGAxioms2075-16802023-02-0112219210.3390/axioms12020192Best Approximation Results for Fuzzy-Number-Valued Continuous FunctionsJuan J. Font0Sergio Macario1Institut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Avda. Sos Baynat s/n, 12071 Castelló, SpainInstitut Universitari de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Avda. Sos Baynat s/n, 12071 Castelló, SpainIn this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem.https://www.mdpi.com/2075-1680/12/2/192best approximationfuzzy-valued continuous functionMichael selection theorem |
| spellingShingle | Juan J. Font Sergio Macario Best Approximation Results for Fuzzy-Number-Valued Continuous Functions Axioms best approximation fuzzy-valued continuous function Michael selection theorem |
| title | Best Approximation Results for Fuzzy-Number-Valued Continuous Functions |
| title_full | Best Approximation Results for Fuzzy-Number-Valued Continuous Functions |
| title_fullStr | Best Approximation Results for Fuzzy-Number-Valued Continuous Functions |
| title_full_unstemmed | Best Approximation Results for Fuzzy-Number-Valued Continuous Functions |
| title_short | Best Approximation Results for Fuzzy-Number-Valued Continuous Functions |
| title_sort | best approximation results for fuzzy number valued continuous functions |
| topic | best approximation fuzzy-valued continuous function Michael selection theorem |
| url | https://www.mdpi.com/2075-1680/12/2/192 |
| work_keys_str_mv | AT juanjfont bestapproximationresultsforfuzzynumbervaluedcontinuousfunctions AT sergiomacario bestapproximationresultsforfuzzynumbervaluedcontinuousfunctions |