On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications
In the present study, we introduce and characterize the class of r-generalized fuzzy ℓ-closed sets in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. Also, we show that r-generalized fuzzy closed set by Kim and Park (2002) ⟹r-generalized fuzzy ℓ-closed set, but the converse need not be true....
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4483481 |
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| _version_ | 1832566332594323456 |
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| author | I. M. Taha |
| author_facet | I. M. Taha |
| author_sort | I. M. Taha |
| collection | DOAJ |
| description | In the present study, we introduce and characterize the class of r-generalized fuzzy ℓ-closed sets in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. Also, we show that r-generalized fuzzy closed set by Kim and Park (2002) ⟹r-generalized fuzzy ℓ-closed set, but the converse need not be true. Moreover, if we take ℓ=ℓ0, the r-generalized fuzzy ℓ-closed set and r-generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ-continuous multifunctions, and some properties of these multifunctions along with their mutual relationships are studied with the help of examples. Finally, some separation axioms of r-generalized fuzzy ℓ-closed sets are introduced and studied. Also, the notion of r-fuzzy G∗-connected sets is defined and studied with help of r-generalized fuzzy ℓ-closed sets. |
| format | Article |
| id | doaj-art-3e6315073c484dcea0781e7faa9cb903 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3e6315073c484dcea0781e7faa9cb9032025-02-03T01:04:21ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/4483481On r-Generalized Fuzzy ℓ-Closed Sets: Properties and ApplicationsI. M. Taha0Department of Basic SciencesIn the present study, we introduce and characterize the class of r-generalized fuzzy ℓ-closed sets in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. Also, we show that r-generalized fuzzy closed set by Kim and Park (2002) ⟹r-generalized fuzzy ℓ-closed set, but the converse need not be true. Moreover, if we take ℓ=ℓ0, the r-generalized fuzzy ℓ-closed set and r-generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ-continuous multifunctions, and some properties of these multifunctions along with their mutual relationships are studied with the help of examples. Finally, some separation axioms of r-generalized fuzzy ℓ-closed sets are introduced and studied. Also, the notion of r-fuzzy G∗-connected sets is defined and studied with help of r-generalized fuzzy ℓ-closed sets.http://dx.doi.org/10.1155/2021/4483481 |
| spellingShingle | I. M. Taha On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications Journal of Mathematics |
| title | On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications |
| title_full | On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications |
| title_fullStr | On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications |
| title_full_unstemmed | On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications |
| title_short | On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications |
| title_sort | on r generalized fuzzy l closed sets properties and applications |
| url | http://dx.doi.org/10.1155/2021/4483481 |
| work_keys_str_mv | AT imtaha onrgeneralizedfuzzylclosedsetspropertiesandapplications |