Novel categories of spaces in the frame of fuzzy soft topologies
In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their p...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024307?viewType=HTML |
| _version_ | 1797299774790041600 |
|---|---|
| author | Tareq M. Al-shami Salem Saleh Alaa M. Abd El-latif Abdelwaheb Mhemdi |
| author_facet | Tareq M. Al-shami Salem Saleh Alaa M. Abd El-latif Abdelwaheb Mhemdi |
| author_sort | Tareq M. Al-shami |
| collection | DOAJ |
| description | In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology. |
| first_indexed | 2024-03-07T22:56:30Z |
| format | Article |
| id | doaj.art-a2c3a8e3f50e40b7b18ea683bb703396 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T22:56:30Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a2c3a8e3f50e40b7b18ea683bb7033962024-02-23T01:32:05ZengAIMS PressAIMS Mathematics2473-69882024-02-01936305632010.3934/math.2024307Novel categories of spaces in the frame of fuzzy soft topologiesTareq M. Al-shami0Salem Saleh 1Alaa M. Abd El-latif 2Abdelwaheb Mhemdi31. Department of Mathematics, Sana'a University, Sana'a, Yemen2. Department of Computer Science, Cihan University-Erbil, Erbil, Iraq 3. Department, Department of Mathematics, Hodeidah University, Hodeidah, Yemen4. Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha 91911, Saudi Arabia5. Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi ArabiaIn the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called $ FS\delta $-separation and $ FS\delta $-regularity axioms by using fuzzy soft $ \delta $-open sets and the quasi-coincident relation. We provide a comprehensive study of their properties with some supporting examples. Our analysis includes more characterizations, results, and theorems related to these notions, which contributes to a deeper understanding of fuzzy soft separability properties. We show that the $ FS\delta $-separation and $ FS\delta $-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between $ FS{\delta }^* $-compactness and $ FS\delta $-separation axioms and explore the relationships between them. Overall, this work offers a new perspective on the theory of separation properties in fuzzy soft topological spaces, as well as provides a robust foundation for further research in the transmission of properties from fuzzy soft topologies to fuzzy and soft topologies and vice-versa by swapping between the membership function and characteristic function in the case of fuzzy topology and the set of parameters and a singleton set in the case of soft topology.https://www.aimspress.com/article/doi/10.3934/math.2024307?viewType=HTMLfuzzy soft setfuzzy soft $ \delta $-open setfuzzy soft topology$ fs\delta $-separation axioms$ fs\delta $-regularity axioms |
| spellingShingle | Tareq M. Al-shami Salem Saleh Alaa M. Abd El-latif Abdelwaheb Mhemdi Novel categories of spaces in the frame of fuzzy soft topologies AIMS Mathematics fuzzy soft set fuzzy soft $ \delta $-open set fuzzy soft topology $ fs\delta $-separation axioms $ fs\delta $-regularity axioms |
| title | Novel categories of spaces in the frame of fuzzy soft topologies |
| title_full | Novel categories of spaces in the frame of fuzzy soft topologies |
| title_fullStr | Novel categories of spaces in the frame of fuzzy soft topologies |
| title_full_unstemmed | Novel categories of spaces in the frame of fuzzy soft topologies |
| title_short | Novel categories of spaces in the frame of fuzzy soft topologies |
| title_sort | novel categories of spaces in the frame of fuzzy soft topologies |
| topic | fuzzy soft set fuzzy soft $ \delta $-open set fuzzy soft topology $ fs\delta $-separation axioms $ fs\delta $-regularity axioms |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024307?viewType=HTML |
| work_keys_str_mv | AT tareqmalshami novelcategoriesofspacesintheframeoffuzzysofttopologies AT salemsaleh novelcategoriesofspacesintheframeoffuzzysofttopologies AT alaamabdellatif novelcategoriesofspacesintheframeoffuzzysofttopologies AT abdelwahebmhemdi novelcategoriesofspacesintheframeoffuzzysofttopologies |