A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces
Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As a result, we introduce the concept of infra-fuzzy topology, which is a subset family that degrades the concept of fuzzy topology by omitting the condition of closedness under arbitrary unions. Fu...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/9778069 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832562510175141888 |
|---|---|
| author | Zanyar A. Ameen Tareq M. Al-shami A. A. Azzam Abdelwaheb Mhemdi |
| author_facet | Zanyar A. Ameen Tareq M. Al-shami A. A. Azzam Abdelwaheb Mhemdi |
| author_sort | Zanyar A. Ameen |
| collection | DOAJ |
| description | Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As a result, we introduce the concept of infra-fuzzy topology, which is a subset family that degrades the concept of fuzzy topology by omitting the condition of closedness under arbitrary unions. Fundamental properties of infra-fuzzy topological spaces are investigated, including infra-fuzzy open and infra-fuzzy closed sets, infra-fuzzy interior and infra-fuzzy closure operators, and the infra-fuzzy boundary of a fuzzy set. It is not possible to expect the latter concepts to have properties identical to those in ordinary fuzzy topological spaces. More precisely, the infra-fuzzy interior of a set need not be infra-fuzzy open, and the infra-fuzzy closure and boundary of a set may not be infra-fuzzy closed. Then, employing infra-fuzzy neighborhood systems, infra-fuzzy Q-neighborhood systems, the basis of infra-fuzzy topology, and infra-fuzzy relative topology, we propose several approaches for generating infra-fuzzy topologies. Finally, we define the notions of continuity, openness, closedness, and homeomorphism of mappings in the context of infra fuzziness and investigate some of their properties and characterizations. We show that the usual characterization of earlier notions in the infra-fuzzy structure is incorrect. We demonstrate that the family of all infra-fuzzy homeomorphisms on an infra-fuzzy topological space forms a group under mappings composition. We finish this work by proving that each infra-fuzzy homeomorphism between two infra-fuzzy topological spaces produces an isomorphism on groups of infra-fuzzy homeomorphisms of the corresponding spaces. |
| format | Article |
| id | doaj-art-055b91af93ed4f8db4605fa3da7125c0 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-055b91af93ed4f8db4605fa3da7125c02025-02-03T01:22:26ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/9778069A Novel Fuzzy Structure: Infra-Fuzzy Topological SpacesZanyar A. Ameen0Tareq M. Al-shami1A. A. Azzam2Abdelwaheb Mhemdi3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsObtaining a weaker condition that preserves some inspired topological properties is always desirable. As a result, we introduce the concept of infra-fuzzy topology, which is a subset family that degrades the concept of fuzzy topology by omitting the condition of closedness under arbitrary unions. Fundamental properties of infra-fuzzy topological spaces are investigated, including infra-fuzzy open and infra-fuzzy closed sets, infra-fuzzy interior and infra-fuzzy closure operators, and the infra-fuzzy boundary of a fuzzy set. It is not possible to expect the latter concepts to have properties identical to those in ordinary fuzzy topological spaces. More precisely, the infra-fuzzy interior of a set need not be infra-fuzzy open, and the infra-fuzzy closure and boundary of a set may not be infra-fuzzy closed. Then, employing infra-fuzzy neighborhood systems, infra-fuzzy Q-neighborhood systems, the basis of infra-fuzzy topology, and infra-fuzzy relative topology, we propose several approaches for generating infra-fuzzy topologies. Finally, we define the notions of continuity, openness, closedness, and homeomorphism of mappings in the context of infra fuzziness and investigate some of their properties and characterizations. We show that the usual characterization of earlier notions in the infra-fuzzy structure is incorrect. We demonstrate that the family of all infra-fuzzy homeomorphisms on an infra-fuzzy topological space forms a group under mappings composition. We finish this work by proving that each infra-fuzzy homeomorphism between two infra-fuzzy topological spaces produces an isomorphism on groups of infra-fuzzy homeomorphisms of the corresponding spaces.http://dx.doi.org/10.1155/2022/9778069 |
| spellingShingle | Zanyar A. Ameen Tareq M. Al-shami A. A. Azzam Abdelwaheb Mhemdi A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces Journal of Function Spaces |
| title | A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces |
| title_full | A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces |
| title_fullStr | A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces |
| title_full_unstemmed | A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces |
| title_short | A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces |
| title_sort | novel fuzzy structure infra fuzzy topological spaces |
| url | http://dx.doi.org/10.1155/2022/9778069 |
| work_keys_str_mv | AT zanyaraameen anovelfuzzystructureinfrafuzzytopologicalspaces AT tareqmalshami anovelfuzzystructureinfrafuzzytopologicalspaces AT aaazzam anovelfuzzystructureinfrafuzzytopologicalspaces AT abdelwahebmhemdi anovelfuzzystructureinfrafuzzytopologicalspaces AT zanyaraameen novelfuzzystructureinfrafuzzytopologicalspaces AT tareqmalshami novelfuzzystructureinfrafuzzytopologicalspaces AT aaazzam novelfuzzystructureinfrafuzzytopologicalspaces AT abdelwahebmhemdi novelfuzzystructureinfrafuzzytopologicalspaces |