Version 1
: Received: 12 May 2024 / Approved: 13 May 2024 / Online: 13 May 2024 (12:30:17 CEST)
How to cite:
Alsharari, F.; Alqurashi, W.; Taha, I. M. A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies. Preprints2024, 2024050781. https://doi.org/10.20944/preprints202405.0781.v1
Alsharari, F.; Alqurashi, W.; Taha, I. M. A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies. Preprints 2024, 2024050781. https://doi.org/10.20944/preprints202405.0781.v1
Alsharari, F.; Alqurashi, W.; Taha, I. M. A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies. Preprints2024, 2024050781. https://doi.org/10.20944/preprints202405.0781.v1
APA Style
Alsharari, F., Alqurashi, W., & Taha, I. M. (2024). A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies. Preprints. https://doi.org/10.20944/preprints202405.0781.v1
Chicago/Turabian Style
Alsharari, F., Wafa Alqurashi and Islam M. Taha. 2024 "A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies" Preprints. https://doi.org/10.20944/preprints202405.0781.v1
Abstract
In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.
Keywords
intuitionistic fuzzy set; double fuzzy topology; (r, s) − g f sc set; (r, s) − g⊛ f sc set; continuity; (r, s)-GF S-regular space; (r, s)-GF S-normal space; compactness
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
