Version 1
: Received: 12 February 2024 / Approved: 13 February 2024 / Online: 13 February 2024 (12:46:23 CET)
How to cite:
Taha, I.; Alqurashi, W. Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies. Preprints2024, 2024020734. https://doi.org/10.20944/preprints202402.0734.v1
Taha, I.; Alqurashi, W. Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies. Preprints 2024, 2024020734. https://doi.org/10.20944/preprints202402.0734.v1
Taha, I.; Alqurashi, W. Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies. Preprints2024, 2024020734. https://doi.org/10.20944/preprints202402.0734.v1
APA Style
Taha, I., & Alqurashi, W. (2024). Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies. Preprints. https://doi.org/10.20944/preprints202402.0734.v1
Chicago/Turabian Style
Taha, I. and Wafa Alqurashi. 2024 "Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies" Preprints. https://doi.org/10.20944/preprints202402.0734.v1
Abstract
In this manuscript, we first introduce some properties of r-fuzzy soft α-open sets in fuzzy soft topological spaces based on the manuscript Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). In addition, we define the concepts of fuzzy soft α-closure (α-interior) operators, and investigate some properties of them. Furthermore, the concept of r-fuzzy soft α-connected sets is defined and characterized with help of fuzzy soft α-closure operators. Thereafter, we introduce and study the concepts of fuzzy soft almost (weakly) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings, and we discuss some properties of fuzzy soft α-continuity. Moreover, we establish that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. It is also we show that the composition is fuzzy soft almost α-continuous mapping if, is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some new types of compactness via r-fuzzy soft α-open sets are defined, and the relationships between them are examined.
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.
