Version 1
: Received: 17 December 2023 / Approved: 17 December 2023 / Online: 18 December 2023 (06:01:28 CET)
Version 2
: Received: 21 January 2024 / Approved: 23 January 2024 / Online: 24 January 2024 (02:52:14 CET)
How to cite:
Alshammari, I.; Alqahtani, M. H.; Taha, I. M. On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies. Preprints2023, 2023121240. https://doi.org/10.20944/preprints202312.1240.v2
Alshammari, I.; Alqahtani, M. H.; Taha, I. M. On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies. Preprints 2023, 2023121240. https://doi.org/10.20944/preprints202312.1240.v2
Alshammari, I.; Alqahtani, M. H.; Taha, I. M. On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies. Preprints2023, 2023121240. https://doi.org/10.20944/preprints202312.1240.v2
APA Style
Alshammari, I., Alqahtani, M. H., & Taha, I. M. (2024). On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies. Preprints. https://doi.org/10.20944/preprints202312.1240.v2
Chicago/Turabian Style
Alshammari, I., Mesfer H. Alqahtani and Islam M. Taha. 2024 "On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies" Preprints. https://doi.org/10.20944/preprints202312.1240.v2
Abstract
In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.
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.
