Novel categories of spaces in the frame of fuzzy soft topologies

Tareq M. Al-shami; Salem Saleh; Alaa M. Abd El-latif; Abdelwaheb Mhemdi; Tareq M. Al-shami; Salem Saleh; Alaa M. Abd El-latif; Abdelwaheb Mhemdi

doi:10.3934/math.2024307

AIMS Mathematics

2024, Volume 9, Issue 3: 6305-6320. doi: 10.3934/math.2024307

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Research article

Novel categories of spaces in the frame of fuzzy soft topologies

1.
Department of Mathematics, Sana'a University, Sana'a, Yemen
2.
Department of Computer Science, Cihan University-Erbil, Erbil, Iraq
3.
Department, Department of Mathematics, Hodeidah University, Hodeidah, Yemen
4.
Mathematics Department, College of Sciences and Arts, Northern Border University, Rafha 91911, Saudi Arabia
5.
Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia

Received: 12 December 2023 Revised: 18 January 2024 Accepted: 29 January 2024 Published: 04 February 2024
MSC : 54A40, 54D10

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.
- fuzzy soft set,
- fuzzy soft $ \delta $-open set,
- fuzzy soft topology,
- $ FS\delta $-separation axioms,
- $ FS\delta $-regularity axioms
Citation: Tareq M. Al-shami, Salem Saleh, Alaa M. Abd El-latif, Abdelwaheb Mhemdi. Novel categories of spaces in the frame of fuzzy soft topologies[J]. AIMS Mathematics, 2024, 9(3): 6305-6320. doi: 10.3934/math.2024307

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Abstract

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.

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