@article{Al-shami2024, 
author = {Tareq M. Al-shami and Salem Saleh and Alaa M. Abd El-latif and Abdelwaheb Mhemdi},
title = {Novel categories of spaces in the frame of fuzzy soft topologies},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6305-6320},
keywords = {fuzzy soft set, fuzzy soft δ-open set, fuzzy soft topology, FSδ-separation axioms, FSδ-regularity axioms},
url = {https://www.sciopen.com/article/10.3934/math.2024307},
doi = {10.3934/math.2024307},
abstract = {In the present paper, we introduce and discuss a new set of separation properties in fuzzy soft topological spaces called    F  S  δ-separation and    F  S  δ-regularity axioms by using fuzzy soft    δ-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    F  S  δ-separation and    F  S  δ-regularity axioms are harmonic and heredity property. Additionally, we examine the connections between    F  S            δ        ∗  -compactness and    F  S  δ-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.}
}