Compactness on Fuzzy Soft r-Minimal Spaces

Taha, I. M.

doi:10.5391/ijfis.2021.21.3.251

Cited by 11 publications

(13 citation statements)

References 9 publications

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“…In the upcoming papers, we shall discuss the concepts given here in the frames of a fuzzy idealization [42,43] and fuzzy soft r-minimal structures [44,45]. Moreover, we will study the main properties of classical compactness in the frame of double fuzzy topologies.…”

Section: Discussionmentioning

confidence: 99%

A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies

Alsharari,

Alqurashi,

Taha

2024

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies

Alsharari,

Alqurashi,

Taha

2024

Preprint

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“…A fuzzy soft set h C ∈ (W, N) is called an r-fuzzy soft regularly open [19] (resp. β-open [20], pre-open [20], α-open [26] and semi-open [26])…”

Section: Of 15mentioning

confidence: 99%

“…The complement of an r-fuzzy soft α-open [26] (resp. semi-open [26], β-open [20] and pre-open [20]) set is an r-fuzzy soft α-closed (resp. semi-closed, β-closed and pre-closed) set.…”

Section: On R-fuzzy Soft α-Open Setsmentioning

confidence: 99%

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

Taha,

Alqurashi

2024

Preprint

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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.

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“…A fuzzy soft function ϕ ψ : (U, E) −→ (V, F) is said to be fuzzy soft continuous if τ e (ϕ −1 ψ (g B )) ≥ τ * k (g B ) for every g B ∈ (V, F), e ∈ E and (k = ψ(e)) ∈ F. Definition 1.5. [16,18] Let (U, τ E ) be a FSTS. A fuzzy soft set f A ∈ (U, E) is said to be r-fuzzy soft regularly open (resp.…”

Section: Of 13mentioning

confidence: 99%

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

Alshammari,

Alqahtani,

Taha

2023

Preprint

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In this work, we introduce the concepts of r-fuzzy soft δ-open (resp. semi-open and α-open) sets on fuzzy soft topological space, the relations of these sets with each other are established. Next, we introduce the concepts of fuzzy soft δ-continuous (resp. β-continuous, semi-continuous, pre-continuous and α-continuous) functions, and some properties of these functions along with their mutual relationships are investigated. Also, a decomposition of fuzzy soft semi-continuity and a decomposition of fuzzy soft α-continuity are given. Finally, as a weaker form of fuzzy soft continuity by Aygunoglu et al. (2014), the concepts of fuzzy soft almost (resp. weakly) continuous functions are introduced, and some properties are specified. Moreover, we explore the notion of continuity in a very general setting namely fuzzy soft (L, M, N, O)-continuous functions, and a historical justification are obtained.

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Compactness on Fuzzy Soft r-Minimal Spaces

Cited by 11 publications

References 9 publications

A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies

A Novel Types of Fuzzy Closed Sets, Separation Axioms, and Compactness via Double Fuzzy Topologies

Novel Approach to Study Soft α-Open Sets and Its Applications via Fuzzy Soft Topologies

On R-fuzzy Soft δ-Open Sets and Applications via Fuzzy Soft Topologies

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