Some new results on fuzzy soft $ r $-minimal spaces

Taha, I. M.

doi:10.3934/math.2022691

Cited by 6 publications

(4 citation statements)

References 22 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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Section: Discussionmentioning

confidence: 99%

On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness

Taha

2024

Preprint

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In this article, we first introduced new types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) and discussed some topological properties of them. Thereafter, we defined a stronger form of (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 new 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. Finally, some new types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

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“…Definition 1.2. [23] The difference between two fuzzy soft sets h C and g B is a fuzzy soft set defined as follows, for each n ∈ N:…”

Section: Of 15mentioning

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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Some new results on fuzzy soft $ r $-minimal spaces

Cited by 6 publications

References 22 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

On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness

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

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