Some properties of  (r,s)-generalized fuzzy semi-closed sets and some applications

Taha, I. M.

doi:10.22436/jmcs.027.02.06

Cited by 3 publications

(12 citation statements)

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“…Thereafter, the concept of (r, s) − sg f c sets was introduced by Zahran et al [30] on double fuzzy topological space based on the sense of Šostak. Also, Taha [31] defined the concept of (r, s) − g f sc sets and some characterizations were given. So far, lots of spectacular and creative studies about the theories of an intuitionistic fuzzy set have been considered by some scholars, see e. g. [32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…• Firstly, as a stronger form of (r, s) − g f sc sets [31], the notion of (r, s) − g ⊛ f sc sets is introduced and some properties are investigated. Moreover, we introduce new types of fuzzy mappings between double fuzzy topological spaces and relationships are obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Definition 1.2 ([37,38]). Let (U, η, η * ) be a dfts, ν ∈ I U , r ∈ I • , and s ∈ I 1 , then we have (i) ν is called an (r, s)-f sc ⟨resp., (r, s)-f pc and (r, [29][30][31]). Let (U, η, η * ) be a dfts, µ, ν ∈ I U , r ∈ I • , and s ∈ I 1 , then we have (i) µ is called an (r, s)-generalized fuzzy closed ⟨briefly, (r, s)-g f c⟩ set if C η,η * (µ, r, s) ≤ ν whenever µ ≤ ν and η(ν) ≥ r, η * (ν) ≤ s.…”

mentioning

confidence: 99%

“…Definition 1.5 (29,31,37). Let h : (U, τ, τ * ) → (V, η, η * ) be a mapping, r ∈ I • , and s ∈ I 1 , then h is said to be (i) DF S-continuous ⟨resp., DF GS-continuous and DF G-continuous⟩ if h −1 (µ) is (r, s)-f so ⟨resp., (r, s)-g f so and (r, s)-g f o⟩ set for each µ ∈ I V with η(µ) ≥ r , η * (µ) ≤ s.…”

mentioning

confidence: 99%

“…The basic results and notions that we need in the next sections are found in [29][30][31][39][40][41].…”

mentioning

confidence: 99%

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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The basic results and notions that we need in the next sections are found in [29][30][31][39][40][41].…”

mentioning

confidence: 99%

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

Alsharari,

Alqurashi,

Taha

2024

Preprint

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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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Survivability of AIDS Patients via Fractional Differential Equations with Fuzzy Rectangular and Fuzzy b-Rectangular Metric like Spaces

et al. 2022

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As it is not always true that the distance between the points in fuzzy rectangular metric spaces is one, so we introduce the notions of rectangular and b-rectangular metric-like spaces in fuzzy set theory that generalize many existing results, which can be regarded as the main advantage of this paper. In these spaces, the symmetry property is preserved, but the self distance may not be equal to one. We discuss topological properties and demonstrate that neither of these spaces is Hausdorff. Using α−ψ-contraction and Geraghty contractions, respectively, in our main results, we establish fixed point results in these spaces. We present examples that justify our definitions and results. We use our main results to demonstrate that the solution of a nonlinear fractional differential equation for HIV is unique.

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Some properties of (r,s)-generalized fuzzy semi-closed sets and some applications

Cited by 3 publications

References 0 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

Survivability of AIDS Patients via Fractional Differential Equations with Fuzzy Rectangular and Fuzzy b-Rectangular Metric like Spaces

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