The category of double fuzzy preproximity spaces

Zahran, A. M.; Abd-Allah, M. Azab; El-Saady, Kamal; Ghareeb, A.

doi:10.1016/j.camwa.2009.06.052

Cited by 6 publications

(7 citation statements)

References 12 publications

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“…Definition 1.1. [25,30] A double fuzzy topology on U is a pair (η, η * ) of the mappings η, η * : I U → I, which satisfy the following conditions.…”

Section: Of 14mentioning

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 1.1. [25,30] A double fuzzy topology on U is a pair (η, η * ) of the mappings η, η * : I U → I, which satisfy the following conditions.…”

Section: Of 14mentioning

confidence: 99%

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

Taha

2024

Preprint

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“…The concept of (r, s) − g f c sets was introduced and investigated by Abbas [29]. 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.…”

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.…”

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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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“…The concept of fuzzy proximity has met the attention of many researchers (see Zahran et al. [13,14], Abbas and Abd-Allah [1], Çetkin and Aygün [2]).…”

Section: Introductionmentioning

confidence: 99%