On Fuzzy Point Applications of Fuzzy Topological Spaces

Abu-Gdairi, Radwan; Nasef, A. A.; El-Gayar, Mostafa A.; El-Bably, Mostafa K.

doi:10.5391/ijfis.2023.23.2.162

Cited by 4 publications

(3 citation statements)

References 34 publications

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“… Further Applications: Apply our approaches to additional medical and economic domains [ 26 , 35 , 39 ] to explore their efficacy in diverse real-world settings. Framework Expansion: Emphasize the utilization of nearly

-initial approximations in various frameworks such as soft rough sets [ 27 , 28 ], rough fuzzy sets [ 29 ], fuzzy topological spaces [ 40 ], and graph theory applications [ 41 ]. Exploring Integration: Explore collaborative opportunities to integrate likelihood-based methods, like maximizing posterior or likelihood functions, with our proposed approach centered around nearly

-initial approximations.…”

Section: Discussionmentioning

confidence: 99%

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The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

Abu-Gdairi,

El-Bably

2024

Heliyon

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-initial approximations.…”

Section: Discussionmentioning

confidence: 99%

“…Framework Expansion: Emphasize the utilization of nearly

-initial approximations in various frameworks such as soft rough sets [ 27 , 28 ], rough fuzzy sets [ 29 ], fuzzy topological spaces [ 40 ], and graph theory applications [ 41 ].…”

Section: Discussionmentioning

confidence: 99%

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

Abu-Gdairi,

El-Bably

2024

Heliyon

Self Cite

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“…Moreover, Abu-Gdairi et al [2] have explored the application of fuzzy point concepts to fuzzy topological spaces, opening up new possibilities for understanding topological structures. El-Bably and El-Sayed [17], have introduced innovative methods to generalize Pawlak approximations using simply open concepts, with specific applications in economics.…”

Section: Introductionmentioning

confidence: 99%

n-polar Z-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras

Alsager,

2023

MJMS

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This paper introduces an innovative concept known as n-polar Z-hesitant Anti-Fuzzy Soft Sets (MZHAFSs) within the framework of BCK/BCI-algebras. Soft set theory originates in the captivating field of fuzzy set theory. Our approach is a harmonious synthesis of n-polar anti-fuzzy set theory, soft set models, and Z-hesitant anti-fuzzy sets, skillfully applied within the framework of BCK/BCI-algebras. This effort leads to the introduction of a new variant of fuzzy sets termed MZHAFSs (n-polar Z-hesitant anti-fuzzy soft sets) in the context of BCK/BCI-algebras. Additionally, we elucidate the concept of n-polar Z-hesitant anti-fuzzy soft sets to provide a comprehensive understanding. Furthermore, we introduce and define various related concepts, including n-polar Z-hesitant anti-fuzzy soft subalgebras, n-polar Z-hesitant anti-fuzzy soft ideals, n-polar Z-hesitant anti-fuzzy soft closed ideals, and n-polar Z-hesitant anti-fuzzy soft commutative ideals, and establish meaningful connections between them. We also present and rigorously prove several theorems that are pertinent to these newly introduced notions.

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Decision-making in diagnosing heart failure problems using basic rough sets

Taher,

Abu-Gdairi,

El-Bably

et al. 2024

MATH

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<p>This manuscript introduces novel rough approximation operators inspired by topological structures, which offer a more flexible approach than existing methods by extending the scope of applications through a reliance on a general binary relation without constraints. Initially, four distinct types of neighborhoods, termed basic-minimal neighborhoods, are generated from any binary relation. The relationships between these neighborhoods and their properties are elucidated. Subsequently, new rough set models are constructed from these neighborhoods, outlining the main characteristics of their lower and upper approximations. These approximations are applied to classify the subset regions and to compute the accuracy measures. The primary advantages of this approach include its ability to achieve the highest accuracy values compared to all approaches in the published literature and to maintain the monotonicity property of the accuracy and roughness measures. Furthermore, the efficacy of the proposed technique is demonstrated through the analysis of heart failure diagnosis data, showcasing a 100% accuracy rate compared to previous methods, thus highlighting its clinical significance. Additionally, the topological properties of the proposed approaches and the topologies generated from the suggested neighborhoods are discussed, positioning these methods as a bridge to more topological applications in the rough set theory. Finally, an algorithm and flowchart are developed to illustrate the determination and utilization of basic-minimal exact sets in decision-making problems.</p>

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On Fuzzy Point Applications of Fuzzy Topological Spaces

Cited by 4 publications

References 34 publications

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets

n-polar Z-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras

Decision-making in diagnosing heart failure problems using basic rough sets

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