Generalized Topological Approximation Spaces and Their Medical Applications

Salama, A. S.

doi:10.21608/joems.2018.2891.1045

Cited by 6 publications

(18 citation statements)

References 10 publications

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“…In this section, we define new rough approximations and accuracy measures using the concepts of somewhat open and somewhat closed sets which are one of the open sets generalizations. We establish their main properties and prove that our approach offers accuracy measures and approximations better than those displayed by open, α-open, and semi-open sets [1,14,37]. Also, we compare between the approximations induced from our approach and show that the accuracy measures given in cases of ρ ∈ {i, i } are the best.…”

Section: Approximations Using Somewhat Open Setsmentioning

confidence: 84%

“…In fact, there are four main motivations to study these models are, first, to improve the approximations and increase their accuracy measures displayed in the published literature. This matter was illustrated with the help of some comparisons that validate that our approach is better than those given in [1,14,37]. Second, to keep most properties of Pawlak's approximations that are evaporated by the previous approximations as illustrated in Proposition 3 and Proposition 4.…”

Section: Introductionmentioning

confidence: 91%

“…Definition 9 [14,37] For every k ∈ {semi, α}, the ρk-lower and ρk-upper approximations of a set Ω in a ρ-NS (U , E, φ ρ ) are defined, respectively, by…”

Section: Remark 1 the Classes Of ρα-Open ρ-Semi-open ρα-Closedmentioning

confidence: 99%

“…Definition 10 [14,37] The ρk-boundary, ρk-positive and ρknegative regions and ρk-accuracy and ρk-roughness measures of a set Ω in a ρ-NS (U , E, φ ρ ) are, respectively, defined by…”

Section: Remark 1 the Classes Of ρα-Open ρ-Semi-open ρα-Closedmentioning

confidence: 99%

“…In this subsection, we compare our approach with the previous approaches introduced in [1,14,37]. In [1], the authors approximated a subset using interior and closure topological operators, whereas the authors of [14,37] approximated a subset using some generalizations of interior and closure topological operators, such as α-interior and αclosure and semi-interior and semi-closure topological operators. Through this subsection, we show that our approach…”

Section: Comparison Of Our Approach With the Previous Onesmentioning

confidence: 99%

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Topological approach to generate new rough set models

Al-shami

2022

Complex Intell. Syst.

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In this paper, we introduce a topological method to produce new rough set models. This method is based on the idea of “somewhat open sets” which is one of the celebrated generalizations of open sets. We first generate some topologies from the different types of $$N_\rho $$ N ρ -neighborhoods. Then, we define new types of rough approximations and accuracy measures with respect to somewhat open and somewhat closed sets. We study their main properties and prove that the accuracy and roughness measures preserve the monotonic property. One of the unique properties of these approximations is the possibility of comparing between them. We also compare our approach with the previous ones, and show that it is more accurate than those induced from open, $$\alpha $$ α -open, and semi-open sets. Moreover, we examine the effectiveness of the followed method in a problem of Dengue fever. Finally, we discuss the strengths and limitations of our approach and propose some future work.

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Section: Approximations Using Somewhat Open Setsmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 91%

“…Definition 9 [14,37] For every k ∈ {semi, α}, the ρk-lower and ρk-upper approximations of a set Ω in a ρ-NS (U , E, φ ρ ) are defined, respectively, by…”

Section: Remark 1 the Classes Of ρα-Open ρ-Semi-open ρα-Closedmentioning

confidence: 99%

Section: Remark 1 the Classes Of ρα-Open ρ-Semi-open ρα-Closedmentioning

confidence: 99%

Section: Comparison Of Our Approach With the Previous Onesmentioning

confidence: 99%

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Topological approach to generate new rough set models

Al-shami

2022

Complex Intell. Syst.

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Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets

Al-shami

2021

Soft Comput

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A topological tool to develop novel rough set

Azzam

2024

J. Math. Computer Sci.

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Here, we introduce a new rough set model-building topological method. This concept is based on "somewhat open sets," one of the popular generalizations of open sets. First, we create a few topologies using different kinds of M ξ -adhesion neighborhoods. Then, we create new kinds of rough approximations and accuracy metrics with respect to somewhat closed and somewhat open sets. We examine their key characteristics and demonstrate that the monotonic requirement is maintained by the accuracy and roughness metrics. Their ability to be compared is one of their special qualities. We demonstrate that our method is more accurate than those resulting from open, α-open, and semi-open sets by comparing it with the previous approaches. We also evaluate the applicability of the technique in a heart failure problem. Lastly, we evaluate the benefits and drawbacks of our approach and make some recommendations for further research.

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Generalized Topological Approximation Spaces and Their Medical Applications

Cited by 6 publications

References 10 publications

Topological approach to generate new rough set models

Topological approach to generate new rough set models

Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets

A topological tool to develop novel rough set

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