Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

Al-shami, Tareq M.; Hosny, Mona

doi:10.1109/access.2022.3194562

Cited by 20 publications

(5 citation statements)

References 35 publications

(55 reference statements)

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“…One can study new types of approximations on graph theory to obtain better accuracy measures by using different methods studied in [31][32][33]. These new methods can also be studied by applying them to various real-life problems.…”

Section: Discussionmentioning

confidence: 99%

Novel Graph Neighborhoods Emerging from Ideals

et al. 2023

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Rough set theory is a mathematical approach that deals with the problems of uncertainty and ambiguity in knowledge. Neighborhood systems are the most effective instruments for researching rough set theory in general. Investigations on boundary regions and accuracy measures primarily rely on two approximations, namely lower and upper approximations, by using these systems. The concept of the ideal, which is one of the most successful and effective mathematical tools, is used to obtain a better accuracy measure and to decrease the boundary region. Recently, a generalization of Pawlak’s rough set concept has been represented by neighborhood systems of graphs based on rough sets. In this research article, we propose a new method by using the concepts of the ideal and different neighborhoods from graph vertices. We examine important aspects of these techniques and produce accuracy measures that exceed those previously = reported in the literature. Finally, we show that our method yields better results than previous techniques utilized in chemistry.

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Section: Discussionmentioning

confidence: 99%

Novel Graph Neighborhoods Emerging from Ideals

et al. 2023

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“… Investigate the manuscript concepts with respect to different types of neighborhoods such as containment and subset rough neighborhoods. As we know that adding ideal structures to topology guarantees good performance for approximation operators and accuracy values, so we will examine the structure consisting of ideal and infra-topology following similar approach displayed in Al-shami and Hosny ( 2022 ), Hosny ( 2020 ), Hosny et al. ( 2021 ), Hosny and Al-shami ( 2022 ), Kandil et al.…”

Section: Discussionmentioning

confidence: 99%

Approximation operators and accuracy measures of rough sets from an infra-topology view

Al-shami

Mhemdi

2022

Soft Comput

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In this work, our target point is to focus on rough approximation operators generated from infra-topology spaces and examine their features. First, we show how infra-topology spaces are constructed from -neighborhood systems under an arbitrary relation. Then, we exploit these infra-topology spaces to form new rough set models and scrutinize their master characterizations. The main advantages of these models are to preserve all properties of Pawlak approximation operators and produce accuracy values higher than those given in several methods published in the literature. One of the unique characterizations of the current approach is that all the approximation operators and accuracy measures produced by the current approach are identical under a symmetric relation. Finally, we present two medical applications of the current methods regarding Dengue fever and COVID-19 pandemic. Some debates regarding the pros and cons of the followed technique are given as well as some upcoming work are proposed.

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“…They also talked about how generalized nanotopology might be used in medicine. Numerous works, including [3,14,18,24,27,31,32,34,44,45,53], focused on topology and rough set theory's link. Various topological extensions, include bitopology [39] and minimum structure [19,23], were covered in this line of research.…”

Section: Introductionmentioning

confidence: 99%

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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Improvement of Approximation Spaces Using Maximal Left Neighborhoods and Ideals

Cited by 20 publications

References 35 publications

Novel Graph Neighborhoods Emerging from Ideals

Novel Graph Neighborhoods Emerging from Ideals

Approximation operators and accuracy measures of rough sets from an infra-topology view

A topological tool to develop novel rough set

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