Topological structures in rough set theory: A survey

Singh, Pankaj Kumar; Tiwari, Surabhi

doi:10.15672/hujms.662711

Cited by 23 publications

(8 citation statements)

References 69 publications

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“…They also discussed a medical application using the concept of generalized nanotopology. Studying the interaction between topology and rough set theory was the main target for many articles such as [2,19,25,26,28,39,40,48]. This path of study also included some topology's extensions such as minimal structure [15,17] and bitopology [36].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Topological approach to generate new rough set models

Al-shami

2022

Complex Intell. Syst.

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“…Järvinen and Radeleczki ( 2020 ) introduced the optimistic lower and upper approximations with respect to two equivalence relations. Many studies were contacted to explore and develop rough set notions depending on topological ideas such as Abo-Tabl ( 2014 ), Al-shami ( 2021b , 2022 ), Hosny ( 2018 ), Kondo and Dudek ( 2006 ), Salama ( 2020a ) and Singh and Tiwari ( 2020 ). Moreover, it was applied rough set concepts induced from some generalizations of topology such as minimal structure (Azzam et al.…”

Section: Introductionmentioning

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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“…is interaction also included some generalizations of topology such as minimal structure [12]. We refer the reader to [13] to see the main contributions which investigated the relationships between topology and rough set theory. Ideals in a topological space have been taken into account by Kuratowski [14] and defined as a nonempty collection I of subsets of a universe which is closed under finite union and subsets.…”

Section: Introductionmentioning

confidence: 99%

Various Topologies Generated from E_j‐Neighbourhoods via Ideals

et al. 2021

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One of the considerable subjects in mathematics is the study of topology. Deducing topology from arbitrary binary relations has enticed the attention of many researchers. So, we devote this article to generate some kinds of topologies from ideals and E j -neighborhoods which are induced from any binary relation. We define new types of approximations and accuracy measures from these topologies and then compare them with their counterparts induced directly from E j -neighborhoods and ideals. Also, we show that the approximations and accuracy measures given, herein, are better than those introduced in some previous studies under any arbitrary relation.

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Topological structures in rough set theory: A survey

Cited by 23 publications

References 69 publications

Topological approach to generate new rough set models

Topological approach to generate new rough set models

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

Various Topologies Generated from E_j‐Neighbourhoods via Ideals

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Topological structures in rough set theory: A survey

Cited by 23 publications

References 69 publications

Topological approach to generate new rough set models

Topological approach to generate new rough set models

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

Various Topologies Generated from Ej‐Neighbourhoods via Ideals

Contact Info

Product

Resources

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Various Topologies Generated from E_j‐Neighbourhoods via Ideals