Topological Approaches for Rough Continuous Functions with Applications

Salama, A. S.; Mhemdi, Abdelwaheb; Elbarbary, O. G.; Al-shami, Tareq M.

doi:10.1155/2021/5586187

Cited by 14 publications

(8 citation statements)

References 40 publications

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“…Study of the rough set theory via topology is an enjoyable topic that received the attention of many researchers, see, for example [2,[13][14][15][16][17][18][19]]. An ideal I [20] on a nonempty finite set (universe) U is a nonempty family of subsets of U with heredity property, as well as it is closed under finite unions.…”

Section: Introductionmentioning

confidence: 99%

Some Topological Approaches for Generalized Rough Sets via Ideals

Al-shami

Işık

Nawar

et al. 2021

Mathematical Problems in Engineering

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The idea of neighborhood systems is induced from the geometric idea of “near,” and it is primitive in the topological structures. Now, the idea of neighborhood systems has been extensively applied in rough set theory. The master contribution of this manuscript is to generate various topologies by means of the concepts of j -adhesion neighborhoods and ideals. Then, we define a new rough set model derived from these topologies and discussed main features. We show that these topologies are finer than those given in the previous ones under arbitrary binary relations. In addition, we elucidate that these topologies are finer than those topologies initiated based on different neighborhoods and ideals under reflexive relations. Several examples are provided to validate that our model is better than the previous ones.

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Section: Introductionmentioning

confidence: 99%

Some Topological Approaches for Generalized Rough Sets via Ideals

Al-shami

Işık

Nawar

et al. 2021

Mathematical Problems in Engineering

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“…Recently, topology has been applied to model some real-life issues as showed in [1,11,15,16,32,46,56,64]. To study topology via S-set theory, C ¸aǧman et al [51] and Shabir and Naz [65], in 2011, introduced the concept of soft topology(ST).…”

Section: Introductionmentioning

confidence: 99%

On b-open Sets via Infra Soft Topological Spaces

Abu-Gdairi¹,

Al-Shamiri²,

Saleh³

et al. 2022

Eur. J. Pure Appl. Math.

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This work aims to present the concept of infra soft $b$-open sets(IS-b-open sets) as a generalized new class of infra open sets(IS-open sets). We first investigate their basic properties and study their behaviours under infra soft homeomorphism maps and finite product of soft spaces. Then, we establish some soft operators such as interior, closure, limit and boundary using IS-b-open sets and IS-$b$-closed sets. The relationships between them are illustrated and discussed. Finally, we display some soft maps(S-map) defined using IS-$b$-open and IS-$b$-closed sets and scrutinize their master properties.

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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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Topological Approaches for Rough Continuous Functions with Applications

Cited by 14 publications

References 40 publications

Some Topological Approaches for Generalized Rough Sets via Ideals

Some Topological Approaches for Generalized Rough Sets via Ideals

On b-open Sets via Infra Soft Topological Spaces

Topological approach to generate new rough set models

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