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

Al-shami, Tareq M.

doi:10.1007/s00500-021-06358-0

Cited by 63 publications

(28 citation statements)

References 35 publications

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“…It should be noted that the above approximations and accuracy measures were also studied via topological spaces; see, (Al-shami 2021b ; Al-shami et al. 2021a ; El-Bably and Al-shami 2021 ; Lashin et al.…”

Section: Preliminariesmentioning

confidence: 99%

Maximal rough neighborhoods with a medical application

Al-shami

2022

J Ambient Intell Human Comput

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In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply -neighborhoods to define -lower and -upper approximations and elucidate which one of Pawlak’s properties are preserved (evaporated) by these approximations. Moreover, we research -accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when . To show the importance of -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.

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Section: Preliminariesmentioning

confidence: 99%

Maximal rough neighborhoods with a medical application

Al-shami

2022

J Ambient Intell Human Comput

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“…Set X is called a rough set with respect to σ if σ (X ) = σ (X ) otherwise, it is called definable. Some recent rough approximations were defined on binary relations to extend the scope of applications of the RS theory; see, for example, [39][40][41].…”

Section: Definition 21 ([2]mentioning

confidence: 99%

Novel Bipolar Soft Rough-Set Approximations and Their Application in Solving Decision-Making Problems

Gul

Shabir

Mashwani

et al. 2022

IJFIS

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The rough set (RS) theory is a successful approach for studying the uncertainty in data. In contrast, the bipolar soft sets (BSS) can deal with the uncertainty, as well as bipolarity of the data in many situations. In 2018, Karaaslan and C ¸agman proposed bipolar soft rough sets (BSRSs), a hybridization of RS and BSS. However, certain shortcomings with BSRS violate Pawlak's RS theory. To overcome these shortcomings, the concept of the modified bipolar soft rough set (MBSRS) has been proposed in this study. Moreover, this idea has been investigated through illustrative examples, where the important properties are inspected deeply. Furthermore, certain significant measures associated with MBSRS are also provided. Finally, an application of the MBSRS to multi-attribute group decision-making (MAGDM) problems is proposed. In addition, among various alternatives, an algorithm for decisionmaking accompanied by a practical example is presented as the optimal alternative . A brief comparative analysis of the proposed approach with some existing techniques is also provided to indicate the validity, flexibility, and superiority of the suggested MAGDM model.

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

Cited by 63 publications

References 35 publications

Maximal rough neighborhoods with a medical application

Maximal rough neighborhoods with a medical application

Novel Bipolar Soft Rough-Set Approximations and Their Application in Solving Decision-Making Problems

On b-open Sets via Infra Soft Topological Spaces

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