Some New Types of Approximations via Minimal Structure

Sharkasy, Mohammed El; Altwme, Fatma

doi:10.21608/joems.2018.2646.1031

Cited by 3 publications

(5 citation statements)

References 58 publications

(51 reference statements)

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“…Consequently, for any relation, the new kind of rough approximations J MSAS is more accurate than the preceding ones [6,22,23].…”

Section: Propositionmentioning

confidence: 97%

“…Some characteristics of the proposed method are obtained. Furthermore, the relations between the new approach J MSAS and the previous ones in [6,22,23] are studied.…”

Section: Preliminariesmentioning

confidence: 99%

“…The best approximations and degrees of accuracy have been achieved. A novel approach has been compared with the other approaches in the references [6,22,23] via counterexamples that has been examined as indicated in Theorem 1 and Table 1. From Remark 3, some principal properties of rough sets concerning g J r ð Þ, and " g J r ð Þ were deduced.…”

Section: Biochemical Applicationsmentioning

confidence: 99%

“…Various consequences of minimal spaces can be viewed in [21]. EL-Sharkasy [22,23] studied several sorts of sets in minimal structure spaces with some of their characterizations. The notion of the ideal J , which is a nonempty class of sets of Ã fulfills the finite additivity and the hereditary property, is famed in the study of topological problems and their other usages defined by Kuratowski [24].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Approximations by Ideal Minimal Structure with Chemical Application

Hosny¹,

Abu-Gdairi²,

El-Bably³

2023

Intelligent Automation &Amp; Soft Computing

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The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information. It can be characterized by two crisp sets, named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset. This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J . The novel approach (indicated by J MSAS) modifies the approximation space to diminish the boundary region and enhance the measure of accuracy. The suggested method is more accurate than Pawlak's and EL-Sharkasy techniques. Via illustrated examples, several remarkable results using these notions are obtained and some of their properties are established. Several sorts of near open (resp. closed) sets based on J MSAS are studied. Furthermore, the connections between these assorted kinds of near-open sets in J MSAS are deduced. The advantages and disadvantages of the proposed approach compared to previous ones are examined. An algorithm using MATLAB and a framework for decision-making problems are verified. Finally, the chemical application for the classification of amino acids (AAs) is treated to highlight the significance of applying the suggested approximation.

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“…Consequently, for any relation, the new kind of rough approximations J MSAS is more accurate than the preceding ones [6,22,23].…”

Section: Propositionmentioning

confidence: 97%

“…Some characteristics of the proposed method are obtained. Furthermore, the relations between the new approach J MSAS and the previous ones in [6,22,23] are studied.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Biochemical Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Approximations by Ideal Minimal Structure with Chemical Application

Hosny¹,

Abu-Gdairi²,

El-Bably³

2023

Intelligent Automation &Amp; Soft Computing

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“…The notion of minimal structure has been introduced by V. Popa and T. Noiri [6]. Rough set theory introduced by Pawlak [7], the relation between rough set and topological spaces, data-mining and graph theory studied in [8,9,10,11,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Reduction of Knowledge via Minimal Approximation Space and Graphs

El-Sharkasy

2018

Journal of the Egyptian Mathematical Society

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In this paper, we introduce a simple undirected graph based on a binary relation by using the notion of right neighborhood and minimal approximation space. Also, we investigate the lower approximation and the upper approximation of a subgraph to compute the rough subgraph. Finally, we will make a reduction of an information system and compute the core of knowledge by using a minimal approximation space and a graph theory.

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Minimal structure approximation space and some of its application

El-Sharkasy

2021

IFS

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Topological concepts play an important role in applications and solving real-life problems. Among of these concepts are neighbourhood and minimal structure. In this paper, we introduce a new space-based on a generalized system with a binary relation on a nonempty set by using the concept of a minimal structure, which is called a minimal structure approximation space (briefly, MSAS), and study some of its properties. Also, we compare the advantages of MSAS with neighbourhood approximation space which are based on the same starting point, and apply the concept of MSAS in some examples of chemistry to extraction and reduct the information. Finally, we investigate the concepts of the separation axioms on MSAS and study some of its properties in the information system as the process of approximation of information.

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Some New Types of Approximations via Minimal Structure

Cited by 3 publications

References 58 publications

Approximations by Ideal Minimal Structure with Chemical Application

Approximations by Ideal Minimal Structure with Chemical Application

Reduction of Knowledge via Minimal Approximation Space and Graphs

Minimal structure approximation space and some of its application

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