New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications
There are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. They introduced the concept of soft rough sets, in which parameterized subsets of a universe set serve as the bu...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2559495 |
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| author | Mostafa K. El-Bably Muhammad I. Ali El-Sayed A. Abo-Tabl |
| author_facet | Mostafa K. El-Bably Muhammad I. Ali El-Sayed A. Abo-Tabl |
| author_sort | Mostafa K. El-Bably |
| collection | DOAJ |
| description | There are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. They introduced the concept of soft rough sets, in which parameterized subsets of a universe set serve as the building blocks for lower and upper approximations of a subset. Topological notions play a vital role in rough sets and soft rough sets. So, the basic objectives of the current work are as follows: first, we find answers to some very important questions, such as how to determine the probability that a subset of the universe is definable. Some more similar questions are answered in rough sets and their extensions. Secondly, we enhance soft rough sets from topological perspective and introduce topological soft rough sets. We explore some of their properties to improve existing techniques. A comparison has been made with some existing studies to show that accuracy measure of proposed technique shows an improvement. Proposed technique has been employed in decision-making problem for diagnosing heart failure. For this two algorithms have been given. |
| format | Article |
| id | doaj-art-3d7eefe94c9146e481bddde233ea5a8d |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3d7eefe94c9146e481bddde233ea5a8d2025-08-20T03:35:51ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2559495New Topological Approaches to Generalized Soft Rough Approximations with Medical ApplicationsMostafa K. El-Bably0Muhammad I. Ali1El-Sayed A. Abo-Tabl2Mathematics DepartmentMathematics DepartmentMathematics DepartmentThere are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. They introduced the concept of soft rough sets, in which parameterized subsets of a universe set serve as the building blocks for lower and upper approximations of a subset. Topological notions play a vital role in rough sets and soft rough sets. So, the basic objectives of the current work are as follows: first, we find answers to some very important questions, such as how to determine the probability that a subset of the universe is definable. Some more similar questions are answered in rough sets and their extensions. Secondly, we enhance soft rough sets from topological perspective and introduce topological soft rough sets. We explore some of their properties to improve existing techniques. A comparison has been made with some existing studies to show that accuracy measure of proposed technique shows an improvement. Proposed technique has been employed in decision-making problem for diagnosing heart failure. For this two algorithms have been given.http://dx.doi.org/10.1155/2021/2559495 |
| spellingShingle | Mostafa K. El-Bably Muhammad I. Ali El-Sayed A. Abo-Tabl New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications Journal of Mathematics |
| title | New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications |
| title_full | New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications |
| title_fullStr | New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications |
| title_full_unstemmed | New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications |
| title_short | New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications |
| title_sort | new topological approaches to generalized soft rough approximations with medical applications |
| url | http://dx.doi.org/10.1155/2021/2559495 |
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