Unavoidable corrections for $ \theta\beta $-ideal approximation spaces
The short article in hand introduces some amendments for the relationships and claims presented in <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup> with the investigation of their correct forms. To elucidate those failures and to support the results...
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241553?viewType=HTML |
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| author | Tareq M. Al-shami Mohammed M. Ali Al-Shamiri Murad Arar |
| author_facet | Tareq M. Al-shami Mohammed M. Ali Al-Shamiri Murad Arar |
| author_sort | Tareq M. Al-shami |
| collection | DOAJ |
| description | The short article in hand introduces some amendments for the relationships and claims presented in <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup> with the investigation of their correct forms. To elucidate those failures and to support the results obtained herein, we provide an illustrative example. We also elucidate that the rough set models proposed by <sup>[<xref ref-type="bibr" rid="b11">11</xref>]</sup> and <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup> are incomparable. Moreover, we demonstrate that the observations, given in the application section of <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup>, contradict the computations of lower and upper approximations, boundary regions, and accuracy measures as well as violate some well-known properties of Pawlak approximation space. |
| format | Article |
| id | doaj-art-e8f71c52c6f5446e959d31ac1470a853 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e8f71c52c6f5446e959d31ac1470a8532025-08-20T02:22:40ZengAIMS PressAIMS Mathematics2473-69882024-11-01911323993240810.3934/math.20241553Unavoidable corrections for $ \theta\beta $-ideal approximation spacesTareq M. Al-shami0Mohammed M. Ali Al-Shamiri1Murad Arar21. Mathematics Department, Sana'a University, Sana'a, Yemen 2. Jadara University Research Center, Jadara University, Jordan3. Department of Mathematics, College of Sciences and Arts Muhayil Asir, King Khalid University, 61913, Saudi Arabia4. Mathematics Department, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi ArabiaThe short article in hand introduces some amendments for the relationships and claims presented in <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup> with the investigation of their correct forms. To elucidate those failures and to support the results obtained herein, we provide an illustrative example. We also elucidate that the rough set models proposed by <sup>[<xref ref-type="bibr" rid="b11">11</xref>]</sup> and <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup> are incomparable. Moreover, we demonstrate that the observations, given in the application section of <sup>[<xref ref-type="bibr" rid="b16">16</xref>]</sup>, contradict the computations of lower and upper approximations, boundary regions, and accuracy measures as well as violate some well-known properties of Pawlak approximation space.https://www.aimspress.com/article/doi/10.3934/math.20241553?viewType=HTMLrough settopologylower and upper approximation |
| spellingShingle | Tareq M. Al-shami Mohammed M. Ali Al-Shamiri Murad Arar Unavoidable corrections for $ \theta\beta $-ideal approximation spaces AIMS Mathematics rough set topology lower and upper approximation |
| title | Unavoidable corrections for $ \theta\beta $-ideal approximation spaces |
| title_full | Unavoidable corrections for $ \theta\beta $-ideal approximation spaces |
| title_fullStr | Unavoidable corrections for $ \theta\beta $-ideal approximation spaces |
| title_full_unstemmed | Unavoidable corrections for $ \theta\beta $-ideal approximation spaces |
| title_short | Unavoidable corrections for $ \theta\beta $-ideal approximation spaces |
| title_sort | unavoidable corrections for theta beta ideal approximation spaces |
| topic | rough set topology lower and upper approximation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241553?viewType=HTML |
| work_keys_str_mv | AT tareqmalshami unavoidablecorrectionsforthetabetaidealapproximationspaces AT mohammedmalialshamiri unavoidablecorrectionsforthetabetaidealapproximationspaces AT muradarar unavoidablecorrectionsforthetabetaidealapproximationspaces |