Unavoidable corrections for $ \theta\beta $-ideal approximation spaces

Tareq M. Al-shami; Mohammed M. Ali Al-Shamiri; Murad Arar; Tareq M. Al-shami; Mohammed M. Ali Al-Shamiri; Murad Arar

doi:10.3934/math.20241553

AIMS Mathematics

2024, Volume 9, Issue 11: 32399-32408. doi: 10.3934/math.20241553

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Commentary

Unavoidable corrections for $ \theta\beta $-ideal approximation spaces

1.
Mathematics Department, Sana'a University, Sana'a, Yemen
2.
Jadara University Research Center, Jadara University, Jordan
3.
Department of Mathematics, College of Sciences and Arts Muhayil Asir, King Khalid University, 61913, Saudi Arabia
4.
Mathematics Department, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia
Commentary of: AIMS Mathematics 7: 2479-2497

Received: 12 August 2024 Revised: 09 November 2024 Accepted: 13 November 2024 Published: 15 November 2024
MSC : 03E72, 54A10, 68T30, 91B06

The short article in hand introduces some amendments for the relationships and claims presented in ^[16] 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 ^[11] and ^[16] are incomparable. Moreover, we demonstrate that the observations, given in the application section of ^[16], 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.
- rough set,
- topology,
- lower and upper approximation
Citation: Tareq M. Al-shami, Mohammed M. Ali Al-Shamiri, Murad Arar. Unavoidable corrections for $ \theta\beta $-ideal approximation spaces[J]. AIMS Mathematics, 2024, 9(11): 32399-32408. doi: 10.3934/math.20241553

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Abstract

The short article in hand introduces some amendments for the relationships and claims presented in ^[16] 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 ^[11] and ^[16] are incomparable. Moreover, we demonstrate that the observations, given in the application section of ^[16], 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.

References

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