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AIMS Mathematics

2022, Volume 7, Issue 7: 13104-13138. doi: 10.3934/math.2022724
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Research article

Generalization of rough sets using maximal right neighborhood systems and ideals with medical applications

  • 1.
    Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha 61471, Saudi Arabia
  • 2.
    Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
  • Received: 12 March 2022 Revised: 17 April 2022 Accepted: 21 April 2022 Published: 10 May 2022

  • MSC : 03E99, 54A05, 54A10, 54E99

  • Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. An ideal is considered to be a crucial extension of this theory. It is an efficacious tool to dispose of vagueness and uncertainties by helping us to approximate the rough set in a more general manner. Minimizing the boundary region is one of the pivotal and substantial themes for studying the rough sets which consequently aim to maximize the accuracy measure. An ideal is one of the effective and successful followed methods to achieve this goal perfectly. So, the objective of this work is to present new methods for rough sets by using ideals. Some important characteristics of these methods are scrutinized and demonstrated to show that they yield accuracy measures greater and higher than the former ones in the other approaches. Finally, two medical applications are introduced to show the significance of utilizing the ideals in the proposed methods.

    Citation: Mona Hosny. Generalization of rough sets using maximal right neighborhood systems and ideals with medical applications[J]. AIMS Mathematics, 2022, 7(7): 13104-13138. doi: 10.3934/math.2022724

    Related Papers:

  • Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. An ideal is considered to be a crucial extension of this theory. It is an efficacious tool to dispose of vagueness and uncertainties by helping us to approximate the rough set in a more general manner. Minimizing the boundary region is one of the pivotal and substantial themes for studying the rough sets which consequently aim to maximize the accuracy measure. An ideal is one of the effective and successful followed methods to achieve this goal perfectly. So, the objective of this work is to present new methods for rough sets by using ideals. Some important characteristics of these methods are scrutinized and demonstrated to show that they yield accuracy measures greater and higher than the former ones in the other approaches. Finally, two medical applications are introduced to show the significance of utilizing the ideals in the proposed methods.


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