Idealization of rough sets and medical applications in decision-making the impact factors of COVID-19 infections and heart attacks

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Abstract Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. It relies mainly on two approximations namely, lower and upper approximations which are used to study the boundary region and accuracy measure. Ideal is considered as a crucial research of extension this theory. As, it is efficacious tool to dispose of vagueness and uncertainties by helping us to approximate the rough set in a more general manner, accurate and increase the accuracy measure. Minimizing the boundary region is one of the pivotal and substantial themes for studying the rough sets which consequently aims to maximize the accuracy measure. Ideal is one of the effective and successful followed methods to achieve this goal perfectly. So, the object through this work is to present new methods in rough set via ideals. Moreover, these methods are also based on the maximal right neighborhood generated by binary relations not similarity relations as in the previous studies. Accordingly, the present techniques are extended the applications fields of the rough sets. As, the similarity relations do not always hold in many real-life applications and consequently this restriction limits the wide applications of this set as it is shown in the end of this paper. Some important characteristics of these methods are scrutinized and demonstrated that they are generated accuracy measures greater and higher than the former ones in the other approaches. Afterwards, it is elucidated that the corresponding upper and lower approximations, boundary regions, accuracy measures and roughness measures are monotonic. Finally, two medical applications are introduced to show the significance of utilizing the ideals in the proposed methods and how it plays an intrinsical and a substantial role in the decision making problems. It enables us to decide the impact factors of COVID-19 infections and heart attacks. As, it handles any imperfect data in symptoms of the diseases and this automatically makes the diagnosis of patients easily and perfectly. Consequently, this help the medical staff to make a precise decision about the diagnosis of patients

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