An improvement of rough sets' accuracy measure using containment neighborhoods with a medical application

The rough set theory is a nonstatistical mathematical approach to address the issues of vagueness and uncertain knowledge. The rationale of this theory relies on associating a subset with two crisp sets called lower and upper approximations which are utilized to determine the boundary region and accuracy measure of that subset. Neighborhoods systems are pivotal technique to reduce the boundary region and improve the accuracy mea-sure. Therefore, we aim through this paper to introduce new types of neighborhoods called containment neighborhoods (briefly, C-j-neighborhoods). They are defined depending on the inclusion relations between j-neighborhoods under arbitrary binary relation. We study their relationships with some previous types of neighborhoods, and determine the conditions under which they are equivalent. Then, we applied C-j-neighborhoods to present the concepts of C-j-lower and C-j-upper approximations and reveal main properties with the help of examples. We also prove that a C-j-accuracy measure is the highest in cases of j = i, < i >. Furthermore, we compare our approach with two approaches given in published literatures and show that accuracy measure induced from our technique is the best. Finally, we successfully applied C-j-neighborhoods, N-j-neighborhoods and E-j- neighborhoods in a medical application aiming to classify medical staff in terms of suspected infection with the new corona-virus (COVID-19). (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The rough set theory introduces new types of neighborhoods called containment neighborhoods and defines concepts of C-j-lower and C-j-upper approximations. The approach is successfully applied in a medical application aiming to classify medical staff in terms of suspected infection with COVID-19, showing the effectiveness of the technique.