Rough Approximation Spaces via Maximal Union Neighborhoods and Ideals with a Medical Application

One of the most popular and important tools to deal with imperfect knowledge is the rough set theory. It starts from dividing the universe to obtain blocks utilizing an equivalence relation. To make it more flexibility and expand its scope of applications, many generalized rough set models have been proposed and studied. To contribute to this area, we introduce new generalized rough set models inspired by "maximal union neighborhoods and ideals."These models are created with the aim to help decision-makers to analysis and evaluate the given data more accurately by decreasing the ambiguity regions. We confirm this aim by illustrating that the current models improve the approximations operators (lower and upper) and accuracy measures more than some existing method approaches. We point out that almost all major properties with respect to rough set model can be kept using the current models. One of the interesting obtained characterizations of the current models is preserving the monotonic property, which enables us to evaluate the vagueness in the data and enhance the confidence in the outcomes. Moreover, we compare the current approximation spaces with the help of concrete examples. Finally, we show the performance of the current models to discuss the information system of dengue fever disease and eliminate the ambiguity of the medical diagnosis, which produces an accurate decision.