Rough approximations derived from novel topologies based on neighborhoods and their application

The accuracy value is a numerical concept that measures the imprecision or uncertainty of the knowledge in a given data table. The main objective of this study is to obtain a higher accuracy value than those reported in the literature. For this purpose, topological tools will be used. In this study, new topologies are obtained using the existing Nj-neighborhoods and τθ-topology concepts from the literature. It is proven that these newly obtained topologies are finer than many of the topologies previously introduced in the literature. The relationships among the new topologies are examined based on the criterion of being coarser. While some of these topologies can be compared, it is shown that many cannot be compared with each other. By utilizing these topologies, new concepts of lower and upper approximations, boundaries, and accuracy values are defined. These new concepts are compared with previously defined concepts, and their properties are investigated. It is observed that the accuracy values obtained in this study are higher than many of those previously defined. All these comparisons are supported by examples. Additionally, an information table is provided based on the symptoms specified in the guidelines published by the World Health Organization (WHO) and its website. Based on this information table, it is demonstrated that the newly defined accuracy values, with the help of the algorithm presented in this study, are higher than the previously presented accuracy values. In addition, new dependency measures have been defined to show the extent to which decision attributes depend on condition attributes. The newly defined dependency measures are then compared.