Novel approaches of generalized rough approximation spaces inspired by maximal neighbourhoods and ideals

Abstract

The theory of rough set is a robust approach to face uncertainty by classifying the data under study into three main regions. The main principles of this theory are approximation operators and accuracy measures, so improving them has been a major goal for several works. The intrinsic aim of this study is to create new methods with high accuracy measures to classify subsets of data. These methods are established by combining an ideal structure with four types of maximal neighbourhoods. The essential characterizations and properties of these methods are amply studied. Thereafter, the relationships between these methods are elucidated with the assistance of some numerical examples. In this regard, we prove that the approximation operators and accuracy measures induced from rough set model defined by intersection minimal-maximal neighborhoods are the best. In addition to that, some comparisons are provided to demonstrate the importance of the introduced techniques compared to the previous ones in terms of improving the approximation operators and increasing the values of accuracy. Finally, a numerical example is given to confirm the efficiency of the followed techniques to maximize the value of accuracy and shrink the boundary regions compared to the existing techniques.

Keywords

• Rough set
• Maximal neighbourhood
• Ideal
• Approximation operators
• Accuracy measure