Bitopological approach for generalized rough sets via minimal structures

Document Type : Original Article

Authors

1 mathematics department-faculty of science-zagazig university

2 mathematics department-faculty of science- zagazig university

3 mathematics department faculty of science zagazig university

Abstract

The concept of bitopological spaces was introduced by J.C.Kelly [11]. He studied some of separation axioms properties in bitopological spaces. Many authors studied the relation between rough set and topology[1, 3, 6, 10, 13, 15]. The relation between rough set and minimal structure was studied in[20,9,23]. In this paper we used the right and the left neighborhood of any relation to introduce a biminimal approximation space of uncertain sets as a mathematical tool to modify the approximations. we discussed some definitions and properties of rough sets and applied them in two minimal structures generated by using the right and left neighborhoods. Moreover, several important measures such as accuracy measure and quality of approximation would be studied. We proved that biminimal structure is more efficient and accurate in obtaining results than bitopology. Finally, we show the importance of our new approximations with medical science by applying these approximations in corona virus problem.

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