Bitopological approach for generalized rough sets via minimal structures | ||
| Bulletin of Faculty of Science, Zagazig University | ||
| Article 35, Volume 2025, Issue 1, April 2025, Pages 17-27 PDF (1.13 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/bfszu.2025.254375.1351 | ||
| Authors | ||
| heba mustafa ibrahim1; fawzia sleim2; yasmin tohamy abdoh* 3 | ||
| 1mathematics department-faculty of science-zagazig university | ||
| 2mathematics department-faculty of science- zagazig university | ||
| 3mathematics 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. | ||
| Keywords | ||
| minimal space; biminimal structure; left and right neighborhood; MxR (MRx)open (closed) sets | ||
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