Ayşegül ÇAKSU GÜLER, Oya BEDRE ÖZBAKIR, Esra DALAN YILDIRIM

Rough approximations based on different topologies via ideals

In this paper, we generalize the notations of rough sets based on the topological space. Firstly, we produce various topologies by using the concept of ideal, $C_j$ -neighbourhoods and $P_j$ -neighbourhoods. When we compare these topologies with previous topologies, we see that these topologies are more general. Then we introduce new methods to find the approximations by using these generated topologies. When we compare these methods with the previous methods, we see that these methods are more accurate.

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[1] Abd El-Monsef ME, Salama AS, Embaby OA. Granular computing using mixed neighborhood systems. Journal of Institute of Mathematics and Computer Sciences 2009; 20 (2): 233-243.
[2] Abd El-Monsef ME, Embaby OA, El-Bably MK. Comparison between rough set approximations based on different topologies. International Journal of Granular Computing, Rough Sets and Intelligent Systems 2014; 3 (4): 292- 305.
[3] Abd El-Monsef ME, Kozae AM, El-Bably MK. On generalizing covering approximation space. Journal of the Egyptian Mathematical Society 2015; 23: 535-545.
[4] Amer WS, Abbas MI, El-Bably MK. On j -near concepts in rough sets with some applications. Journal of Intelligent and Fuzzy Systems 2017; 32: 1089-1099.
[5] Atef M, Khalil AM, Li S, Azzam A, El-Atik AEF. Comparison of six types of rough approximations based on j -neighborhood space and j -adhesion neighborhood space. Journal of Inteligent and Fuzzy Systems 2020; 39 (3): 4515-4531.
[6] Al-shami TM, Fu WQ, Abo-Tabl EA. New rough approximations based on E -neighbourhoods. Complexity 2021; 2021: 1-6.
[7] Al-shami TM. An improvement of rough set’s accuracy measure using containment neighborhoods with a medical application. Information Sciences 2021; 569: 110-124.
[8] Hosny M. Idealization of j -approximation spaces. Filomat 2020; 34 (2): 287- 301.
[9] Hosny M. Topological approach for rough sets by using j -nearly concepts via ideals. Filomat 2020; 34 (2): 273-286.
[10] Liu G, Zhu W. The algebraic structures of generalized rough set theory. Information Sciences 2008; 178 (21): 4105-4113.
[11] Lin TY. Granular computing on binary relations I: data mining and neighborhood systems, II: rough set representations and belief functions. In: Polkowski L, Skowron A (editors). Rough Sets in Knowledge Discovery 1. Physica-Verlag Heidelberg, 1998, pp. 107-140.
[12] Pawlak Z. Rough sets. International Journal of Computer and Information Sciences 1982; 11 (5): 341-356.
[13] Pawlak Z. Rough sets: theoretical aspects of reasoning about data. Dordrecht, The Netherlands: Kluwer Academic Publishers, 1991.
[14] Pawlak Z, Skowron A. Rough sets: some extensions. Information Sciences 2007; 177: 28-40.
[15] Yao YY. On generalizing Pawlak approximation operators. Lecture Notes in Artificial Intelligence 1998; 1424: 298-307.
[16] Yao YY. Rough sets, neighborhood systems and granular computing. In: 1999 IEEE Canadian Conference on Electrical and Computer Engineering Proceedings; Canada; 1999. pp. 1553-1558.