Rough Sets on Topological Spaces

Anitha K; Venkatesan P

doi:https://doi.org/10.14445/22315373/IJMTT-V10P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 10 | Number 1 | Year 2014 | Article Id. IJMTT-V10P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V10P509

Rough Sets on Topological Spaces

Anitha K , Venkatesan P

Abstract

Rough Set Theory propsed by Zdzilaw Pawlak as a mathematical tool for approaching imprecise knowledge and it has many applications in Datamining, Machine Learning,Morphology, Control Theory and Medicine etc., The basic concept of Rough Set Theory depends on equivalence relation. In this paper we introduce topologies into the realm of Rough Sets and investigate their properties.Mathematical properties of Rough Set Theory can be constructed from fragments of Algebra, Logical Implications and Topology. We aim at presenting a properties of Rough Set Theory by Topological Methods

Keywords

Approximations, Indiscernibility Function, Equivalence Relation, Topological Spaces, Rough Metric, Isometric.

References

[1]. Abo Khadra , A.A., Kozae .A.M., Lashin . E.F., Medhat . T., (2005), Rough Set Theory for Topological Spaces,International Journal of Approximate Reasoning , 35-43
[2]. Feifei Xu, Duoqian Miao, Yiyu Yao. (1991), Rough Set Approximations in Formal Concept Analysis and Knowledge Spaces, Kluwer academic publishers (London).
[3]. Lukshmi R.A, Geetha P.V, Venkatesan, P., (2013) Rough Set Theory for Attribute Reduction,Indian Journal of Automation and Artificial Intelligence,1(3),2320-4001.
[4]. Milan Vlach,(2008) , Algebraic and Topological Aspects of Rough Set Theory, Fourth International Workshop on Computational Intelligence and Applications, IEEE
[5]. Nguyen Duc Thuan, (2009), Covering Rough Sets From a Topological Point of View , International Journal of Computer Theroy and Engineering , 1(5),1793-8201
[6]. Raghavan,R., Tripathy,B.K.., (2011) On Some Topological Properties of Multigranular Rough Sets, Advances in Applied Science Research,2(3),536-543
[7]. Salma.A.S., (2011), Some Topological Properties of Rough Sets with Tools for Data Mining,IJCSI,1694-0814
[8]. Polkowski.L.,(2002), Rough Sets- Mathematical Foundations, Springer-Verlag Berlin Heidelberg GmbH.
[9]. Sankar.K.Pal., Pradipta Maji, (2012),Rough –Fuzzy Pattern Recognition, IEEE

Citation :

Anitha K , Venkatesan P, "Rough Sets on Topological Spaces," International Journal of Mathematics Trends and Technology (IJMTT), vol. 10, no. 1, pp. 47-50, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V10P509