I-Rough Product Topology
T. K. Sheeja1
1Department of Mathematics, T. M. Jacob Memorial Government College, Manimalakunnu, Kerala, India.
Abstract: In this paper, the concept of product topology is extended to I-rough topological spaces. The properties of the proposed I-rough product topology are explored. Akin to the classical product topology, the I-rough product topology makes each projection mapping an I-rough continuous function and it is found to be the weakest topology in the product rough universe having this property. Also, the projection functions are shown to be open mappings. Further, the I-rough interior of an I-rough set on the product space is expressed as the product of the corresponding I-rough interiors of the component I-rough sets.
Keywords: I-rough functions, I-rough sets, I-rough topology, I-rough product topology, Projection functions.
Cite this article as: T. K. Sheeja, I-Rough Product Topology, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 119-126.References
- M. E. Abd El-Monsef, O. A. Embaby and M. K. El-Bably, Comparison between Rough Set Approximations Based on Different Topologies, International Journal of Granular Computing, Rough Sets and Intelligent Systems, 3(4)(2014), 292-305.
- T. B. Iwinski, Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences-Mathematics, 35(1987), 673–683.
- J. L. Kelley, General Topology, Van Nostrand Company, (1955).
- E. F. Lashin, A. M. Kozae, A. A. Abo Khadra and T. Medhat, Rough Set Theory for Topological Spaces, International Journal of Approximate Reasoning, 40(2005), 35-43.
- W. J. Liu, Topological Space Properties of Rough Sets, Proceedings of the third IEEE International Conference on Machine Learning and Cybernetics, Shanghai, (2004), 2353-2355.
- B. P. Mathew and S. J. John, I-Rough Topological Spaces, International Journal of Rough Sets and Data Analysis, 3(1)(2016), 98-113.
- B. P. Mathew and S. J. John, Some Special Properties of I-rough Topological Spaces, Annals of Pure and Applied Mathematics, 12(2)(2016), 111-120.
- B. P. Mathew and S. J. John, I-Rough Continuous Functions, International Journal of Scientific Research in Mathematical and Statistical Sciences, 7(1)(2020), 111-113.
- Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences, 11(5)(1982), 341-356.
- R. Sikorski, Boolean Algebras, Springer-Verlag Berlin, Heidelberg, (1969).
- T. K. Sheeja, On Product Approximation Spaces, IOSR Journal of Mathematics, 17(3)(2021), 52-58.
- T. K. Sheeja and A. Sunny Kuriakose, Continuity on Approximation Spaces, Journal of Mathematical and Computational Sciences, 11(4)(2021), 4104-4117.
- T. K. Sheeja and A. Sunny Kuriakose, Rough Topology on Approximation Spaces, International Journal of Advanced Research in Computer Science, 8(9)(2017), 379-384.
- Y. Y. Yao, S. K. M. Wong and T. Y. Lin, A review of rough set models, in: Rough Sets and Data Mining, Kluwer Academic Publishers, Boston, (1997), 47–75.
- H. Yu and W. R. Zhan, On the Topological Properties of Generalized Rough Sets, Information Sciences, 263(2014), 141-152.
- Q. Zhang, Q. Xie and G. Wang, A survey on rough set theory and its applications, CAAI Transactions on Intelligence Technology, 1(4)(2016), 323-333.