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Dimension of Topologies Associated with Information Systems

American Journal of Mathematical and Computational Sciences
Vol.2 , No. 5, Publication Date: Sep. 20, 2017, Page: 40-48

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Authors

[1]	Malak Raslan, Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt.
[2]	Abdelmonem Mohamed Kozae, Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.
[3]	Sally Haroun, Mathematics Department, Faculty of Science, Damietta University, Damietta, Egypt.

Abstract

Many phenomena in quantum mechanics and theories of modern dynamics systems are represented in topological spaces with high dimensions and modern information systems use topological space as mathematical model which express it. As far as linking between dimensions of topological spaces and accuracy of approximation are not taught before and mentioned only in Pawlak space. The topology associated with Pawlak approximation space has a zero dimension, the generalized space generated by general binary relation is not generally of zero dimension. The purpose of this paper is to compute dimensions of topologies associated with information systems which resulted from general relations and connection between the dimension of topologies and approximation accuracy of uncertain concepts. Examples for topologies resulted from various subsets of features are given. We use the concept of topology, boundary, basis, the upper and lower approximation for calculation approximation accuracy. Also, we construct topologies from data table (information systems) by using general relations and compute dimensions of these topologies for its importance in finding connection between accuracy of approximation and dimensions.

Keywords

Topologies, Information Systems, Inductive Dimension, Approximation Accuracy

Reference

[01]	Adam, Cand Franzosa R., Introduction to topology (pure and applied), Indian edition published by Dorling Kindersley India Pvt. Ltd, copyright@2009.
[02]	Allam, A. A., Bakeir, M. Y. and Abo-Tabl, E. A., New approach for basic rough set concepts, LNCS, Vol. 3641, pp. 64-73, 2005.
[03]	Cain. G. L, Introduction to General Topology, Addison-Wesely publishing company (1994).
[04]	Kadzinski, M., Słowinski, R., Greco, S.: Robustness analysis for decision under uncertainty with rule-based preference model. Information Sciences 328 (2016) 321–339
[05]	Kelley, J., General topology, Van Nostrand Company, 1955.
[06]	Kozae. A. M, On Topological Dimension and Digital Topology, International Journal of Pure and Applied Mathematics, Vol. 41, pp. 647-657, 2007.
[07]	Grzymala-Busse. J. W, Rough SetTheory with Applications to Data Mining, studfuzz 197, pp. 223-244 (2005).
[08]	Lashina. E. F, Kozae. A. M, Abo Khadra. A. A and Medhat. T, Rough set Theory for Topological Structures, International journal of approximation reasoning, Vol. 40, pp. 35-43, 2005.
[09]	Shaaban M. Shaaban, Hossam A. Nabwey, "Rough Approximations Based on Supra Topology", European Journal of Scientific Research, ISSN 1450-216X / 1450-202X Vol. 139 No. 3, May, 2016 pp. 237-245.
[10]	Shen, Q. and Jensen, R., Rough Sets, their extensions and application, International journal of automation and computing, Vol. 4, pp. 217-228, 2007.
[11]	Stadler, B. M. R. and Stadler, P. F., Generalized topological spaces in evolutionary theory and combinatorial chemistry, Journal of chemical information and computer sciences, Vol. 42, pp. 577-585, 2002.
[12]	Wasilewski, P. and Slezak, D., Foundations of rough sers from vagueneenperspective: Rough computing: theories, technologies, and applications, Hershey. New York (2008).
[13]	Yao, Y. Y.: Two views of the theory of rough sets in finite universes, International Journal of Approximate-Reasoning, 15 (1996), No. 4, 291-377.