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Approximations of Rough Sets via Filter by using g-increasing and g-decreasing Sets

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
N. Durga Devi, R. Raja Rajeswari, P. Thangavelu

Durga N Devi, Raja R Rajeswari and P Thangavelu. Approximations of Rough Sets via Filter by using g-increasing and g-decreasing Sets. International Journal of Computer Applications 161(8):23-30, March 2017. BibTeX

	author = {N. Durga Devi and R. Raja Rajeswari and P. Thangavelu},
	title = {Approximations of Rough Sets via Filter by using g-increasing and g-decreasing Sets},
	journal = {International Journal of Computer Applications},
	issue_date = {March 2017},
	volume = {161},
	number = {8},
	month = {Mar},
	year = {2017},
	issn = {0975-8887},
	pages = {23-30},
	numpages = {8},
	url = {},
	doi = {10.5120/ijca2017913246},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


In this paper, we introduce a way of constructing a rough set via grill ordered topological spaces. Increasing and decreasing sets are defined based on grill and comparisons between current approximations and previous approximations by Shafei and Kandil are carried out. Also it is shown that the chances of getting better approximation by our method of approximations are greater than any of the available methods.


  1. A. A. Abo Khadra, B. M. Taher and M. K. El-Bably, Generalization of Pawlak approximation space, International Journal of Mathematical Archive, 4 (11), (2013), 78-89.
  2. E.A. AboTabl, A comparison of two kinds of definitions of rough approximations basedon a similarity relation, Inform. Sci., 181, (2011), 2587-2596.
  3. G. Choquet, Sur les notions de filtre et grille, ComptesRendus Acad. Sci. Paris,224(1947), 171-173.
  4. M. E. EL-Shafei, A. M. Kozae and M. Abo-Elhamayel, Rough Set Approximations viaTopological Ordered Spaces, Annals of Fuzzy Sets, Fuzzy Logic and Fuzzy Systems, 2(2), (2013), 49-60.
  5. A. Kandil, O. Tantawy, S. A. El-Sheikh and M. Hosny, A generalization of rough setsin topological ordered spaces, Journal of Mathematical and Computational Science, 4(2), (2014),278-297.
  6. A. Kandiletal.Ann. A generalization of rough sets via filter by using I-increasing andI-decreasing sets, Fuzzy Math. Inform., 10 (2015), No. 3, 361-379.
  7. M. Kondo and W. A. Dudek, Topological structures of rough sets induced by equivalence relations, Journal of Advanced Computational Intelligence and Intelligent Informatics, 10 (5), (2006), 621-624.
  8. A. M. Kozae, S. A. El-Sheikh and M. Hosny, On generalized rough sets and closurespaces, International Journal of Applied Mathematics, 23 (6), (2010) , 997-1023.
  9. A. M. Kozae, S. A. El-Sheikh, E.H. Aly and M. Hosny, Rough sets and its applicationsin a computer network, Ann. Fuzzy Math. Inform., 6 (3), (2013), 605-624.
  10. E. F. Lashin, A. M. Kozae, A. A. Abo Khadra and T. Medhat, Rough set theory fortopological spaces, International Journal of Approximate Reasoning, 40 (2005), 35-43.
  11. G. M. Murdeshwar, General Topology, New Age International (P) Ltd., Publishers,1990.
  12. L. Nachbin, Topology and Order, Van Nostrand Mathematical studies, Princeton, NewJersey, 1965.
  13. Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences,11 (5), (1982), 341-356.
  14. Y. Y. Yao, Relational interpretations of neighborhood operators and rough set approximation operators, Inform. Sci., 1119 (1-4), (1998), 239-259.
  15. Y. Y. Yao, Rough sets, neighborhood systems, and granular computing, Proceedingsiof IEEE Canadian Conference on Electrical and Computer Engineering, Edmonton, Alberta, Canada, 3 (1999), 1553-1558.


G-increasing, G-decreasing.