International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 4, No. 8, 8 Jul. 2012
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On Some Topological Properties of Pessimistic Multigranular Rough Sets
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Author(s)
B.K. Tripathy
1,*
M. Nagaraju
1
Index Terms
Rough Sets, Equivalence Relations, Tolerance Relations, Type of Rough Sets, Multi Granular Rough Sets
Abstract
Rough set theory was introduced by Pawlak as a model to capture impreciseness in data and since then it has been established to be a very efficient tool for this purpose. The definition of basic rough sets depends upon a single equivalence relation defined on the universe or several equivalence relations taken one each at a time. There have been several extensions to the basic rough sets introduced since then in the literature. From the granular computing point of view, research in classical rough set theory is done by taking a single granulation. It has been extended to multigranular rough set (MGRS) model, where the set approximations are defined by taking multiple equivalence relations on the universe simultaneously. Multigranular rough sets are of two types; namely optimistic MGRS and pessimistic MGRS. Topological properties of rough sets introduced by Pawlak in terms of their types were studied by Tripathy and Mitra to find the types of the union, intersection and complement of such sets. Tripathy and Raghavan have extended the topological properties of basic single granular rough sets to the optimistic MGRS context. Incomplete information systems take care of missing values for items in data tables. MGRS has also been extended to such type of incomplete information systems. In this paper we have carried out the study of topological properties of pessimistic MGRS by finding out the types of the union, intersection and complement of such sets. Also, we have provided proofs and examples to illustrate that the multiple entries in the table can actually occur in practice. Our results hold for both complete and incomplete information systems. The multiple entries in the tables occur due to impreciseness and ambiguity in the information. This is very common in many of the real life situations and needed to be addressed to handle such situations in efficient manner.
Cite This Paper
B.K.Tripathy, M. Nagaraju, "On Some Topological Properties of Pessimistic Multigranular Rough Sets", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.8, pp.10-17, 2012. DOI:10.5815/ijisa.2012.08.02
Reference
[1]Kryszkiewicz, K.: Rough set approach to incomplete information systems, Information Sciences, vol.112, (1998), pp.39 – 49.
[2]Liang, J.Y and Shi, Z.Z.: The information entropy, rough entropy and knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.12(1),(2001),pp. 37 – 46.
[3]Liang, J.Y, Shi, Z.Z., Li, D. Y. and Wierman, M. J.: The information entropy, rough entropy and knowledge granulation in incomplete information system, International Journal of general systems, vol.35(6), (2006),pp.641 – 654.
[4]Liang, J.Y and Li, D. Y.: Uncertainty and Knowledge acquisition in Information Systems, Science Press, Beijing, China, (2005).
[5]Pawlak, Z., Rough sets, Int. jour. of Computer and Information Sciences,11, (1982), pp.341-356.
[6]Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data, Kluwer academic publishers (London), (1991).
[7]Pawlak, Z. and Skowron, A., Rudiments of rough sets, Information Sciences-An International Journal, Elsevier Publications, 177(1), (2007), pp.3-27.
[8]Pawlak, Z. and Skowron, A., Rough sets: Some extensions, Information Sciences-An International Journal, Elsevier Publications, 177(1), (2007), pp.28-40.
[9]Pawlak, Z. and Skowron, A., Rough sets and Boolean reasoning,. Information Sciences-An International Journal, Elsevier Publications, 177(1), (2007), pp. 41-73.
[10]Qian, Y.H and Liang, J.Y.: Rough set method based on Multi-granulations, Proceedings of the 5th IEEE Conference on Cognitive Informatics, vol.1, (2006),pp.297 – 304.
[11]Qian, Y.H, Liang, J.Y. and Dang, C.Y.: MGRS in Incomplete Information Systems, IEEE Conference on Granular Computing,(2007),pp.163 -168.
[12]Qian, Y.H, Liang, J.Y. and Dang, C.Y.: Incomplete Multigranulation Rough set, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, Vol.40, No.2, March 2010, pp.420 – 431.
[13]Qian, Y.H., Liang, J.Y and Dang, C.Y.: Pessimistic rough decision, proceedings of RST 2010, Zhoushan, China, (2010), pp. 440-449.
[14]Tripathy, B.K.: On Approximation of classifications, rough equalities and rough equivalences, Studies in Computational Intelligence, vol.174, Rough Set Theory: A True Landmark in Data Analysis, Springer Verlag, (2009), pp.85 - 136.
[15]Tripathy, B.K.: Rough Sets on Fuzzy Approximation Spaces and Intuitionistic Fuzzy Approximation Spaces, Studies in Computational Intelligence, vol.174, Rough Set Theory: A True Landmark in Data Analysis, Springer Verlag, (2009), pp.03 - 44.
[16]Tripathy, B.K. and Mitra, A.: Topological Properties of Rough Sets and their Applications, International Journal of Granular Computing, Rough Sets and Intelligent Systems (IJGCRSIS), (Switzerland),vol.1, no.4, (2010),pp.355-369.
[17]Tripathy, B.K. and Raghavan, R.: On Some Topological Properties of Multigranular Rough Sets, Journal of Advances in Applied science Research, Vol.2, no.3, (2011), pp.536-543.