International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 5, No. 6, 8 May 2013
Cover page and Table of Contents: PDF (size: 429KB)
On Some Comparison Properties of Rough Sets Based on Multigranulations and Types of Multigranular Approximations of Classifications
Full Text (PDF, 429KB), PP.70-77
Views: 0 Downloads: 0
Author(s)
R. Raghavan
1,*
B.K. Tripathy
1
Index Terms
Rough Sets, Pessimistic Multigranulation, Optimistic Multigranulation, Classification, Types of Rough Sets
Abstract
In this paper we consider the inclusion properties for upper and lower approximation of union and intersection of sets for both pessimistic and optimistic multigranulations. We find that two inclusions for pessimistic cases are actually equalities. For other six cases we provide examples to show that actually the proper inclusions hold true. On the approximation of classifications a theorem was proved in Tripathy et al to establish sufficient type properties. We establish here that actually the result is both necessary and sufficient one. Also, we consider types of elements in classifications with respect to both types of multigranulations and establish a general theorem on them.
Cite This Paper
R. Raghavan, B.K.Tripathy, "On Some Comparison Properties of Rough Sets Based on Multigranulations and Types of Multigranular Approximations of Classifications", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.6, pp.70-77, 2013. DOI:10.5815/ijisa.2013.06.09
Reference
[1]Pawlak, Z.: Rough Sets, International Journal of Information and Computer Science, (1982), pp.341-346.
[2]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.
[3]Qian, Y.H., Liang, J.Y and Dang, C.Y.: Pessimistic rough decision, in: Proceedings of RST 2010, Zhoushan, China, (2010), pp. 440-449.
[4]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.
[5]Tripathy, B.K. and Nagaraju, M.: On Some Topological Properties of Pessimistic Multigranular Rough Sets, International Journal of Intelligent Systems and Applications, Vol.4, No.8, (2012), pp.10-17.
[6]Tripathy, B.K. and Raghavan, R.: Some Algebraic properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications, accepted for publication in the International Journal of Information Technology and Computer Science (2013).
[7]Tripathy, B.K. and Nagaraju, M.: A Comparative Analysis of Multigranular Approaches and on Topological Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets, International Intelligent Systems and Applications, Vol.11, (2012), pp.99-109.
[8]Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, (1991).
[9]Grzymala Busse, J.: Knowledge acquisition under uncertainty- a rough set approach, Journal of Intelligent and Robotics systems, 1, (1988), pp. 3 -1 6.
[10]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.
[11]Tripathy, B.K., Ojha, J., Mohanty, D. and Prakash Kumar, Ch. M.S: On rough definability and types of approximation of classifications, vol.35, no.3, (2010), pp.197-215.
[12]Pawlak, Z.: Rough Classifications, International Journal of Man Machine Studies, 20, (1983), pp.469 – 483.
[13]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.