International Journal of Information Technology and Computer Science (IJITCS)
IJITCS Vol. 5, No. 7, 8 Jun. 2013
Cover page and Table of Contents: PDF (size: 445KB)
Some Algebraic Properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications
Full Text (PDF, 445KB), PP.63-70
Views: 0 Downloads: 0
Author(s)
B. K. Tripathy
1,*
R.Raghavan
1
Index Terms
Rough Sets, Optimistic Multigranulation, Pessimistic Multigranulation, Classification, Approximations
Abstract
Ever since the introduction of rough sets by Pawlak as a model to capture uncertainty, it has drawn much attention from both theoretical and application point of view. Classifications of universes play very important roles in several fields of study. The study of rough definability of classifications was initiated by Busse. The properties of approximations of classifications were established in the form of four theorems and were used to define the types of classifications. These results were generalised to develop two theorems of necessary and sufficient type were established by Tripathy et al , from which several results including the four theorems of Busse could be derived as corollaries. Recently, rough sets based on Multigranulation were introduced and studied by Qian et al. Also, it has been extended to include incomplete information systems. Many of these results are extended to the multigranular cases. In this paper, we extend the properties of types of classifications to the multigranular context. Also, we introduce some parameters like the accuracy of approximation and the quality of approximation of classifications with respect to Multigranulations. We have obtained interesting criteria under which both types of Multigranulations reduce to single granulation. Also, some algebraic properties of Multigranulations are derived.
Cite This Paper
B.K.Tripathy, R.Raghavan, "Some Algebraic Properties of Multigranulations and an Analysis of Multigranular Approximations of Classifications", International Journal of Information Technology and Computer Science(IJITCS), vol.5, no.7, pp.63-70, 2013. DOI:10.5815/ijitcs.2013.07.08
Reference
[1]Pawlak, Z.: Rough Sets, International Journal of Information and Computer Science, (1982), pp.341-346.
[2]Grzymala Busse, J.: Knowledge acquisition under uncertainty- a rough set approach, Journal of Intelligent and Robotics systems, 1, (1988), pp. 3 -1 6.
[3]Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, (1991).
[4]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.
[5]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.
[6]Chan, C.C. and Grzymala Busse, J.: Rough Set boundaries as a tool for learning rules from examples, In: Proceedings of the ISMIS-89, 4th Int. Symposium on Methodologies for intelligent Systems, (1989), pp.281-288.
[7]Chan, C.C. and Grzymala Busse, J.: On the attribute redundancy and the learning programs ID3, PRISM and LEM2, Department of Computer science, University of Kansas, TR-91-14, 20 December, (1991).
[8]Pawlak, Z.: Rough Classifications, international Journal of Man Machine Studies, 20, (1983), pp.469 – 483.
[9]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
[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.: Pessimistic rough decision, in: Proceedings of RST 2010, Zhoushan, China, (2010), pp. 440-449.
[12]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.
[13]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.