Covering Based Optimistic Multigranular Approximate Rough Equalities and their Properties

Full Text (PDF, 643KB), PP.70-79

Views: 0 Downloads: 0


B.K. Tripathy 1,* S.C.Parida 2

1. School of Computing Science and Engineering VIT University, Vellore-632014 Tamil Nadu, India

2. Lecturer in Mathematics, K.B.V Mahavidyalaya, Kabisurya Nagar, Ganjam, Odisha -761104

* Corresponding author.


Received: 20 Aug. 2015 / Revised: 1 Dec. 2015 / Accepted: 11 Feb. 2016 / Published: 8 Jun. 2016

Index Terms

Rough Sets, Covering Based Rough Sets, Multigranulations, Covering Based Multigranulations, Approximate Equality


Since its inception rough set theory has proved itself to be one of the most important models to capture impreciseness in data. However, it was based upon the notion of equivalence relations, which are relatively rare as far as applicability is concerned. So, the basic rough set model has been extended in many directions. One of these extensions is the covering based rough set notion, where a cover is an extension of the concept of partition; a notion which is equivalent to equivalence relation. From the granular computing point of view, all these rough sets are unigranular in character; i.e. they consider only a singular granular structure on the universe. So, there arose the necessity to define multigranular rough sets and as a consequence two types of multigranular rough sets, called the optimistic multigranular rough sets and pessimistic rough sets have been introduced. Four types of covering based optimistic multigranular rough sets have been introduced and their properties are studied. The notion of equality of sets, which is too stringent for real life applications, was extended by Novotny and Pawlak to define rough equalities. This notion was further extended by Tripathy to define three more types of approximate equalities. The covering based optimistic versions of two of these four approximate equalities have been studied by Nagaraju et al recently. In this article, we study the other two cases and provide a comparative analysis.

Cite This Paper

B.K.Tripathy, S.C.Parida, "Covering Based Optimistic Multigranular Approximate Rough Equalities and their Properties", International Journal of Intelligent Systems and Applications (IJISA), Vol.8, No.6, pp.70-79, 2016. DOI:10.5815/ijisa.2016.06.08


[1]Lin GP, Qian YH, Li J.J.: a covering-based pessimistic multi-granulation rough set, in: Proceedings of International Conference on Intelligent Computing, August 11-14, (2011), Zhengzhon, China.
[2]Liu, C. H. and Miao, D.Q.: Covering rough set model based on multi-granulations, in: Proceedings of Thirteenth International Conference on Rough Sets, Fuzzy Set, Data Mining and Granular Computing, LNCS(LNAI) 6743, (2011), pp. 87-90.
[3]Liu C. L., Miao D. and Quain J.: On multi-granulation covering rough sets, International Journal of Approximate Reasoning, November (2012).
[4]Pawlak, Z.: Rough sets, Int. jour. of Computer and Information Sciences, 11, (1982), pp.341-356.
[5]Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data, Kluwer academic publishers (London), (1991).
[6]Qian, Y. H and Liang, J.Y.: Rough set method based on Multi-granulations, Proceedings of the 5th IEEE Conference on Cognitive Informatics, (2006), 1, pp.297 – 304.
[7]Qian, Y. H, , Liang, J.Y. and Dang, C. Y.: MGRS in Incomplete Information Systems, IEEE Conference on Granular Computing, (2007), pp.163 -168.
[8]Qian, Y. H. , Liang, J. Y. and Dang, C. Y.: Incomplete Multi-granulation Rough set, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, 40, 2, (2010), pp.420 – 431.
[9]Qian, Y. H. , Liang, J. Y and Dang, C.Y.: Pessimistic rough decision, proceedings of RST 2010, Zhoushan, China, (2010), pp.440-449.
[10]Qian, Y. H, Liang, J. Y and Dang, C. Y.: MGRS: A multi-granulation rough set, Information Sciences, 180, (2010), pp. 949-970.
[11]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.
[12]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), (2010), 1, pp.4:355-369.
[13]Tripathy, B. K. and Raghavan, R.: On Some Topological Properties of Multi-granular Rough Sets, Journal of Advances in Applied science Research, 2(3), (2011), pp.536-543.
[14]Tripathy, B.K.: An analysis of Approximate Equalities based on Rough Set Theory, International Journal of Advanced Science and Technology, vol.31, June, (2011),pp.23-36.
[15]Tripathy, B.K. and Nagaraju, M.: On Some Topological Properties of Pessimistic Multi-granular Rough Sets, International Journal Intelligent Systems and Applications, 4(8), [2012], pp.10-17.
[16]Tripathy, B.K. and Mitra, A.: Approximate Equivalences of Multigranular rough sets and approximate reasoning, International Journal of Information Technology and Computer Science, 10, (2013), pp.103-113.
[17]Tripathy, B.K. and Govindarajulu, K.: On Covering based Pessimistic Multigranular Rough Sets, 2014 Sixth International Conference on Computational Intelligence and Communication Networks, 978-1-4799-6929-6/14, (2014), pp.708 -713.
[18]Tripathy, B.K., Rawat, R., Divya Rani, V. and Parida, S.C.: Approximate Reasoning through Multigranular Approximate Rough Equalities, IJISA, vol.6, no.8, (2014), pp. 69-76.
[19]Tripathy, B.K., Saraf, P. and Parida, S.C.:: On Multigranular Approximate Rough Equivalence of sets and Approximate reasoning, Proceedings of the International Conference on CIDM, 20-21, December 2014, Computational Intelligence in Data Mining, vol.2, Smart Innovation, Systems and technologies, vol.32, (2015), pp.605-616.
[20]Tripathy, B.K. and. Govindarajulu, K: Some more properties of Covering based Multigranular rough sets, INDIA 2015, Kalyani University, J.K.Mandal et al (Eds),Information system design and applications, Advances in Intelligent Systems and Computing, 339, (2015), pp.555-564.
[21]Tripathy, B.K. and Parida, S.C.: Covering Based Pessimistic Multigranular Rough Equalities and their Properties, Accepted for publication in International Journal of Information Technology and Computer Science, (2015).
[22]Yao, Y.Y.: Perspectives of Granular Computing, Proceedings of 2005 IEEE International Conference on Granular Computing, 1, (2005), pp.85-90.
[23]Yao, Y.Y and Yao, B.: Covering based rough set approximations, Information Sciences, 200, (2012), pp.91-107.
[24]Zakowski, W.: Approximations in the space (U II), Demonstration Mathematics, 16, (1993), pp.761-769.