Covering Based Pessimistic Multigranular Rough Equalities and their Properties

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Author(s)

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

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

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

* Corresponding author.

DOI: https://doi.org/10.5815/ijitcs.2016.04.07

Received: 10 May 2016 / Revised: 2 Sep. 2015 / Accepted: 16 Nov. 2015 / Published: 8 Apr. 2016

Index Terms

Rough sets, covering based rough sets, Multigranulations, Covering Based multigranulations, approximate equality

Abstract

The basic rough set theory introduced by Pawlak as a model to capture imprecision in data has been extended in many directions and covering based rough set models are among them. Again from the granular computing point of view, the basic rough sets are unigranular by nature. Two types of extensions to the context of multigranular computing are done; called the optimistic and pessimistic multigranulation by Qian et al in 2006 and 2010 respectively. Combining these two concepts of covering and multigranulation, covering based multigranular models have been introduced by Liu et al in 2012. Extending the stringent concept of mathematical equality of sets rough equalities were introduced by Novotny and Pawlak in 1985. Three more types of such approximate equalities were introduced by Tripathy in 2011. In this paper we study the approximate equalities introduced by Novotny and Pawlak from the pessimistic multigranular computing point of view and establish several of their properties. These concepts and properties are shown to be useful in approximate reasoning.

Cite This Paper

B.K.Tripathy, S.C.Parida, "Covering Based Pessimistic Multigranular Rough Equalities and their Properties", International Journal of Information Technology and Computer Science(IJITCS), Vol.8, No.4, pp.52-62, 2016. DOI:10.5815/ijitcs.2016.04.07

Reference

[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]Novotny, M. and Pawlak, Z.: Black Box Analysis and Rough Top Equality, Bull. Polish Acad. Sci. Math., 33, (1985), pp.105-113.

[7]Novotny, M. and Pawlak, Z.: Rough Top Equalities and Rough Bottom Equalities, Bull. Polish Acad. Sci. Math., 33, (1985), pp.91-97. 

[8]Novotny, M. and Pawlak, Z.: On Rough Equalities, Bull. Polish Acad. Sci. Math., 33, (1985), pp.99-104. 

[9]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.

[10]Qian, Y. H., Liang, J. Y and Dang, C.Y.:  Pessimistic rough decision, proceedings of RST 2010, Zhoushan, China, (2010), pp.440-449.

[11]Tripathy, B. K.: An Analysis of Approximate Equalities based on Rough Set Theory, International journal of Advances in Science and Technology,vol.31, June, (2011),pp.23-36.

[12]Tripathy, B.K., Rawat, R., Divya Vani Y, and Parida, S. C.: Approximate Rough Equalities, International Journal of Intelligent Systems and Applications 6: (2014), pp.69-76.

[13]Tripathy, B.K. and Mitra, A.: On Approximate Equivalences of Multigranular Rough Sets and Approximate Reasoning, International Journal of Information Technology and Computer Science, 10, (2013), pp.103-113.

[14]Tripathy, B. K. and Panda, G.K.: Approximate Equalities on Rough Intuitionistic Fuzzy Sets and an Analysis of Approximate Equalities, International Journal of Computer Science Issues (IJCSI) ,9, (2012), pp.371-380.

[15]Tripathy, B. K. and Nagaraju, M.: On Some Topological Properties of Pessimistic Multigranular Rough Sets, International Journal of Intelligent Systems and Applications, 8, (2012), pp.10-17.

[16]Tripathy, B. K. and Nagaraju, M.: A Comparative Analysis of Multigranular approaches and on Topological Properties of Incomplete Pessimistic Multigranular Rough Fuzzy sets, International Journal of Intelligent Systems and Applications, 11, (2012), pp.99-109.

[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.

[18]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.

[19]Tripathy, B. K.: Rough sets on Fuzzy approximation spaces and Intuitionistic Fuzzy approximation spaces, Springer International studies in computational intelligence, vol.174, Rough Set Theory: A True landmark in Data Analysis, Ed: A. Abraham, R.Falcon and R.Bello, (2009), pp.3 – 44.

[20]Tripathy, B. K. and Panda, G.K.: On Covering Based Approximations of Classifications of Sets”, IEA/AIE 2009, LNAI 5579, (2009), pp.777-786.

[21]Tripathy, B. K.: On Approximation of Classifications, Rough Equalities and Rough Equivalences”, Springer International studies in computational intelligence, vol.174, Rough Set Theory: A True landmark in Data Analysis, Ed: A. Abraham, R.Falcon and R.Bello: (2009), pp.85 – 133

[22]Tripathy, B. K. and Tripathy, H.. K.: Covering Based Rough Equivalence of Sets and Comparison of Knowledge”, Proceedings of the IACSIT Spring Conference 2009, Singapore, 17-20 April 2009, pp.303-307.

[23]Tripathy, B. K., Mitra, A. and Ojha, J.: On Rough Equalities and Rough Equivalence of Sets”, ”, RSCTC 2008-Akron, U.S.A., Springer-Verlag Berlin Heidelberg 2008, LNAI 5306: pp.92–102.

[24]Yao, Y.Y and Yao, B.: Covering based rough set approximations, Information Sciences, 200, (2012), pp.91-107.

[25]Yao, Y. Y.: Perspectives of Granular Computing”, Proceedings of 2005 IEEE International Conference on Granular Computing, I: (2005), pp. 85-90.

[26]Zadeh, L.A: Fuzzy sets and information granularity, In: Advances in Fuzzy set Theory and Applications”, N.Gupta, R.Regade and R.Yager (Eds.), (1979), pp.3-18.

[27]Zadeh, L.A: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy sets and systems, 19, (1997),pp.111-127

[28]Zakowski W.: Approximations in the space (U II), Demonstration Mathematics, 16, (1998), pp.761-769.