International Journal of Information Technology and Computer Science (IJITCS)
IJITCS Vol. 7, No. 8, 8 Jul. 2015
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Study of Covering Based Multi Granular Rough Sets and Their Topological Properties
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Author(s)
M.Nagaraju
1,*
B. K. Tripathy
1
Index Terms
Covering Based Multi-Granular Rough Sets (CBMGRS), Minimal and Maximal Descriptors, Roughly Definable, Internally Un-Definable, Externally Un-Definable, Totally Un-Definable
Abstract
The notions of basic rough sets introduced by Pawlak as a model of uncertainty, which depends upon a single equivalence relation has been extended in many directions. Over the years, several extensions to this rough set model have been proposed to improve its modeling capabilities. From the granular computing point of view these models are single granulations only. This single granulation model has been extended to multi-granulation set up by taking more than one equivalence relations simultaneously. This led to the notions of optimistic and pessimistic multi-granulation. One direction of extension of the basic rough set model is dependent upon covers of universes instead of partitions and has better modeling power as in many real life scenario objects cannot be grouped into partitions but into covers, which are general notions of partitions. So, multigranulations basing on covers called covering based multi-granulation rough sets (CBMGRS) were introduced. In the literature four types of CBMGRSs have been introduced. The first two types of CBMGRS are based on minimal descriptor and the other two are based on maximal descriptor. In this paper all these four types of CBMGRS are studied from their topological characterizations point of view. It is well known that there are four kinds of basic rough sets from the topological characterisation point of view. We introduce similar characterisation for CBMGRSs and obtained the kinds of the complement, union, and intersection of such sets. These results along with the accuracy measures of CBMGRSs are supposed to be applicable in real life situations. We provide proofs and counter examples as per the necessity of the situations to establish our claims.
Cite This Paper
M.Nagaraju, B.K.Tripathy, "Study of Covering Based Multi Granular Rough Sets and Their Topological Properties", International Journal of Information Technology and Computer Science(IJITCS), vol.7, no.8, pp.61-67, 2015. DOI:10.5815/ijitcs.2015.08.09
Reference
[1]Lin G.P., Qian Y.H., 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.H., Wang M.Z.: Covering fuzzy rough set based on multi-granulation, in: Proceedings of International Conference on Uncertainty Reasoning and Knowledge Engineering, 2(2011), pp.146-149.
[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, vol.1, (2006), pp.297 – 304.
[7]Qian Y.H. and 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. and Liang J.Y. and Dang C.Y.: Incomplete Multi-granulation Rough set, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, Vol.40, No.2, March 2010, pp.420 – 431.
[9]Qian Y.H. and Liang J.Y. and Dang C.Y.: Pessimistic rough decision, proceedings of RST 2010, Zhoushan, China, (2010), pp. 440-449.
[10]Qian Y.H., and 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), (Switzerland),vol.1, no.4, (2010),pp.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, Vol.2, no.3, (2011), pp.536-543.
[14]Tripathy, B.K., and Nagaraju M.: Topological properties of Incomplete Multi-granulation Based on Rough Fuzzy Sets, International Conference, ObCom2011.
[15]Tripathy B.K., and Nagaraju M.: On Some Topological Properties of Pessimistic Multi-granular Rough Sets, International Journal Intelligent Systems and Applications, Vol.4, no.8, (2012), pp.10-17.
[16]Tripathy, B.K. and Raghavan, R.: On Some Comparison properties of rough set based multi-granulations and types of multi-granular approximations of classifications, International Journal of Intelligent Systems and Applications, vol.6, (2013), pp.70-77
[17]Tripathy, B. K. and Raghavan, R.: Some Algebraic properties of Multi-granulations and an Analysis of multi-granular approximations of classifications, I.J. Information Technology and Computer Science, vol.7, (2013),pp. 63-70.
[18]Tripathy,B.K. and Mitra, A.: On Approximate Equivalences of Multi-granular Rough Sets and Approximate Reasoning, I.J. Information Technology and Computer Science,10(5), (2013), pp.103-113.
[19]Tripathy, B. K: Multi granular computing through rough sets, (Ed(s): B.K.Tripathy and D.P.Acharjya), Advances in Secure Computing, Internet Services and Applications – Advances in Information Security, Privacy and Ethics (AISPE) Book Series, IGI Publications, (2014), pp.1-34
[20]Tripathy, B.K., Rawat, R., Divya Rani, V. and Parida, S.C.: Approximate Reasoning through Multi-granular Approximate Rough Equalities, IJISA, vol.6, no.8, (2014), pp. 69-76.
[21]Yao Y.Y.: Perspectives of Granular Computing, Proceedings of 2005 IEEE International Conference on Granular Computing, I (2005), 85-90.
[22]Yao Y.Y., Yao B.: Covering based rough set approximations, Information Sciences 200 (2012), 91-107.
[23]Zakowski W.: Approximations in the space (U II), Demonstration Mathematics 16 (1983), 761-769.
[24]Zadeh, L.A.: Fuzzy sets and informational granularity, In: Gupta, M. M., R.K.Ragade and R.R.Yager, eds., Advances in Fuzzy Set Theory and Applications, North-Holland, New York, (1979), pp.3-18.
[25]Zadeh, L.A.: Some reflections on soft computing, granular computing and their role in the conception, design and utilization of information/intelligent systems, Soft computing, vol.2, Springer Verlag, (1998), pp. 23 – 25.