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International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.4, No.11, Oct. 2012

A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets

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Author(s)

B.K.Tripathy, M. Nagaraju

Index Terms

Rough Sets;Rough Fuzzy Sets;Tolerance Relations;Pessimistic Multi Granular Rough Fuzzy Sets

Abstract

Rough sets, introduced by Pawlak as a model to capture impreciseness in data have been a very useful tool in several applications. These basic rough sets are defined by taking equivalence relations over a universe. In order to enhance the modeling powers of rough sets, several extensions to the basic definition has been introduced over the past few years. Extending the single granular structure of research in classical rough set theory two notions of Multigranular approaches; Optimistic Multigranulation and Pessimistic Multigranulation have been introduced so far. Topological properties of rough sets along with accuracy measures are two important features of rough sets from the application point of view. Topological properties of Optimistic Multigranular rough sets Optimistic Multigranular rough fuzzy sets and Pessimistic Multigranular rough sets have been studied. Incomplete information systems take care of missing values for items in data tables. Optimistic and pessimistic MGRS have also been extended to such type of incomplete information systems. In this paper we provide a comparative study of the two types of Multigranular approaches along with other related notions. Also, we extend the study to topological properties of incomplete pessimistic MGRFS. These results hold both for complete and incomplete information systems.

Cite This Paper

B.K.Tripathy, M. Nagaraju,"A Comparative Analysis of Multigranular Approaches and on Topoligical Properties of Incomplete Pessimistic Multigranular Rough Fuzzy Sets", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.11, pp.99-109, 2012. DOI: 10.5815/ijisa.2012.11.12

Reference

[1]Kryszkiewicz, K.: Rough set approach to incomplete information systems, Information Sciences, vol.112, (1998), pp.39 – 49.

[2]Liang, J.Y and Shi, Z.Z.: The information entropy, rough entropy and knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol.12(1),(2001),pp. 37 – 46.

[3]Liang, J.Y, Shi, Z.Z., Li, D. Y. and Wierman, M. J.: The information entropy, rough entropy and knowledge granulation in incomplete information system, International Journal of general systems, vol.35(6), (2006),pp.641 – 654.

[4]Liang, J.Y and Li, D. Y.: Uncertainty and Knowledge acquisition in Information Systems, Science Press, Beijing, China, (2005).

[5]Pawlak, Z., Rough sets, Int. jour. of Computer and Information Sciences,11, (1982), pp.341-356.

[6]Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data, Kluwer academic publishers (London), (1991).

[7]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.

[8]Qian, Y.H, Liang, J.Y. and Dang, C.Y.: MGRS in Incomplete Information Systems, IEEE Conference on Granular Computing,(2007),pp.163 -168.

[9]Qian, Y.H, Liang, J.Y. and Dang, C.Y.: Incomplete Multigranulation Rough set, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, Vol.40, No.2, March 2010, pp.420 – 431. 

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

[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.: Rough Sets on Fuzzy Approximation Spaces and Intuitionistic Fuzzy Approximation Spaces, Studies in Computational Intelligence, vol.174, Rough Set Theory: A True Landmark in Data Analysis, Springer Verlag, (2009), pp.03 - 44.

[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.

[14]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.

[15]Tripathy, B. K. and Nagaraju, M. : Topological Properties of Incomplete Multigranulation Based on Rough Fuzzy Sets, Global Trends in Information Systems and Software Applications, Springer Verlag, ObCom2011, Part II S CCIS 270, (2012), pp.92-102

[16]Tripathy, B.K., Panda, G.K. and Mitra, A.: Incomplete Multigranulation Based on Rough Intuitionistic Fuzzy Sets, In: Universal Journal of Applied Computer Science and Technology (UNIASCIT), Vol.2 (1), (Jan 2012), pp.118-124.

[17]Tripathy, B.K., Panda, G.K. and Mitra, A.: Some Concepts of Incomplete Multigranulation based on Rough Intuitionistic Fuzzy Sets, In: proceedings of the 2nd International Conference on Computer Science, Engineering and Applications (ICCSEA, 2012), New Delhi, Advances in Intelligent and Soft Computing Book Series, Springer, (May 2012), pp.683-694.

[18]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.

[19]Wu, M. and Kou, G.: Fuzzy Rough Set Model Based on Multi-Granulations, In: proceedings of the 2010 2nd International Conference on Computer Engineering and Technology, (2010), pp.V2-71-75.