On Multigranular Approximate Rough Equivalence of Sets and Approximate Reasoning

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 32)

Abstract

As the notion of equality in mathematics is too stringent and less applicable in real life situations, Novotny and Pawlak introduced approximate equalities through rough sets. Three more types of such equalities were introduced by Tripathy et al. as further generalisations of these equalities. As rough set introduced by Pawlak is unigranular from the granular computing point of view, two types of multigranulations rough sets called the optimistic and the pessimistic multigranular rough sets have been introduced. Three of the above approximate equalities were extended to the multigranular context by Tripathy et al. recently. In this paper, we extend the last but the most general of these approximate equalities to the multigranular context. We establish several direct and replacement properties of this type of approximate equalities. Also, we illustrate the properties as well as provide counter examples by taking a real life example.

Keywords

Rough sets Approximate equalities Approximate equivalence Optimistic multigranulation Pessimistic multigranulation Replacement properties 

References

  1. 1.
    Novotny, M., Pawlak, Z.: Characterization of rough top equalities and rough bottom equalities. Bull. Polish Acad. Sci. Math. 33, 91–97 (1985)MathSciNetMATHGoogle Scholar
  2. 2.
    Novotny, M., Pawlak, Z.: On rough equalities. Bull. Polish Acad. Sci. Math. 33, 99–103 (1985)MathSciNetMATHGoogle Scholar
  3. 3.
    Novotny, M., Pawlak, Z.: Black box analysis and rough top equality. Bull. Polish Acad. Sci. Math. 33, 105–113 (1985)MathSciNetMATHGoogle Scholar
  4. 4.
    Tripathy, B.K.: On approximation of classifications, rough equalities and rough equivalences. In: Studies in computational intelligence. Rough set theory: a true landmark in data analysis, vol. 174, pp. 85–136. Springer, Berlin (2009)Google Scholar
  5. 5.
    Tripathy, B.K. and Mitra, A.: On the approximate equalities of multigranular rough sets and approximate reasoning. In: Proceedings of 4th IEEE International Conference on Computing, Communication and Networking Technologies (ICCCNT 2013), 4–6 July 2013Google Scholar
  6. 6.
    Tripathy, B.K.: An analysis of approximate equalities based on rough set theory. Int. J. Adv. Sci. Technol. 31, 23–36 (2011)MathSciNetGoogle Scholar
  7. 7.
    Pawlak, Z.: Rough sets, Int. J. Inf. Comput. Sci. 341–346 (1982)Google Scholar
  8. 8.
    Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)MATHGoogle Scholar
  9. 9.
    Qian, Y.H and Liang, J.Y.: Rough set method based on multi-granulations. In: Proceedings of the 5th IEEE Conference on Cognitive Informatics, vol. 1, pp. 297–303 (2006)Google Scholar
  10. 10.
    Qian, Y.H., Liang, J.Y., Dang, C.Y.: Pessimistic rough decision. In: Proceedings of RST 2010, pp. 440–449, Zhoushan, China (2010)Google Scholar
  11. 11.
    Tripathy, B.K., Mitra, A.: On approximate equivalences of multigranular rough sets and approximate reasoning. Int. J. Inf. Technol. Comput. Sci. 10, 103–113 (2013)Google Scholar
  12. 12.
    Tripathy, B.K., Rawat, R., Divya, V Parida, S.Ch.: Approximate reasoning through multigranular approximate rough equalities. Int. J. Intell. Syst. Appl. 6, 69–76 (2014)Google Scholar
  13. 13.
    Tripathy, B.K., Nagaraju, M.: A comparative analysis of multigranular approaches and on topological properties of incomplete pessimistic multigranular rough fuzzy sets. Int. Intell. Syst. Appl. 11, 99–109 (2012)Google Scholar
  14. 14.
    Tripathy, B.K., Raghavan, R.: Some algebraic properties of multigranulations and an analysis of multigranular approximations of classifications. Int. J. Inf. Technol. Comput. Sci. 7, 63–70 (2013)Google Scholar
  15. 15.
    Tripathy, B.K., Raghavan, R.: On some comparison properties of rough sets based on multigranulations and types of multigranular approximations of classifications. Int. J. Intell. Syst. Appl. 06, 70–77 (2013)Google Scholar
  16. 16.
    Tripathy, B.K., Mitra, A., Ojha, J.: On Rough Equalities and Rough Equivalences of Sets, SCTC 2008-Akron, U.S.A., LNAI, vol. 5306, pp. 92–102. Springer, Berlin (2008)Google Scholar
  17. 17.
    Tripathy, B.K., Mitra, A., Ojha, J.: Rough equivalence and algebraic properties of rough sets. Int. J. Artif. Intell. Soft Comput. 1(2/3/4), 271–289 (2009)CrossRefGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • B. K. Tripathy
    • 1
  • Prateek Saraf
    • 1
  • S. Ch. Parida
    • 2
  1. 1.School of Computer Science and EngineeringVIT UniversityVelloreIndia
  2. 2.Department of MathematicsK.B.V. MahavidyalayaGanjamIndia

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