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Core Rough Algebras and its Connection with Core Regular Double Stone Algebra


Affiliations
1 G V P College of Engineering(A), Madhurawada, Visakhapatnam, Andhra Pradesh, 530048, India
2 University College of Engineering, JNTUK, Kakinada, Andhra Pradesh, 533003, India
     

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In this paper a special sub class of rough set algebra (RSA) is identied and coined as core rough set algebra(CRSA). Further we studied the relationship between CRSA and core regular double Stone algebra (CRDSA) introduced in [10]. In fact, a representation theorem for CRDSA in terms of rough sets is established.

Keywords

Core Regular Double Stone Algebra, Approximation Space, Rough Sets.
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  • A.R.J.Srikanth and R.V.G Ravi Kumar., Centre of Core Regular Double Stone Algebra, European Journal of Pure and Applied Mathematics, 10(4) (2017), 717 – 729.

  • A.R.J.Srikanth and R. V. G. Ravi Kumar., Ideals of Core Regular double Stone algebra, Asian-European J. Math, 11(6) (2018), 1850083-1 - 1850083-14.

  • Balbes R. and Dwinger PH., Distributive lattices, U.Missouri Press (1974).

  • Bonikowski Z., Algebraic Structures of Rough Sets, in Rough Sets, Fuzzy Sets and Knowledge Discovery (W. P.Ziarko, Ed.), Springer-Verlag, London, 242 – 247, 1994.

  • Gr¨atzer.George, Lattice Theory. First concepts and distributive lattices, W. H. Freeman and Co. San Francisco, 1971.

  • G. C. MoislL, Sur les logiques de,Lukasiewicz a un nombre fini de valeurs, Rev. Roumaine Math. Pures Appl, 9 (1964), 905 – 920.

  • I. D¨untsch, Rough Sets and Algebras of Relations, E. Orlowska (Ed.), Incomplete Information: Rough Set Analysis, Physica-Verlag, Heidelberg New York (1998), 95 – 108.

  • J. Pomyka la, J.A. Pomyka la The Stone algebra of rough sets Bull. Polish Acad. Sci. Math, 36 (1988), 495 – 508.

  • M. Banerjee, M.K. Chakraborty, Rough sets through algebraic logic, Fundamenta Informaticae, 28 (1996) 211 -– 221.

  • Ravi Kumar. R.V.G, M.P.K.Kishore and A.R.J.Srikanth, Core Regular double Stone algebra, Journal of Calcutta Mathematical Society, 11 (2015) 1 – 10.

  • S.D.Comer,Perfect extensions of regular double Stone algebras Algebra Universalis, 34 (1995) 96 – 109.

  • S. Comer, On connections between information systems, rough sets, and algebraic logic, Algebraic Methods in Logic and Computer Science, Banach Center Publications 28 (1993) 117 – 124.

  • Varlet,J., A regular variety of type < 2, 2, 1, 1, 0, 0 >, Algebra Universalis, 2 (1972) 218 – 223.

  • Y.Y. Yao, Two views of the theory of rough sets in finite universes, International Journal of Approximate Reasoning, 15 (19962) 291 – 317.

  • Zbingniew Bonikowski., A Certain Conception of the Calculus of Rough Sets, Notre Dame Journal of Formal Logic, 33(3) (1992) 412 – 421.

  • Z. Pawlak, Rough classification, International Journal of Man-Machine Studies, 20 (1984) 469 – 483.

  • Z. Pawlak, Rough sets, International Journal of Computer and Information, 11 (1982) 341 – 356.


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  • Core Rough Algebras and its Connection with Core Regular Double Stone Algebra

Abstract Views: 364  |  PDF Views: 1

Authors

A. R. J. Srikanth
G V P College of Engineering(A), Madhurawada, Visakhapatnam, Andhra Pradesh, 530048, India
R. V. G. Ravi Kumar
G V P College of Engineering(A), Madhurawada, Visakhapatnam, Andhra Pradesh, 530048, India
G. V. S. R. Deekshitulu
University College of Engineering, JNTUK, Kakinada, Andhra Pradesh, 533003, India

Abstract


In this paper a special sub class of rough set algebra (RSA) is identied and coined as core rough set algebra(CRSA). Further we studied the relationship between CRSA and core regular double Stone algebra (CRDSA) introduced in [10]. In fact, a representation theorem for CRDSA in terms of rough sets is established.

Keywords


Core Regular Double Stone Algebra, Approximation Space, Rough Sets.

References





DOI: https://doi.org/10.18311/jims%2F2019%2F23448