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Algebra of Rough Sets based on Quasi Order

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Języki publikacji
EN
Abstrakty
EN
In this paper, we give a characterization theorem for rough sets based on quasi order. We obtain an algebra on the rough sets system determined by a quasi order which is the generalization of the algebra of rough sets system determined by an equivalence relation given in [1]. The properties of this algebra are abstracted at various levels and define new class of algebras. Further we give a representation theorem for the new class of algebras.
Wydawca
Rocznik
Strony
83--101
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
  • Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College (Autonomous), Sivakasi - 626 124, Tamil Nadu, India
autor
  • Department of Mathematics, Kamaraj College of Engineering and Technology, Virudhunagar, Tamil Nadu, India
Bibliografia
  • [1]. M. Banerjee and M. K. Chakraborty, Rough sets through algebraic logic, Fund. Inform. 28(3-4) (1996), 211-221
  • [2]. M. Banerjee and M. K. Chakraborty, Algebras from rough sets, In: S. K. Pal, L. Polkowski and A. Skowron (Eds.), Rough-Nero computing techniques for computing with words, Springer-Verlag, Heidelberg, 2004,157 - 185.
  • [3]. G. Cattaneo and D. Ciucci, A Hierarchical Lattice Closure Approach to Abstract Rough Approximation Spaces, In: G. Wang et al (Eds.), Proc. RSKT08, LNAI5009, 2008, 363 - 370.
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  • [7]. T. B. Iwinski, Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math., 35 (1987), 673 - 683.
  • [8]. J. Jarvinen, On the structure of rough approximations, Fund. Inform., 53(2002), 135 - 153.
  • [9]. J. Jarvinen, The ordered set of rough sets, In: S. Tsumoto, R. Slowinski, J. Komorowski, J.W. Grzymala- Busse (Eds.), Proc. Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC2004), LNAI 3066, Springer-Verlag, Heidelberg, 2004,49 - 58.
  • [10]. J. Jarvinen, S. Radeleczki and L. Veres, Rough sets determined by quasiorders, Order, 26(4) (2009), 337 - 355.
  • [11]. J. Jarvinen and S. Radeleczki, Representation of Nelson algebras by rough sets determined by quasiorders, Algebra Unversalis, 66(2011), 163 - 179.
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  • [14]. E.K.R. Nagarajan, D.Umadevi, A Method of Representing Rough Sets System Determined by Quasi Orders, Order, 30(1)(2013), 313-337.
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  • [16]. E. Orlowska, Logic of non-deterministic information, Studia Logica, 44(1) (1985), 91-100.
  • [17]. E. Orlowska, Information algebra, In: V.S. Algar and M. Nivat (Eds.), Proc. Algebraic Methodology and Software Technology, LNCS 936, Springer-Verlag, Heidelberg, 1995, 50 - 65.
  • [18]. P. Pagliani, Rough Sets and Nelson Algebras, Fund. Inform., 27(1996), 205 - 219.
  • [19]. P. Pagliani and M.K. Chakraborty, A geometry of approximation - rough set theory: Logic, algebra and topology of conceptual patterns, Springer, 2008.
  • [20]. Z. Pawlak, Rough sets, Int. J. Comp. Inform. Sci., 11(1982), 341 - 356.
  • [21]. J. Pomykala and J.A. Pomykala, The Stone algebra of rough sets, Bull. Polish Acad. Sci. Math., 36(1988), 495 - 508.
  • [22]. H. Rasiowa, An algebraic approach to Non-classical Logics, North-Holland Publishing Company, 1994.
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  • [27]. Y.Y. Yao, Constructive and algebraic methods of the theory of rough sets, Inform. Sci., 109(1-4) (1998), 21 - 47.
Typ dokumentu
Bibliografia
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