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Abstrakty
In this paper, a solution is given to the problem proposed by J¨arvinen in [8]. A smallest completion of the rough sets system determined by an arbitrary binary relation is given. This completion, in the case of a quasi order, coincides with the rough sets system which is a Nelson algebra. Further, the algebraic properties of this completion has been studied.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
413--424
Opis fizyczny
Bibliogr. 19 poz., wykr.
Twórcy
autor
- Department of Mathematics Kamaraj College of Engineering and Technology Virudhunagar - 626 001, Tamil Nadu, India
Bibliografia
- [1] Banaschewski, B., Bruns, G.: Categorical characterization of the MacNeille Completion. Arch. Math., vol. 18, 369-377(1967).
- [2] Banerjee, M., Chakraborty,M.K.: Rough sets through Algebraic Logic. Fund. Inform. 28, 211 - 221(1996).
- [3] Banerjee,M., Chakraborty,M.K.: Algebras from Rough Sets. In: Pal, S.K., Polkowski,L., Skowron, A. (eds.) Rough - Neural Computing, pp.157 - 185. Springer Verlag, Berlin (1998).
- [4] Cattaneo, G., Ciucci, D.: A Hierarchical Lattice Closure Approach to Abstract Rough Approximation Spaces. In: Wang, G. et al (Eds.), Proc. (RSKT 2008), LNAI 5009, pp.363 - 370. Springer-Verlag, Heidelberg (2008).
- [5] Davey, B., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, New Delhi (2009).
- [6] Gehrke, M., Walker, E.: On the structure of rough sets. Bull. Polish Acad. Sci. Math.. 40, 235 - 245(1992).
- [7] Järvinen, J.: Knowledge Representation and Rough Sets. Ph. D. thesis. University of Turku, Finland (2000).
- [8] Järvinen, J.: The Ordered Set of Rough Sets. In: Tsumoto, S., Slowinski, R., Komorowski, J., Grzymala-Busse J.W.,(eds.) Proc. Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC 2004), LNAI 3066, pp.49 - 58. Springer-Verlag, Heidelberg (2004).
- [9] Järvinen, J.: Lattice theory for rough sets. Transactions on Rough Sets VI. 400 - 498 (2007).
- [10] Järvinen, J., Radeleczki, S., Veres, L.: Rough Sets Determined by Quasiorders. Order. 337 - 355 (2009).
- [11] Järvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasiorders. Algebra Universalis. 66 163 - 179 (2011).
- [12] Järvinen, J., Pagliani, P. and Radeleczki, S.: Information completeness in Nelson algebras of rough sets induced by quasiorders. Studia Logica 101, 1073-1092 (2013).
- [13] Kalman, J.: Lattices with Involution. Trans. Amer. Math. Soc.. 87, 485 - 491 (1958).
- [14] Nagarajan, E.K.R., Umadevi, D.: A Method of Representing Rough Sets System determined by Quasi Order. Order. vol.30(1), 313-337(2013).
- [15] Nagarajan, E.K.R., Umadevi, D.: Algebra of Rough Sets based on Quasi Order. Fund. Inform. 126(1-3), 83-101(2013).
- [16] Orlowska, E.: Introduction: What you always wanted to know about rough sets. In: Orlowska, E (Ed.). Incomplete Information. Rough Set Analysis. pp. 1 - 20. Physica-Verlag, Heidelberg (1998).
- [17] Pagliani, P.: Rough Set Systems and logic-algebraic structures, in : Incomplete Information: Rough Set Analysis (Ewa Orlowska, ed.), Physica-Verlag. 109-190(1998).
- [18] Pawlak, Z.: Rough Sets. Int. J. Comp. Inform. Sci. 5, 341 - 356 (1982).
- [19] Yao, Y.Y.: On generalizing Pawlak approximation operators. In First International Conference of RSCTC’98, LNAI 1424, pp.298 - 307. Springer-Verlag, Heidelberg (1998).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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