Characterizing Topological Quasi-Boolean algebras from Weakly Topological Quasi-Boolean Algebras
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Abstract
In this paper, we have characterized the variety TQBA (Topological Quasi-Boolean algebra) from the variety WTQBA (Weakly Topological Quasi-Boolean Algebra).
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Umadevi, D.
(2017).
Characterizing Topological Quasi-Boolean algebras from Weakly Topological Quasi-Boolean Algebras.
Acta Mathematica Universitatis Comenianae, 86(1), 1-8.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/96/431
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References
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[2] M. Banerjee and M. K. Chakraborty, Rough sets through algebraic logic, Fund. Inform. 28(3-4) (1996), 211 - 221.
[3] 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.
[4] M. Banerjee and Koushik Pal, The Variety of Topological Quasi-Boolean Algebras, Extended abstract, In proceedings of Logic III - Conference in Memoriam of Mostowski, Rasiowa Rauszer, Warsaw, Poland, 2005.
[5] S. Burris and H.P. Sankappanavar, A course in universal algebra, Springer-Verlag, New York, 1981.
[6] G. Cattaneo and D. Ciucci, Algebraic structures for rough sets, Transactions of Rough Sets II(2004), 208- 252.
[7] G. Cattaneo, D. Ciucci, A Hierarchical Lattice Closure Approach to Abstract Rough Approximation Spaces. In: Wang, G. et al (Eds.), Proc. (RSKT 2008), LNAI 5009, Springer-Verlag, Heidelberg (2008), 363 - 370.
[8] S. D. Comer, On connections between Information systems, rough sets and algebraic logic, In: Algebraic methods in logic and in computer science, Banach Center Publications, 28(1993), 117 - 124.
[9] S. D. Comer, Perfect extensions of regular double Stone algebras, Algebra Universalis, 34 (1995), 96 - 109.
[10] B. Davey and H. A. Priestley, Introduction to lattices and order, Second Edition, Cambridge University Press, Cambridge 2002.
[11] G. Gratzer, General lattice theory, Second edition, Birkhauser-Verlag, Boston, 1998.
[12] T. B. Iwinski, Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math., 35 (1987), 673 - 683.
[13] 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 (RSCTC 2004), LNAI 3066, Springer-Verlag, Heidelberg, 2004, 49 - 58.
[14] J. Jarvinen, S. Radeleczki and L. Veres, Rough sets determined by quasiorders, Order, 26(4) (2009), 337 - 355.
[15] J. Jarvinen and S. Radeleczki, Representation of Nelson algebras by rough sets determined by quasiorders, Algebra Unversalis, 66(2011), 163 - 179.
[16] E.K.R. Nagarajan, D. Umadevi, A Method of Representing Rough Sets System Determined by Quasi Order, Order, vol. 30(1), (2013) 313 - 337.
[17] E.K.R. Nagarajan and D. Umadevi, Algebra of Rough Sets based on Quasi Order, Fundamenta Informaticae, 126(1-3)(2013), 83-101.
[18] P. Pagliani, Rough Sets and Nelson Algebras, Fund. Inform., 27(1996), 205 - 219.
[19] Z. Pawlak, Rough sets, Int. J. Comp. Inform. Sci., 11(1982), 341 - 356.
[20] J. Pomykala and J.A. Pomykala, The Stone algebra of rough sets, Bull. Polish Acad. Sci. Math., 36(1988), 495 - 508.
[21] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland Publishing Company, 1994.
[2] M. Banerjee and M. K. Chakraborty, Rough sets through algebraic logic, Fund. Inform. 28(3-4) (1996), 211 - 221.
[3] 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.
[4] M. Banerjee and Koushik Pal, The Variety of Topological Quasi-Boolean Algebras, Extended abstract, In proceedings of Logic III - Conference in Memoriam of Mostowski, Rasiowa Rauszer, Warsaw, Poland, 2005.
[5] S. Burris and H.P. Sankappanavar, A course in universal algebra, Springer-Verlag, New York, 1981.
[6] G. Cattaneo and D. Ciucci, Algebraic structures for rough sets, Transactions of Rough Sets II(2004), 208- 252.
[7] G. Cattaneo, D. Ciucci, A Hierarchical Lattice Closure Approach to Abstract Rough Approximation Spaces. In: Wang, G. et al (Eds.), Proc. (RSKT 2008), LNAI 5009, Springer-Verlag, Heidelberg (2008), 363 - 370.
[8] S. D. Comer, On connections between Information systems, rough sets and algebraic logic, In: Algebraic methods in logic and in computer science, Banach Center Publications, 28(1993), 117 - 124.
[9] S. D. Comer, Perfect extensions of regular double Stone algebras, Algebra Universalis, 34 (1995), 96 - 109.
[10] B. Davey and H. A. Priestley, Introduction to lattices and order, Second Edition, Cambridge University Press, Cambridge 2002.
[11] G. Gratzer, General lattice theory, Second edition, Birkhauser-Verlag, Boston, 1998.
[12] T. B. Iwinski, Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math., 35 (1987), 673 - 683.
[13] 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 (RSCTC 2004), LNAI 3066, Springer-Verlag, Heidelberg, 2004, 49 - 58.
[14] J. Jarvinen, S. Radeleczki and L. Veres, Rough sets determined by quasiorders, Order, 26(4) (2009), 337 - 355.
[15] J. Jarvinen and S. Radeleczki, Representation of Nelson algebras by rough sets determined by quasiorders, Algebra Unversalis, 66(2011), 163 - 179.
[16] E.K.R. Nagarajan, D. Umadevi, A Method of Representing Rough Sets System Determined by Quasi Order, Order, vol. 30(1), (2013) 313 - 337.
[17] E.K.R. Nagarajan and D. Umadevi, Algebra of Rough Sets based on Quasi Order, Fundamenta Informaticae, 126(1-3)(2013), 83-101.
[18] P. Pagliani, Rough Sets and Nelson Algebras, Fund. Inform., 27(1996), 205 - 219.
[19] Z. Pawlak, Rough sets, Int. J. Comp. Inform. Sci., 11(1982), 341 - 356.
[20] J. Pomykala and J.A. Pomykala, The Stone algebra of rough sets, Bull. Polish Acad. Sci. Math., 36(1988), 495 - 508.
[21] H. Rasiowa, An Algebraic Approach to Non-Classical Logics, North-Holland Publishing Company, 1994.