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Characterizing Rough Algebras

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Języki publikacji
EN
Abstrakty
EN
In this paper, a characterization for the class of all rough algebras from the class of all Q-rough algebras is obtained.
Wydawca
Rocznik
Strony
167--183
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
  • Department of Mathematics, Alliance College of Engineering and Design, Alliance University, Bengaluru, Karnataka, India
Bibliografia
  • [1] Banerjee M, and Chakraborty MK. Rough algebra, Bull. Polish Acad. Sc. (Math.), 1993;41(4):293–297.
  • [2] Banerjee M, and Chakraborty MK. Rough sets through algebraic logic, Fund. Inform. 1996;28(3-4):211–221. URL http://dl.acm.org/citation.cfm?id=246662.246665.
  • [3] Banerjee M, and Chakraborty MK. 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, pp. 157–185. doi:10.1007/978-3-642-18859-6_7.
  • [4] Cattaneo G, Ciucci D. Algebraic structures for rough sets, Transactions of Rough Sets II (2004), pp.208–252. doi:10.1007/978-3-540-27778-1_12.
  • [5] 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, Springer-Verlag, Heidelberg 2008, pp. 363–370. doi:10.1007/978-3-540-79721-0_51.
  • [6] Comer SD. On connections between Information systems, rough sets and algebraic logic, In: Algebraic methods in logic and in computer science, Banach Center Publications, 1993;28(1):117–124.
  • [7] Comer SD. Perfect extensions of regular double Stone algebras, Algebra Universalis, 1995;34:96–109. doi:10.1007/BF01200492.
  • [8] Davey B, and Priestley HA. Introduction to lattices and order, Second Edition, Cambridge University Press, Cambridge 2002. ISBN-13:9780521784511, 10:0521784514.
  • [9] Grätzer G. General lattice theory, Second edition, Birkhauser-Verlag, Boston, 1998. ISBN:3764369965, 9783764369965.
  • [10] Iwiński TB. Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math., 1987;35:673–683.
  • [11] Järvinen J. On the structure of rough approximations, Fund. Inform., 2002;53:135–153. doi:10.1007/3-540-45813-1_15.
  • [12] Järvinen J. 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), LNAI3066, Springer-Verlag, Heidelberg, 2004, pp. 49–58. doi:10.1007/978-3-540-25929-9_5.
  • [13] Järvinen J, Radeleczki S, and Veres L. Rough sets determined by quasiorders, Order, 2009;26(4):337–355. doi:10.1007/s11083-009-9130-z.
  • [14] Järvinen J, and Radeleczki S. Representation of Nelson algebras by rough sets determined by quasiorders, Algebra Unversalis, 2011;66(1-2):163–179. doi:10.1007/s00012-011-0149-9.
  • [15] Järvinen J, Radeleczki S. Rough sets determined by tolerances, International Journal of Approximate Reasoning, 2014;55(6):1419–1438. doi:10.1016/j.ijar.2013.12.005.
  • [16] Nagarajan EKR, and Umadevi D. A Method of Representing Rough sets system determined by Quasiorder, Order, 2013;30:313–337. doi:10.1007/s11083-011-9245-x.
  • [17] Nagarajan EKR, and Umadevi D. Algebra of Rough Sets based on Quasi Order, Fundamenta Informaticae, 2013;126(1-3):83–101. doi:10.3233/FI-2013-872 .
  • [18] Orłowska E, and Pawlak Z. Representation of non-deterministic information, Theoret. Comput. Sci., 1984;29(1-2):27–39. URL http://dx.doi.org/10.1016/0304-3975(84)90010-0.
  • [19] Orłowska E. Information algebra, In: V.S. Algar and M. Nivat (Eds.), Proc. Algebraic Methodology and Software Technology, LNCS936, Springer-Verlag, Heidelberg, 1995, pp. 50–65.
  • [20] Orłowska E. Introduction: what you always wanted to know about rough sets, In: E. Orłowska (Ed.), Incomplete Information : Rough Set Analysis, Physica-Verlag, Heidelberg, 1998, pp. 1–20. doi:10.1007/978-3-7908-1888-8_1.
  • [21] Pagliani P. Rough Sets and Nelson Algebras, Fund. Inform., 1996;27:205–219. URL http://dl.acm.org/citation.cfm?id=2379560.2379568.
  • [22] Pagliani P, and Chakraborty MK. A geometry of approximation rough set theory: Logic, algebra and topology of conceptual patterns, Springer, 2008. ISBN:1402086210, 9781402086212.
  • [23] Pawlak Z. Rough sets, Int. J. Comp. Inform. Sci., 1982;11(5):341–356. doi:10.1007/BF01001956.
  • [24] Pomykała J, and Pomykała JA. The Stone algebra of rough sets, Bull. Polish Acad. Sci. Math., 1988; 36(7):495–508.
  • [25] Slowinski R, and Vanderpooten D. A generalized definition of rough approximations based on similarity, IEEE Transactions on Knowledge and Data Engineering, 2000;12(2):331–336. doi:10.1109/69.842271.
  • [26] Umadevi D. A Study on the Ordered Structure of Rough Sets, Ph.D. thesis, Madurai Kamaraj University, Tamil Nadu, India (2012).
  • [27] Yao YY. On generalizing Pawlak approximation operators, In: L. Polkowski and A. Skowron (Eds.), Proc. First International Conference on Rough Sets and Current Trends in Computing (RSCTC’98), LNAI1424, Springer-Verlag, Heidelberg, 1998, pp. 298–307. doi:10.1007/3-540-69115-4_41.
  • [28] Zhu W. Generalized rough sets based on relations, Inform. Sci., 2007;177(22):4997–5011. URL http://dx.doi.org/10.1016/j.ins.2007.05.037.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cec3e6a5-fd93-47ae-8caa-2b06e905714b
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