Czasopismo
2014
|
Vol. 131, nr 2
|
205--215
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
The theory of rough sets provides a widely used modern tool, and in particular, rough sets induced by quasiorders are in the focus of the current interest, because they are strongly interrelated with the applications of preference relations and intuitionistic logic. In this paper, a structural characterisation of rough sets induced by quasiorders is given. These rough sets form Nelson algebras defined on algebraic lattices. We prove that any Nelson algebra can be represented as a subalgebra of an algebra defined on rough sets induced by a suitable quasiorder. We also show that Monteiro spaces, rough sets induced by quasiorders and Nelson algebras defined on T0-spaces that are Alexandrov topologies can be considered as equivalent structures, because they determine each other up to isomorphism.
Czasopismo
Rocznik
Tom
Strony
205--215
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Sirkankuja 1, 20810 Turku, Finland, Jouni.Kalervo.Jarvinen@gmail.com
autor
- Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary, matradi@uni-miskolc.hu
Bibliografia
- [1] Alexandroff, P.: Diskrete R¨aume, Matematiˇceskij Sbornik, 2, 1937, 501–518.
- [2] Birkhoff, G.: Rings of sets, Duke Mathematical Journal, 3, 1937, 443–454.
- [3] Cignoli, R.: The class of Kleene algebras satisfying an interpolation property and Nelson algebras, Algebra Universalis, 23, 1986, 262–292.
- [4] Comer, S. D.: On connections between information systems, rough sets, and algebraic logic, in: Algebraic Methods in Logic and Computer Science, number 28 in Banach Center Publications, 1993, 117–124.
- [5] Demri, S. P., Orlowska, E. S.: Incomplete Information: Structure, Inference, Complexity, Springer, 2002.
- [6] Gehrke,M.,Walker, E.: On the structure of rough sets, Bulletin of Polish Academy of Sciences.Mathematics, 40, 1992, 235–245.
- [7] Hassanien, A., Suraj, Z., Slezak, D., Lingras, P., Eds.: Rough Computing: Theories, Technologies and Applications, IGI Global, 2007.
- [8] Iturrioz, L.: Rough sets and three-valued structures, in: Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa (E. Orłowska, Ed.), Physica-Verlag, 1999, 596–603.
- [9] Iwiński, T. B.: Algebraic approach to rough sets, Bulletin of Polish Academy of Sciences. Mathematics, 35, 1987, 673–683.
- [10] Järvinen, J.: Lattice theory for rough sets, Transactions on Rough Sets, VI, 2007, 400–498.
- [11] Järvinen, J., Pagliani, P., Radeleczki, S.: Information completeness in Nelson algebras of rough sets induced by quasiorders, Studia Logica, 101, 2013, 1073–1092.
- [12] Järvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasiorders, Algebra Universalis, 66, 2011, 163–179.
- [13] Järvinen, J., Radeleczki, S., Veres, L.: Rough sets determined by quasiorders, Order, 26, 2009, 337–355.
- [14] Markov, A. A.: Constructive logic (in Russian), Uspekhi Matematicheskih Nauk, 5, 1950, 187–188.
- [15] Monteiro, A.: Construction des alg´ebres de Nelson finies, Bulletin de l’Academie Polonaise des Sciences, 11, 1963, 359–362.
- [16] Nagarajan, E., Umadevi, D.: AMethod of representing rough sets system determined by quasi orders, Order, 30, 2013, 313–337.
- [17] Nelson, D.: Constructible falsity, Journal of Symbolic Logic, 14, 1949, 16–26.
- [18] Pagliani, P., Chakraborty, M.: A Geometry of Approximation. Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns, Springer, 2008.
- [19] Pawlak, Z.: Rough sets, International Journal of Computer and Information Sciences, 11, 1982, 341–356.
- [20] Pomykała, J., Pomykała, J. A.: The Stone algebra of rough sets, Bulletin of Polish Academy of Sciences. Mathematics, 36, 1988, 495–512.
- [21] Rasiowa, H.: An Algebraic Approach to Non-Classical Logics, North-Holland, Amsterdam, 1974.
- [22] Vakarelov, D.: Notes on N-lattices and constructive logic with strong negation, Studia Logica, 36, 1977, 109–125.
- [23] Vakarelov, D.: Nelsons negation on the base of weaker versions of intuitionistic negation, Studia Logica, 80, 2005, 393–430.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-7f8f8735-5331-4f87-9c68-158364d316de