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Fundamenta Informaticae

Tytuł artykułu

Double Approximation and Complete Lattices

Autorzy Haruna, T.  Gunji, Y-P. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN We explore lattice theoretic aspects in rough set theory in terms of the duality between algebra and representation. Approximation spaces are dual to complete atomic Boolean algebras in the sense that there is an adjunction between corresponding suitable categories. This is an analogy with the adjunction between the category of topological spaces and the opposite of the category of frames in pointless topology. In this paper we consider a generalization of approximation spaces called double approximation systems. A double approximation system consists of a set and two equivalence relations on it. We construct an adjunction generalizing this concept for approximation spaces. To achieve this goal, we first introduce a natural generalization of complete atomic Boolean algebras called complete prime lattices. Then we select double approximation systems that can be dual to complete prime lattices and prove the adjunction.
Słowa kluczowe
EN rough set theory   approximation spaces   complete lattices   adjunction   equivalence of categories  
Wydawca IOS Press
Czasopismo Fundamenta Informaticae
Rocznik 2011
Tom Vol. 111, nr 1
Strony 1--14
Opis fizyczny Bibliogr. 15 poz.
autor Haruna, T.
autor Gunji, Y-P.
  • Department of Earth and Planetary Sciences, Graduate School of Science, Kobe University,
[1] Davey, B. A., Priestley, H. A.: Introduction to Lattices and Order, 2nd edition. Cambridge Univ. Press, Cambridge, 2002.
[2] Ganter, B., Wille, R.: Formal Concept Analysis, Mathematical Foundations. Springer, Berlin, 1999.
[3] Gediga, G. and Duntsch, I.: Modal-style operators in qualitative data analysis. Proceedings of the 2002 IEEE International Conference on Data Mining, 2002, 155-162.
[4] Gehrke, M. and Walker, E.: On the structure of rough sets. Bull. Pol. Acad. Sci., Math. 40, 1992, 235-245.
[5] Gunji, Y.-P., Haruna, T.: Non-Boolean Lattices Derived on the Basis of Double Indiscernibility. Transactions on Rough Sets XII, 2010, 211-225.
[6] Haruna, T., Gunji, Y.-P.: Double approximation and complete lattices. In: Rough Sets and Knowledge Technology, 4th International Conference, RSKT 2009 (P. Wen et al., Eds.), Gold Coast, Australia, 2009, 52-59.
[7] Iwiński, T. B.: Algebraic approach to rough sets. Bull. Pol. Acad. Sci., Math. 35, 1987, 673-683.
[8] Järvinen, J.: Lattice theory for rough sets. Transactions on Rough Sets VI, 2007, 400-498.
[9] Järvinen, J., Radeleczki, S., Veres, L.: Rough sets determined by quasiorders. Order 26, 2009, 337-355.
[10] Johnstone, P. T.: Stone spaces. Cambridge Univ. Press, Cambridge, 1982.
[11] MacLane, S.: Categories for the Working Mathematician, 2nd edition. Springer-Verlag, New York, 1998.
[12] Pawlak, Z.: Rough sets. Intern. J. Comp. Sci. 11, 1982, 341-356.
[13] Polkowski, L.: Rough Sets, Mathematical Foundations. Physical-Verlag, Heidelberg, 2002.
[14] Pomykała, J., Pomykała, J. A.: The Stone algebra of rough sets. Bull. Pol. Acad. Sci.,Math. 6, 1988, 495-512.
[15] Yao, Y. Y.: Concept lattices in rough set theory. In: Fuzzy Information, Processing NAFIPS '04, vol. 2, 2004, 796-801.
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Identyfikator YADDA bwmeta1.element.baztech-article-BUS8-0020-0086