PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Rough Relation Algebras Revisited

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Rough relation algebras arise from Pawlak's information systems by considering as object ordered pairs on a fixed set X. Thus, the subsets to be approximated are binary relations over X, and hence, we have at our disposal not only the set theoretic operations, but also the relational operators ;, ˇ , and the identity relation 1˘. In the present paper, which is a continuation of [6], we further investigate the structure of abstract rough relation algebras.
Słowa kluczowe
Wydawca
Rocznik
Strony
283--300
Opis fizyczny
bibliogr. 20 poz.
Twórcy
autor
autor
  • Department of Computer Science, Brock University St.Catharines, Ontario, Canada, L2S 3AI, mwinter@brocku.ca
Bibliografia
  • [1] Balbes, R. and Dwinger, P. (1974). Distributive Lattices. University of Missouri Press, Columbia.
  • [2] Chin, L. and Tarski, A. (1951). Distributive and modular laws in the arithmetic of relation algebras. University of California Publications in Mathematics, 1:341-384.
  • [3] Comer, S. (1993). On connections between information systems, rough sets, and algebraic logic. In Rauszer, C., editor, Algebraic Methods in Logic and Computer Science, volume 28 of Banach Center Publications, pages 117-124. Polish Academy of Science, Warszawa.
  • [4] Düntsch, I. (1987). Injective and projective regular double Stone algebras. Algebra Universalis, 24:197-203.
  • [5] Düntsch, I. (1991). Small integral relation algebras generated by a partial order. Period. Math. Hungar., 23:129-138.
  • [6] Düntsch, I. (1994). Rough relation algebras. Fundamenta Informaticae, 21:321-331.
  • [7] Düntsch, I. and Gediga, G. (1997). Relation restricted prediction analysis. In Sydow, A., editor, Proc. 15th IMACS World Congress, Berlin, volume 4, pages 619-624, Berlin. Wissenschaft und Technik Verlag.
  • [8] Düntsch, I. and Gediga, G. (2000). Rough set data analysis: A road to non-invasive knowledge discovery. Methodos Publishers (UK), Bangor.
  • [9] Gediga, G. and Düntsch, I. (2002). Approximation quality for sorting rules. Computational Statistics and Data Analysis, 40:499-526.
  • [10] Hirsch, R. and Hodkinson, I. (2002). Relation algebras by games, volume 147 of Studies in Logic and the Foundations of Mathematics. Elsevier.
  • [11] Iwinski, T. B. (1987). Algebraic approach to rough sets. Bull. Polish Acad. Sci. Math., 35:673-683.
  • [12] Katriňak, T. (1974). Injective double Stone algebras. Algebra Universalis, 4:259-267.
  • [13] Konrad, E., Orłowska, E., and Pawlak, Z. (1981). Knowledge representation systems - Definability of informations. ICS Research Report 433, Polish Academy of Sciences.
  • [14] Lyndon, R. C. (1950). The representation of relational algebras. Annals of Mathematics (2), 51:707-729.
  • [15] McKenzie, R. (1970). Representations of integral relation algebras. Michigan Math. J., 17:279-287.
  • [16] Orłowska, E., editor (1998). Incomplete Information - Rough Set Analysis. Physica - Verlag, Heidelberg.
  • [17] Pawlak, Z. (1982). Rough sets. Internat. J. Comput. Inform. Sci., 11:341-356.
  • [18] Pomykala, J. and Pomykala, J. A. (1988). The Stone algebra of rough sets. Bull. Polish Acad. Sci. Math., 36:495-508.
  • [19] Tarski, A. (1941). On the calculus of relations. J. Symbolic Logic, 6:73-89.
  • [20] Varlet, J. C. (1972). A regular variety of type h2,2,1,1,0,0i. Algebra Universalis, 2:218-223.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0015-0060
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.