Rough Set Algebras as Description Domains

• Autorzy: Cirulis J.
• Języki publikacji: EN

Abstrakty

EN

Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓α is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.

Słowa kluczowe

EN

description domain; double Stone algebra; inversion; knowledge ordering; rough sets; semi-Boolean domain

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2009
• Tom: Vol. 90, nr 1-2
• Strony: 27--41
• Opis fizyczny: bibliogr. 21 poz.

Twórcy

autor

Cirulis J.

• Department of Computing University of Latvia 19 Raina b., Riga LV-1586, Latvia,

Bibliografia

• [1] Abbott, J.C.: Semi-boolean algebra, Matematični Vesnik, 4(19), 1967, 177-198.
• [2] Abramski, S, Jung, A.: Domain theory, in: Handbook of Logic in Computer Science (S. Abramsky, D.M. Gabbay, T.S.E. Mailbaum, Eds.), vol. 3, Clarendon Press, Oxford, 1994, 1-168.
• [3] Chen, J., Chen, K., Li, W.: Rough sets as BCK-algebras, Far East J. Math. Sci., 5, 2002, 103-111.
• [4] C¯ırulis, J.: Subtractive nearsemilattices, Proc. Latvian Acad. Sci., Sect. B, 52, 1998, 228-233.
• [5] Cırulis, J.: An algebraic approach to belief representation, Proc. Mathenatical Foundations of Computer Science (M. Kutyłowski, L. Pacholski, T. Wierzbicki, Eds.), LNCS 1672, Springer-Verlag, Berlin, 1999, 299-309.
• [6] Cırulis, J.: Rough set systems as semiboolean algebras with inversion, Abstr. Workshop on General Algebra (AAA74), Tampere, Finland, June 7-10, 2007, available at http://atlas-conferences.com/cgi-bin/abstract/catx-01
• [7] Comer, S.D.: On connections between information systems, rough sets and algebraic logic, in: Algebraic Methods in Logic and in Computer Science. Papers of the XXXVIII semester on algebraic methods in logic and their computer science applications held in Warsaw (Poland) between September 15 and December 15, 1991 (C. Rauszer, Ed.), Warszaw, Banach Center Publications 28, Polish Acad. Sci., Warszawa, 1993, 117-124.
• [8] Düntch, I, Gediga, G.: Logical and algebraical techniques for rough set data analysis, in: Rough set methods and applications (Polkowski et al., Eds.), Physics-Verlag, Heidelberg, 2001, 521-544.
• [9] Gehrke, M., Walker, E.: On the structure of rough sets, Bulletin of Polish Acad. Sci., ser. math., 40, 1992, 235-245.
• [10] Guzmán, F.: The poset structure of positive implicative BCK-algebras, Algebra Universalis, 32, 1994, 398-406.
• [11] Iwiński, T.B.: Algebraic approach to rough sets, Bulletin of Polish Acad. Sci., ser. math., 35, 1987, 673-682.
• [12] Marek, V.W, Truszczyński, M.: Contributions to the theory of rough sets, Fundamenta Informaticae, 39, 1999, 389-333.
• [13] Marek, V.W, Truszczyński, M.: Rough Sets and Approximation Schemes, in: Rough Sets and Intelligent Systems Paradigms, LNCS 4585, 2007, 22-28.
• [14] Meinke, K., Tucker, J.V., Universal algebra, in: Handbook of Logic in Computer Science (S. Abramsky, D.M. Gabbay, T.S.E. Mailbaum, Eds.), vol. 1, Clarendon Press, Oxford, 1992, 189-411.
• [15] Mousavi, A., Jabedar-Maralani, P.: Double-faced rough sets and rough communication, Information Sciences, 148, 2002, 41-53.
• [16] Ohori, A.: Semantics of types for database objects, Theoretical Computer Science, 76, 1990, 53-91.
• [17] Pagliani, P.: Rough sets theory and logic-algebraic structures, in: Incomplete information. Rough set analysis (E. Orłowska, Ed.), Studies in Fuzziness and Soft Computing, vol. 13, Physica-Verlag, Heidelberg, 1997, 109-190.
• [18] Polkowski, L.: Rough sets. Mathematical Foundations, Physica-Verlag, Heidelberg, 2002.
• [19] Pomykała, J., Pomykała, J.A.: The Stone algebra of rough sets, Bulletin of Polish Acad. Sci., ser. math., 36, 1988, 495-508.
• [20] Varlet, J.C.: A regular variety of type h2, 2, 1, 1, 0, 0i, Algebra Univeralis, 2, 1972, 218-223.
• [21] Wolski, M.: Complete orders, categories and lattices of approximations, Fundamenta Informaticae, 72, 2006, 421-435.