On (weakly) local approximation spaces of information systems

• Autorzy: Kou H. , Luo M.
• Języki publikacji: EN

Abstrakty

EN

A dependence space is an ordered pair consisting of a nonempty finite set and a congruence on its boolean lattice, and is viewed as a general model to deal with the indiscernibility-type incompleteness of information in rough set analysis. In this paper we consider the question when a dependence space can be locally approximated by a approximation space. We introduce a concept of (weakly) local approximation spaces and establish several important relationships among equivalences, reducts, and sub-reducts with respect to (weakly) local approximation spaces. It is shown that a dependence space is a local approximation space if and only if it is locally reducible if and only if the closure lattice generated by the dependence space is an atomic lattice. This result also gives a partial solution to an open problem posed by M. Novotny.

Słowa kluczowe

EN

dependence space; congruence; approximation space; (weakly) local approximation space; locally reducible dependence space

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2003
• Tom: Vol. 58, nr 2
• Strony: 139--150
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Kou H.

• Department of Mathematics, Sichuan University, Chengdu 610064, P.R.China

autor

Luo M.

• Department of Mathematics, Sichuan University, Chengdu 610064, P.R.China

Bibliografia

• [1] Novotný, J., Novotný, M.: Notes on the algebraic approach to dependence in information systems, Fundamenta Informaticae, 16, 1992, 263-273.
• [2] Novotný, J., Novotný. M.: On dependence in Wille’s contexts, Fundamenta Informaticae, 19, 1993, 343-353.
• [3] Novotný, M.: On sequents defined by means of information systems, Fundamenta Informaticae, 4, 1981, 1041-1048.
• [4] Novotný, M.: Remarks on sequents defined by means of information systems, Fundamenta Informaticae, 6, 1983, 71-79.
• [5] Novotný, M.: Dependence spaces of information systems, Incomplete Information: Rough Set Analysis (E. Orłowska, Ed.), Physica-Verlag, Heidelberg-New York, 1998, 193-246.
• [6] Novotný, M., Pawlak, Z.: On a representation of rough sets by means of information systems, Fundamenta Informaticae, 6, 1983, 289-296.
• [7] Novotný, M., Pawlak, Z.: On rough equalities, Bulletin Polish Academy, Sci. Math., 33, 1985, 99-104.
• [8] Novotný, M., Pawlak, Z.: Independence of attributes, Bulletin Polish Academy, Sci. Math., 36, 1988, 459-465.
• [9] Novotný, M., Pawlak, Z.: Algebraic theory of independence in information systems, Fundamenta Informaticae, 14, 1991, 454-476.
• [10] Orlowska, E.: Logic approach to information systems, Fundamenta Informaticae, 3-4, 1985, 359-378.
• [11] Pawlak, Z.: Rough Sets, Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, 1991.
• [12] Polkowski, L., Tsumoto, S., Lin, T.Y. Eds.: Rough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems, Physica-Verlog, Heidelberg, 2000.
• [13] Quafafou,M.: α-RST: a generalization of rough set theory, Information Science, 124, 2000, 301-316.
• [14] Rauszer, C.M.: Reducts in information systems, Fundamenta Informaticae, 15, 1991, 1-12.
• [15] Skowron, A., Stepaniuk, J.: Intelligent systems based on rough set approach, Foundations of Computing and Decision Sciences, 18: 3-4, 1993, 343-360.