Abstract
Generalization of rough set model is one important aspect of rough set theory study, and it is very helpful to consummate rough set theory. Developing rough set theory using algebra systems has been paid great attention, and some researchers had reported significant developments. But the base algebra systems, on which approximation operators are defined, are confined to special Boolean algebras, including set algebra and atomic Boolean lattice. This paper introduces molecular lattices as base algebra system. Based on molecules of a molecular lattice, a mapping called meta-mapping is defined. Consequently, the approximation operators, which are more general and abstract compared with approximation operators reported in some papers, are defined based on the frame of molecular lattices. The properties of the approximations are also studied.
Preview
Unable to display preview. Download preview PDF.
References
Pawlak, Z.: Rough Sets–Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Lin, T.Y., Liu, Q.: Rough approximate operators: Axiomatic rough set theory. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 256–260. Springer, London (1994)
Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Information Sciences 109(1-4), 21–47 (1998)
Jarvinen, J.: On the structure of rough approximations. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 123–230. Springer, Heidelberg (2002)
Wang, G.J.: On construction of Fuzzy lattice. ACTA Mathematical SINICA(in Chinese) 29(4), 539–543 (1986)
Wang, G.J.: Theory of Topological Molecular Lattices. Fuzzy Sets and Systems 47, 351–376 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dai, JH. (2004). Structure of Rough Approximations Based on Molecular Lattices. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-25929-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22117-3
Online ISBN: 978-3-540-25929-9
eBook Packages: Springer Book Archive