Special Lattice of Rough Algebras

Yonghong Liu
DOI: 10.4236/am.2011.212215                

Abstract

This paper deals with the study of the special lattices of rough algebras. We discussed the basic properties such as the rough distributive lattice; the rough modular lattice and the rough semi-modular lattice etc., some results of lattice are generalized in this paper. The modular lattice of rough algebraic structure can provide academic base and proofs to analyze the coverage question and the reduction question in information system.

Keywords

Lattice, Rough Distributive Lattice, Rough Modular Lattice, Rough Semi-Modular Lattice

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Z. Pawlak, “Rough Sets,” International Journal of Computer and Information Sciences, Vol. 11, No. 5, 1982, pp. 341-356. doi:10.1007/BF01001956
[2]	M. Novotny and Z. Pawlak, “Characterization of Rough Top Equalities and Rough Bottom Equalities,” Bulletin of the Polish Academy of Sciences. Mathematics, Vol. 33, No. 1-2, 1985, pp. 91-97.
[3]	D. Dubois and H. Prade, “Rough Fuzzy Sets and Fuzzy Rough Sets,” International Journal of General Systems, Vol. 17, No. 2-3, 1990, pp. 191-209. doi:10.1080/03081079008935107
[4]	Y. H. Liu, “Lattice to Characterizing Rough Set,” Pattern Recognition and Artificial Intelligence, Vol. 16, No. 2, 2003, pp. 174-177.
[5]	W. Q. Liu and C. X. Wu, “The Approximation Operator on F-Lattice,” Acta Mathematical Seneca, Vol. 46, No. 6, 2003, pp. 1163-1170.
[6]	G. L. Liu, “The Lattice Properties of Rough Set Quotient Spaces,” Computer Engineering & Science, Vol. 26, No. 12, 2004, pp. 82-90.
[7]	D. C. Sheng, “Abstract Algebra,” Science Press, Beijing, 2001, pp. 114-127.
[8]	W. X. Zhang, W. Z. Wu, J. Y. Liang and D. Y. Li, “Rough Sets: Theory and Methods,” Science Press, Beijing, 2001, pp. 72-77.