On strong Pawlak algebras

The rough top equality between subsets of a finite set was introduced by Novotny and Pawlak. Liu extended Pawlak rough set algebra to lattice form, called Pawlak algebra. In this paper, Strong Pawlak algebra which is more similar to Pawlak rough set algebra is introduced. Furthermore, Characterizations of strong Pawlak algebra by a complete subalgebra of a fuzzy lattice are obtained. The top equality on a fuzzy lattice L is also characterized, which is a generalization of the top equality on Pawlak rough set algebra.