In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of R∩R−1 does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we...

An inequality between the number of coverings in the ordered set J(Con L) of join irreducible congruences on a lattice L and the size of L is given. Using this inequality it is shown that this ordered set can be computed in time O(n2 log2 n), where n = |L|. This paper is motivated by the problem of efficiently calculating and representing the congruence lattice Con L of a finite lattice L. Of c...

This talk connects simple lattice path enumeration with a subgroup of the Riordan group, ordered trees, and the Faber polynomials from classical complex analysis. The main tools employed are matrix multiplication, generating functions and a few definitions from group theory and complex functions.

For an abelian lattice ordered group G let convG be the system of all compatible convergences on G; this system is a meet semilattice but in general it fails to be a lattice. Let αnd be the convergence on G which is generated by the set of all nearly disjoint sequences in G, and let α be any element of convG. In the present paper we prove that the join αnd ∨ α does exist in convG.

In this paper, the ordered set of rough sets determined by a quasiorder relation R is investigated. We prove that this ordered set is a complete, completely distributive lattice, whenever the partially ordered set of the equivalence classes of R∩R does not contain infinite ascending chains. We show that on this lattice can be defined three different kinds of complementation operations, and we d...