Constructing implications and coimplications on a complete lattice

In this paper, we firstly give out the formulas for calculating the upper (lower) approximation implications and coimplications of a binary operation on a complete lattice. Then, we discuss some properties of the upper (lower) approximation implications and coimplications. Finally, we investigate the relations between the upper (lower) approximation implications and the lower (upper) approximation coimplications.