Constructions of coimplications and left (right) semi-uninorms on a complete lattice

In this paper, we further study the constructions of coimplications and left (right) semi-uninorms on a complete lattice. We firstly investigate the residual coimplications generated by left (right) semi-uninorms and the left (right) semi-uninorms induced by coimplications. Then, we give out the formulas for calculating the upper and lower approximation disjunctive left (right) semi-uninorms and the upper and lower approximation coimplications, which satisfy the neutrality principle, of a binary operation. Finally, we discuss the relationships between disjunctive left (right) semi-uninorms and coimplications which satisfy the neutrality principle.