Pseudo-uninorms and coimplications on a complete lattice

Pseudo-uninorms are a generalization of uninorms by removing the commutativity from the axioms of the uninorms. In this paper, we further study pseudo-uninorms and coimplications on a complete lattice. Firstly, we discuss the residual coimplications of pseudo-uninorms and give equivalent conditions for left (right) infinitely ∧ -distributive pseudo-uninorms. Then, we study some properties of ( U , N ) - coimplications generated from a pseudo-uninorm and a strong negation. Finally, we investigate the pseudo-uninorms induced by coimplications, present equivalent conditions for right infinitely ∨ -distributive coimplications, and provide some conditions such that the operators induced by coimplications are uninorms.