Congruence relations on and varieties of directed multilattices
A concept of congruence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
A concept of equivalence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
In this paper, we propose the general methods, yielding uninorms on the bounded lattice , with some additional constraints on for a fixed neutral element based on underlying an arbitrary triangular norm on and an arbitrary triangular conorm on . And, some illustrative examples are added for clarity.