Lattice Ordered Monoids and Left Continuous Uninorms and t-norms,

The proposition about generalization of the existence of the residuum for left continuous uninorm U on a commutative, residuated l-monoid, with a neutral element is proved. The question raised previously was whether there are general operation groups which satisfy the residuum-based approximate reasoning, but at the same time are easily comprehensible and acceptable to application-oriented experts. The basic backgrounds of this research are the distance-based operators.