H-transformation of t-norms

Cancellative t-norms are generated only if they do not posses anomalous pairs and then they are isomorphic to subsemigroups of ([0, ∞], +). A new construction method for t-norms, so-called H-transformation of t-norms, is introduced and studied, generalizing a recent example of Hájek. H-transformation allows to construct non-generated cancellative (left-continuous) t-norms with prescribed number of non-trivial Archimedean components. The unique t-norm stable under H-transformation is also described. In an analogous way, H-transformation of residual implications is given. Finally, a general H-transformation based on cancellative discrete t-conorms is proposed and examined.