Generalizations to the constructions of t-norms: Rotation(-annihilation) construction

In this paper, the constructions of triangular norms are investigated. Specially, based on weak negations which are not necessarily involutive, the rotation and the rotation-annihilation constructions are extended. By means of these methods, we can get new families of left-continuous t-norms compatible with weak negations given. However, not all weak negations are suitable for those generalized constructions. To highlight it, some counterexamples are given.