Abstract
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.
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