Left and right distributivity for semi-t-operators

Distributivity was proposed about fifty years ago and it has been studied for several well-known operations, such as, uninorms and nullnorms, specially for t-norms and t-conorms. Over there, we prepare to continue to investigate the same topic as the above by focusing on semi-t-operators, which are generalization of t-operators by omitting commutativity. In fact, this is also the future work recommended by Drygaś in Ref.[3]. Note that, in this paper, we investigate this problem from the left (right) distributivity but not distributivity point of view and find the second operator of this equation is not idempotent on the whole interval [0, 1]. Moreover, our results are not only the full characterization of this distributivity, but also extension of the previous ones about distributivity for semi-nullnorms and semi-t-operators.