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The problem of distributivity was first posed over forty years ago and it has been investigated for families of certain operations such as t-norms, t-conorms, uninorms, and nullnorms. In this paper, we investigate this topic further by focusing on Mayor’s aggregation operators and semi-t-operators, which generalize the t-operators by omitting commutativity. The results that we obtain are complete...
The aim of this paper is to characterize the distributivity equations between quasi-arithmetic means and some binary operators, such as, nullnorms, semi-nullnorms and semi-t-operators. It is shown that the distributivity equations between nullnorms (semi-nullnorms) and quasi-arithmetic means degenerate into the distributivity equations between t-norms or t-conorms (semi-t-norms or semi-t-conorms)...
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...
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