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The distributivity equation for uninorms revisited

机译：再谈单数分布方程

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AbstractThe distributivity equation has been widely studied involving different classes of aggregation functions from t-norms and t-conorms to uninorms, nullnorms and generalizations of them. It is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing. Since uninorms have been used in these topics, the study of the distributivity between two uninorms becomes specially interesting. In a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone. In this paper we want to achieve this study by focusing on the reverse direction, that is, for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm. We show along the paper that this new point of view leads to many new solutions.
机译： 摘要 已经广泛研究了分布方程，涉及从t范数和t范数到单数，零范数和它们的推广的不同类别的聚合函数。由于它在模糊逻辑和近似推理以及图像处理中的应用，它在逻辑连接词的框架中很重要。由于在这些主题中使用了单位制，因此研究两个单位制之间的分配性变得特别有趣。在同一位作者的最新论文中，当第一个单元格在任何研究最多的单元格中，而第二个单元格是任何人时，已经编译并完成了已知的解决方案。在本文中，我们希望通过侧重于相反的方向来完成本研究，也就是说，对于第二个单一类别位于研究最多的单个类别中的任何一个，而第一个单一类别属于任何一个单一类别的情况。我们在论文中表明，这种新观点导致了许多新解决方案。

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