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Distributivity between semi-uninorms and semi-t-operators

机译：半规范与半t运算符之间的分布

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摘要

The problem of distributivity was posed many years ago and it has been investigated for families of certain operations, such as t-norms, t-conorms, uninorms, and nullnorms. In this study, we continue the investigation of this same topic by focusing on semi-uninorms and semi-t-operators, which are generalizations of uninorms and t-operators that are obtained by omitting commutativity and associativity, and commutativity, respectively. The results obtained provide the full characterizations, except for a special subcase, and we extend the previous results regarding distributivity between uninorms and nullnorms, as well as between semi-uninorms and semi-nullnorms. Moreover, we propose a more reasonable method for obtaining a proof to demonstrate the distributivity between semi-uninorms and semi-t-operators. (C) 2015 Elsevier B.V. All rights reserved.
机译：分布性问题是在多年前提出的，并且已经针对某些操作的族进行了研究，例如t范数，t范数，单数和零范数。在本研究中，我们将继续关注同一主题，即半规范和半t运算符，这是对单变量和t运算符的概括，它们分别通过省略可交换性，关联性和可交换性而获得。除特殊子情况外，获得的结果提供了完整的表征，并且我们扩展了先前有关单数和零范数之间以及半标准和半零范数之间的分布的结果。此外，我们提出了一种更合理的方法来获得证明，以证明半规范和半t运算符之间的分布。 （C）2015 Elsevier B.V.保留所有权利。

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