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Characterizing set-valued functions of uninorms with continuous underlying t-norm and t-conorm

机译：表征具有连续基础t范数和t范数的单项的集值函数

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AbstractThe uninorms with continuous underlying functions were characterized by their set of discontinuity points in the previous work of the author, using the characterizing set-valued function. In this paper properties of this characterizing set-valued function are studied. It is shown that the type of the monotonicity of such a set-valued function is always changed in idempotent points of the corresponding uninorm. Several additional properties of the characterizing set-valued function of a uninorm with continuous underlying functions are shown and an example is included. Results shown in this paper are used for a complete characterization of uninorms with continuous underlying functions via the ordinal sum construction, which is shown in the consecutive paper.
机译： 摘要 在作者先前的工作中，使用具有特征性的设定值函数，具有连续基础函数的单身以其间断点集为特征。在本文中，研究了该表征集值函数的性质。可以看出，这种设定值函数的单调性的类型总是在相应的单项的幂等点上改变。显示了具有连续基础函数的单项特征化集值函数的几个其他属性，并包括一个示例。本文中显示的结果可通过序数和构造用于具有连续基础功能的单身的完整表征，该连续性在后续论文中进行了展示。

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