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On the vertical threshold generation method of fuzzy implication and its properties

机译：模糊蕴涵的垂直阈值生成方法及其性质

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摘要

In recent years, some new construction methods of fuzzy implications from other given ones have been proposed. One of them, the so-called threshold generation method, preserves important properties such as the exchange principle or the law of importation under some minimal conditions. This method is based on an adequate scaling on the second variable of the two initial fuzzy implications. In this paper, we propose a new method to generate fuzzy implications from two given ones in the same spirit of the threshold generation method but now through an adequate scaling on the first variable of the given fuzzy implications. The new implications, called vertical threshold generated implications, are deeply studied focusing on the preservation of the most common properties of fuzzy implications from the initial ones to the generated implication. Moreover, they are fully characterized by means of the e-vertical section of the implication.
机译：近年来，已经提出了一些其他给定模糊含义的新构造方法。其中一种，即所谓的阈值生成方法，在某些最小条件下保留了重要的属性，例如交换原理或进口法则。该方法基于对两个初始模糊含义的第二个变量的适当缩放。在本文中，我们提出了一种新方法，可以按照阈值生成方法的相同精神，但通过对给定模糊含义的第一个变量进行适当缩放，从两个给定的模糊含义中生成模糊含义。对新的含义（称为垂直阈值生成的含义）进行了深入研究，重点是保留从初始值到生成的含义的模糊含义最常见的属性。此外，它们通过蕴含的电子垂直部分得以充分表征。

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