In the first part of this paper we consider the α-cut of a sum of two fuzzy sets. We show that the α-cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions, over a set uniquely determined by the considered t-norm. In the second part of the paper we show that not only α-cut of a sum of two fuzzy intervals has this property, but also α-cut of a continuous function of two variables, strictly increasing in each argument as well. Two examples of the presented theory are considered.

中文翻译：

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关于L  -  R模糊数的有限T-和的注记和进一步的考虑

在本文的第一部分，我们考虑两个模糊集之和的α-割。我们表明，在由考虑的t范数唯一确定的集合上，这样一个总和的α割可以写为一个由某些特殊函数的最小值和最大值确定的闭合区间。在本文的第二部分中，我们表明不仅两个模糊区间之和的α- cut具有此属性，而且还具有两个变量的连续函数的α- cut具有严格的性能，每个参数也严格增加。考虑了所提出理论的两个例子。