This paper presents a new and a more general formulation of the min and max operations for gradual intervals, initially proposed for the special case of triangular fuzzy intervals. Gradual intervals generalize the conventional interval representation by increasing its specificity, thereby making it possible to represent the imprecision and the uncertainty via the notion of gradualness. In this context, a new interpretation of fuzzy intervals through the notion of gradual intervals is developed. The originality of the proposed methodology lies in the extension of inter-interval relations to the gradual case according to midpoint-radius representation.

中文翻译：

---

渐进间隔的最小和最大运算符


本文提出了一种新的、更通用的渐进区间最小和最大运算公式，最初是针对三角模糊区间的特殊情况提出的。渐变间隔通过增加其特异性来概括传统的间隔表示，从而可以通过渐变的概念来表示不精确性和不确定性。在此背景下，通过渐进间隔的概念对模糊间隔进行了新的解释。该方法的独创性在于根据中点半径表示将区间关系扩展到渐变情况。