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On interval fuzzy negations

机译：关于区间模糊否定

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There exist infinitely many ways to extend the classical propositional connectives to the set [0, 1], preserving their behaviors in the extremes 0 and 1 exactly as in the classical logic. However, it is a consensus that this issue is not sufficient, and, therefore, these extensions must also preserve some minimal logical properties of the classical connectives. The notions of t-norms, t-conorms. fuzzy negations and fuzzy implications taking these considerations into account. In previous works, the author, joint with other colleagues, generalizes these notions to the set U = {[a, b]ㄧ0≤a≤b≤ 1}, providing canonical constructions to obtain, for example, interval t-norms that are the best interval representations of t-norms. In this paper, we consider the notion of interval fuzzy negation and generalize, in a natural way, several notions related with fuzzy negations, such as the ones of equilibrium point and negation-preserving automorphism. We show that the main properties of these notions are preserved in those generalizations.
机译：有无数种方法可以将经典命题连接词扩展到集合[0，1]，与经典逻辑完全一样，在极端0和1下保留其行为。但是，一个共识是这个问题是不够的，因此，这些扩展还必须保留经典连接词的一些最小逻辑特性。 t-范数，t-conorms的概念。模糊否定和模糊含义将这些考虑因素考虑在内。在以前的工作中，作者与其他同事共同将这些概念推广到集合U = {[a，b]ㄧ0≤a≤b≤1}，提供了规范的构造来获得例如区间t范数，是t范数的最佳区间表示。在本文中，我们考虑了区间模糊否定的概念，并自然地归纳了与模糊否定有关的几个概念，例如平衡点和保持否定的自同构。我们证明了这些概念的主要性质在那些概括中得以保留。

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