The crucial role that fuzzy implications play in many applicable areas was our motivation to revisit the topic of them. In this paper, we apply classical logic’s laws such as De Morgan’s laws and the classical law of double negation in known formulas of fuzzy implications. These applications lead to new families of fuzzy implications. Although a duality in properties of the preliminary and induced families is expected, we will prove that this does not hold, in general. Moreover, we will prove that it is not ensured that these applications lead us to fuzzy implications, in general, without restrictions. We generate and study three induced families, the so-called -implications, -implications, and -implications. Each family is the “closest” to its preliminary-“creator” family, and they both are simulating the same (or a similar) way of classical thinking.

中文翻译：

---

古典逻辑定律在模糊蕴涵公式中的应用

模糊含义在许多适用领域中发挥的关键作用是我们重新审视它们的主题的动机。在本文中，我们将经典逻辑定律（例如De Morgan定律）和双重否定的经典定律应用于已知的模糊含义公式中。这些应用导致了新的模糊含义。尽管可以预见的是，初生和诱导族在性质上有二重性，但我们将证明这通常并不成立。而且，我们将证明，不能保证这些应用程序通常无限制地导致我们产生模糊的含义。我们生成并研究了三个诱导族，即-含义，-含义和-含义。每个家庭都是与其最初的“创造者”家庭“最接近”的家庭，它们都在模仿相同（或相似）的古典思维方式。