In this paper, we introduce a new construction method of a fuzzy implication from n increasing functions gi:0,1⟶0,∞, (g0=0) (i=1,2,…,n, n ∈N) and n+1 fuzzy negations Ni (i=1,2,…,n+1, n ∈N). Imagine that there are plenty of combinations between n increasing functions gi and n+1 fuzzy negations Ni in order to produce new fuzzy implications. This method allows us to use at least two fuzzy negations Ni and one increasing function g in order to generate a new fuzzy implication. Choosing the appropriate negations, we can prove that some basic properties such as the exchange principle (EP), the ordering property (OP), and the law of contraposition with respect to N are satisfied. The worth of generating new implications is valuable in the sciences such as artificial intelligence and robotics. In this paper, we have found a novel method of generating families of implications. Therefore, we would like to believe that we have added to the literature one more source from which we could choose the most appropriate implication concerning a specific application. It should be emphasized that this production is based on a generalization of an important form of Yager’s implications.

中文翻译：

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一种从n个递增函数和n + 1个求反产生模糊蕴涵的方法

本文从n个递增函数gi：0,1⟶0，∞，（g0 = 0）（i = 1,2，…，n，n∈N）和n引入一种模糊蕴涵的新构造方法+1个模糊否定Ni（i = 1,2，…，n + 1，n∈N）。想象一下，在n个递增函数gi和n + 1个模糊取反Ni之间有很多组合，以便产生新的模糊含义。该方法允许我们至少使用两个模糊否定Ni和一个递增函数g来生成新的模糊蕴涵。选择适当的否定式，我们可以证明一些基本性质，例如交换原理（EP），有序性质（OP）以及关于N的对立律，都得到了满足。在人工智能和机器人等科学领域，产生新含义的价值是宝贵的。在本文中，我们发现了一种产生含义族的新颖方法。因此，我们想相信我们已经向文献中增加了一个来源，从中我们可以选择与特定应用有关的最适当的含义。应该强调的是，这种产生是基于对Yager含义的一种重要形式的概括。