In this paper, we research a class of axioms in closed G-V fuzzy matroids. The main research method is to transform fuzzy matroids into matroids. First, we study many properties of the basis family of induced matroids, and define a new mapping which can reflect the relationship between bases of induced matroids of a G-V fuzzy matroid. Second, we discuss the new mapping, and reveal the relationship and properties among the fundamental sequence, the induced basis family and the new mapping of a G-V fuzzy matroid. From these relationships and properties, we extract four key attributes: normativity property, inclusion property, exchange property, and right surjection. Finally, we propose and prove “the induced basis axioms for a closed G-V fuzzy matroid” by these key attributes. With the help of these axioms, a closed G-V fuzzy matroid can be uniquely determined by a finite number sequence, a subset family and a mapping on this subset family when they satisfy above four attributes, and vice versa.

中文翻译：

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封闭GV模糊拟阵的诱导基公理

在本文中，我们研究了封闭GV模糊拟阵中的一类公理。主要研究方法是将模糊拟阵转换为拟阵。首先，我们研究了拟阵拟阵的基本族的许多性质，并定义了一个新的映射，该映射可以反映GV模糊拟阵的拟阵的基础之间的关系。其次，我们讨论了新的映射，并揭示了GV模糊拟阵的基本序列，诱导基族和新映射之间的关系和性质。从这些关系和属性中，我们提取出四个关键属性：规范属性，包含属性，交换属性和权利超越。最后，我们通过这些关键属性提出并证明“闭合GV模糊拟阵的诱导基公理”。在这些公理的帮助下，