In this paper, for a real number $ϵ\in [0,1]$, we put forward the notion of fuzzy ϵ-approximate regular languages and study their properties, especially the Pumping lemma in the context of this kind of languages. By comparing sets of fuzzy ϵ-approximate regular languages under the order of set inclusion, we get an (infinite) hierarchy of fuzzy languages, the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages, and the sets of ϵ-approximate regular languages are different for different $ϵ\in (0,\frac{1}{2})$. We also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy ϵ-approximate regular languages. Furthermore, for a fuzzy ϵ-approximate regular language f, ϵ-approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata ϵ-accepting f. If a fuzzy ϵ-approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton A, then we give a polynomial-time algorithm to construct at least one minimal deterministic fuzzy automaton ϵ-accepting f by means of A. Finally, we point out that the number of states of minimal deterministic fuzzy automata ϵ-accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language.

在本文中，对于一个实数 $\epsilon \in [0,1]$，我们提出了模糊ϵ -近似正则语言的概念并研究了它们的性质，特别是在这种语言的上下文中的 Pumping 引理。通过在集合包含的顺序下比较模糊ϵ-近似正则语言的集合，我们得到一个（无限）模糊语言层次结构，最小的是模糊正则语言的集合，最大的是模糊语言的集合，并且集合的ϵ -近似正则语言对于不同的$\epsilon \in (0,\frac{1}{2})$. 我们还研究了在模糊正则语言集合中关闭的操作是否在模糊ϵ近似正则语言集合中仍然是关闭的。此外，对于模糊ε -approximate正规语言˚F，ε -approximate等价关系的˚F的特点，以构建确定性的模糊自动机ε -accepting ˚F。如果模糊ϵ -近似正则语言f也是模糊正则语言并被给定的可访问确定性模糊自动机A 接受，然后我们给出了一个多项式时间算法来构造至少一个最小确定性模糊自动机ϵ -通过A接受f。最后，我们指出，接受模糊正则语言的最小确定性模糊自动机ϵ的状态数小于或等于接受该语言的最小确定性模糊自动机的状态数。