In this paper, we study fuzzy congruence relations and their classes; so-called fuzzy congruence classes in universal algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Fuzzy congruence relations generated by a fuzzy relation are fully characterized in different ways. The main result in this paper is that, we give several Mal'cev-type characterizations for a fuzzy subset of an algebra $A$ in a given variety to be a class of some fuzzy congruence on $A$. Some equivalent conditions are also given for a variety of algebras to possess fuzzy congruence classes which are also fuzzy subuniverses. Special fuzzy congruence classes called fuzzy congruence kernels are characterized in a more general context in universal algebras.

中文翻译：

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泛代数中的 L 模糊同余类

在本文中，我们研究了模糊同余关系及其类别；泛代数中所谓的模糊同余类，其真值位于满足无限满足分配律的完全格中。由模糊关系产生的模糊同余关系以不同的方式完全表征。本文的主要结果是，我们对代数的模糊子集给出了几个 Mal'cev 类型的表征$\mathrm{一种}$ 在给定的变体中是一类具有某种模糊一致的 $\mathrm{一种}$. 还给出了具有模糊同余类的各种代数的一些等价条件，这些类也是模糊子宇宙。称为模糊同余核的特殊模糊同余类在通用代数的更一般上下文中表征。