ABSTRACT L-equivalence relations on L-fuzzy sets, equivalent to L-valued equalities on ordinary sets, are modelling fuzzy similarity of two objects that are partial members of a fuzzily defined set. This paper deals with construction and representation properties of L-equivalence relations on L-fuzzy sets. To this end, we set up a method for constructing them by means of quasi-pseudo-metrics, and then point out how L-equivalence relations on L-fuzzy sets are represented by families of L-fuzzy subsets of L-fuzzy sets. The present results are applied to locally vague environments to elucidate conceptual structures of locally vague environments, and to show how the points in a locally vague environment are described.

中文翻译：

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L-模糊集上L-等价关系的表示及其在局部模糊环境中的应用

摘要 L 模糊集上的 L 等价关系，相当于普通集上的 L 值等式，是对作为模糊定义集的部分成员的两个对象的模糊相似性进行建模。本文研究L-模糊集上L-等价关系的构造和表示性质。为此，我们建立了一种利用拟伪度量构造它们的方法，然后指出L-模糊集上的L-等价关系如何用L-模糊集的L-模糊子集的族来表示。目前的结果应用于局部模糊环境，以阐明局部模糊环境的概念结构，并展示如何描述局部模糊环境中的点。