Abstract This paper studies local indistinguishability operators, i.e., symmetric and transitive fuzzy relations that do not need to be reflexive. This is an important generalization of global indistinguishability relations (fuzzy relations satisfying the reflexivity property in addition) because there are interesting families of fuzzy relations that are non-reflexive. One case are decomposable relations, that are generated by a fuzzy subset and contains the t-norms as an important subfamily. Also the relations associated naturally to fuzzy subgroups are local indistinguishability operators. In this paper these relations will be studied stressing the way they can be generated. A representation theorem will be proved and related to the concepts of extensionality and of fuzzy rough set. Decomposable local indistinguishability operators will also be studied and related with one-dimensional ones in the sense of the previous representation theorem. The presence of these relations in the study of fuzzy subgroups will also be analyzed.

中文翻译：

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关于局部不可区分性算子的表示

摘要 本文研究了局部不可区分性算子，即不需要自反的对称和传递模糊关系。这是全局不可区分性关系（另外满足自反性属性的模糊关系）的重要概括，因为有一些有趣的非自反性模糊关系族。一种情况是可分解的关系，由模糊子集生成并包含 t 范数作为重要的子族。与模糊子群自然相关的关系也是局部不可区分性算子。在本文中，将研究这些关系，并强调它们的产生方式。将证明一个表示定理，该定理与可拓性和模糊粗糙集的概念有关。也将研究可分解的局部不可区分性算子，并将其与前面表示定理意义上的一维算子相关联。这些关系在模糊子群研究中的存在也将被分析。