In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.

中文翻译：

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模糊二元粗糙集

在本文中，我们基于模糊二元关系的 α 割提供了模糊集的 α 模糊下近似和上近似的定义。我们证明了该定义是前一个定义的适当概括，用于近似清晰集，并将其与模糊容差关系上下文中的现有定义进行比较。