In this article, we introduce a new technique for roughness of a set based on \((\alpha , \beta )\)-indiscernibility, that is, objects are indiscernible up to certain degrees \(\alpha \) and \(\beta \). For this purpose, a bipolar fuzzy tolerance relation has been used. Also we investigate some fundamental properties of these approximations. Finally, we give the notions of accuracy measure and roughness measure for \((\alpha , \beta )\)-bipolar fuzzified rough set.

中文翻译：

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$$（\ alpha，\ beta）$$（α，β）的集的粗糙度-双极模糊关系的不可识别性

在本文中，我们介绍了一种基于\（（\ alpha，\ beta）\）-不区分度的集粗糙度的新技术，也就是说，在一定程度上\（\ alpha \）和\（\ beta \）。为此，已经使用了双极性模糊容差关系。我们还研究了这些近似的一些基本性质。最后，我们给出了（（（\ alpha，\ beta）\）-双极模糊化粗糙集的精度度量和粗糙度度量的概念。