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As a combination of fuzzy sets and covering rough sets, fuzzy β covering has attracted much attention in recent years. The fuzzy β neighborhood serves as the basic granulation unit of fuzzy β covering. In this article, a new discernibility measure with respect to the fuzzy β neighborhood is proposed to characterize the distinguishing ability of a fuzzy covering family. To this end, the parameterized fuzzy β neighborhood is introduced to describe the similarity between samples, where the distinguishing ability of a given fuzzy covering