Both rough set theory and concept lattice theory are important methods for knowledge discovery and uncertainty decision, and they are closely connected. Based on the concepts of  β-upper and lower approximations of variable precision rough sets in a concept lattice, we discuss the properties of the  β-upper and  β-lower approximations of variable precision rough sets in a concept lattice for any given variable precision β, and for any undefinable object in a formal context, we propose an algorithm about  β-upper and  β-ower approximations of variable precision rough sets in a concept lattice, respectively. What’s more, an example is given to verify that the new algorithm can meet the requirements of users’ different approximations and make the approximation results change flexibly. The new algorithm outperforms Yao and Mohanty' algorithms in  β-lower approximations.

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