A generalized definition of rough approximation based on similarity in variable precision rough sets

Variable precision rough set theory (VPRS) is an important extension of rough set theory; it incorporates the use of indiscernibility relation (equivalence relation) to approximate sets of objects by β-lower and β-upper approximation. This paper extends the concepts to the case of more general relation - similarity relation. β-lower and β-upper approximation are proposed, which are extensional definitions of the classical concepts β-lower and β-upper approximation.