Neighborhood system of parameterized binary relations

This paper shows that a variable precision rough sets(VPRS) and a singleton based parameterized binary relation based rough sets (BRS) can be expressed by a neighborhood system. In particular, the lower and upper approximations with the threshold β or α can be rewritten as the interior and closure of a neighborhood system. Moreover, the interior and closure of such NS are definable sets of a partition, which is induced by the NS. This partition is called derived partition and its equivalence classes are called center sets. Hence the knowledge represented by them is called central knowledge. So the lower and upper approximations with the threshold β or α can have AI-interpretation, namely, can be interpreted by central knowledge, but not by elementary knowledge of BRS.