On Exactness, Definability and Vagueness in Partial Approximation Spaces ''

In this paper, lower/upper, boundary, and negative regions of set approximations, the fundamental concepts of classical rough set theory, have been considered as primitive ones. Assuming that they are independent of each other, a generalized framework for their investigations is outlined. Its main building blocks are base sets and definable sets. Lower/upper approximations, boundaries and negative sets are all considered as definable sets and their mutual interactions are studied. Lastly exact/rough sets are discussed. In generalized framework, four groups of formulae are defined for representing different variants of rough sets. They emphasize distinct features of roughness, and so it may be of highly importance which one is used in practical applications. Some possible choices appeared in authors’ publications are mentioned.