From Vagueness to Rough Sets in Partial Approximation Spaces

Vagueness has a central role in the motivation basis of rough set theory. Expressing vagueness, after Frege, Pawlak’s information-based proposal was the boundary regions of sets. In rough set theory, Pawlak represented boundaries by the differences of upper and lower approximations and defined exactness and roughness of sets via these differences. However, defining exactness/roughness of sets have some possibilities in general. In this paper, categories of vagueness, i.e., different kinds of rough sets, are identified in partial approximation spaces. Their formal definitions and intuitive meanings are given under sensible restrictions.

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