Foundations of Rough Sets from Vagueness Perspective

Abstract

We present three types of knowledge, which can be specified according to the Rough Set theory. Then, we present three corresponding types of algebraic structures appearing in the Rough Set theory. This leads to three following types of vagueness: crispness, classical vagueness, and a new concept of “intermediate” vagueness. We also propose two classifications of information systems and approximation spaces. Based on them, we differentiate between information and knowledge.