Rough Sets and Vague Concept Approximation: From Sample Approximation to Adaptive Learning

We present a rough set approach to vague concept approximation. Approximation spaces used for concept approximation have been initially defined on samples of objects (decision tables) representing partial information about concepts. Such approximation spaces defined on samples are next inductively extended on the whole object universe. This makes it possible to define the concept approximation on extensions of samples. We discuss the role of inductive extensions of approximation spaces in searching for concept approximation. However, searching for relevant inductive extensions of approximation spaces defined on samples is infeasible for compound concepts. We outline an approach making this searching feasible by using a concept ontology specified by domain knowledge and its approximation. We also extend this approach to a framework for adaptive approximation of vague concepts by agents interacting with environments. This paper realizes a step toward approximate reasoning in multiagent systems (MAS), intelligent systems, and complex dynamic systems (CAS).