α-RST:: a generalization of rough set theory

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, alpha-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, definability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. Besides, the control of knowledge granularity is natural in a-RST which is based on a parameterized indiscernibility relation, a-RST is developed to recognize non-deterministic relationships using notions as alpha-dependency, alpha-reduct and so forth. On the other hand, we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory. The extension a-RST leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non-empty boundaries. (C) 2000 Elsevier Science Inc. All rights reserved.