A grey-based rough approximation model for interval data processing

A new rough set model for interval data named grey-rough set is proposed in this paper. Information system in the real world are quite complicated. Most of information tables record not only categorical data but also numerical data including a range of interval data. The grey lattice operation in grey system theory is one of the operations for interval data that modifies endpoints non-arithmetically, and which is useful for interval data processing. The grey-rough approximation is based on an interval coincidence relation and an interval inclusion relation instead of an equivalence relation and an indiscernibility relation in Pawlak’s model. Numerical examples and four fields of practical examples, decision-making, information retrieval, knowledge discovery and kansei engineering are shown. The advantages of the proposal include: extending a treatable value compared with classical rough set for non-deterministic information systems, providing a maximum solution and minimum solution both in upper and lower approximations, and not only providing mathematical support to SQL but also functions for further extension in the future.