Tolerance approximation spaces. (English) Zbl 0868.68103

Summary: We generalize the notion of an approximation space introduced in [Z. Pawlak, Rough Sets. Theoretical Aspects of Reasoning about Data (1991; Zbl 0758.68054)]. In tolerance approximation spaces we define the lower and upper set approximations. We investigate some attribute reduction problems for tolerance approximation spaces determined by tolerance information systems. The tolerance relation defined by the so called uncertainty function or the positive region of a given partition of objects have been chosen as invariants in the attribute reduction process. We obtain the solutions of the reduction problems by applying boolean reasoning [F. N. Brown Boolean reasoning (1990; Zbl 0719.03002)]. The solutions are represented by tolerance reducts and relative tolerance reducts.


68T30 Knowledge representation
68T27 Logic in artificial intelligence