TOLERANCE APPROXIMATION SPACES

Abstract

We generalize the notion of an approximation space introduced in [8]. 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 [1]. The solutions are represented by tolerance reducts and relative tolerance reducts.