ROUGH-SET REASONING ABOUT UNCERTAIN DATA

Rough set theory refers to classification of objects described by well-defined values of qualitative and quantitative attributes. The values of attributes defined for each pair [object, attribute], called descriptors, are assumed to be unique and precise. In practice, however, these attribute values may be neither unique nor precise, i.e. they can be uncertain. We are distinguishing four types of uncertainty affecting values of attributes: uncertain discretization of quantitative attributes, imprecision of values of numerical attributes, unknown (missing) values of attributes, multiple values possible for one pair [object, attribute]. We propose a special way of modelling the first three types of uncertainty using fuzzy sets, which boils them down to the fourth type, called shortly, multiple descriptors. Thus, the generalization of the rough set approach consists in handling the case of multiple descriptors for both condition and decision attributes. The generalization preserves all characteristic features of the rough set approach while enabling reasoning about uncertain data. This capacity is illustrated by a simple example.