To formalize decision making in information systems with incomplete data, object attributes may be represented as fuzzy sets. Rough sets abstract such systems by two sets that represent the lower and the upper approximation of which objects satisfy a given predicate. Variable precision multigranulation extends this approach to multiple predicates where a threshold value determines the precision of the approximation. A three-way decision takes a fuzzy rough set and an object and states whether the object is in the positive region of objects that almost certainly satisfy the predicate, in the negative region of objects that do not, or in an undecidable boundary region.

The authors introduce a novel uncertainty measure for fuzzy rough sets, which is based on a decision-theoretic fuzzy set that is directly derived from the three-way decision method; in particular, its membership degree is one or zero, if the object falls into the positive or negative regions. This measure is at the core of a reduction algorithm that removes, from an information system, those attributes that are redundant in the sense that their removal has no influence on any decision. The algorithm is experimentally analyzed on real-world datasets, demonstrating the superiority of the approach over other reduction methods.

The paper is well and systematically written, giving all mathematical details and most of the proofs. It is primarily intended for experts in the field, clearly advancing the state of the art in this area of research.