Xu et al. make a strong point for the necessity of attribute reduction in ordered information systems and offer a convincing solution. Their approach exploits the relationship between the Dempster-Shafer theory (DST) of mathematical evidence and Pawlak’s rough set theory, as well as their plausibility and belief functions. The theories have applications in information system domains where information may be missing, incomplete, or imprecise.

Overall, this is a great overview of mathematical evidence theory, ordered information systems, and the rough set theory. Despite its somewhat distracting format and some English-language glitches, the paper is relatively easy to read and comprehend. It covers a lot of related work, which makes it a useful reference resource. The paper presents many accompanying mathematical foundations; while this is great for readers in this field, it is perhaps too much information for nonmathematicians. Xu et al. set forth a number of propositions and theorems, which are required to establish the relationship between evidence theory and rough set theory for the purposes of attribute reduction, and provide proofs for them. The authors arrive at the conclusion that a classical attribute reduction holds if it is a belief reduction from evidence theory, which in turn is a plausibility reduction, among other things. However, they make it clear that they do not provide for the decision-making aspect of evidence theory.

Readers will notice this paper’s strong correlation with intensional logic [1] and the Lucid programming language, as well as its derivative Lucx [2].