A Decision-Theoretic Rough Set Approach to Lattice-Valued Information System

The decision-theoretic rough set utilizes Bayesian decision to interpret the thresholds of probabilistic rough set model. That provides a novel semantic description for rough regions in the viewpoint of three-way decision theory and has been applied to numerous fields. However, it lacks the ability to deal with lattice-valued information system (LvIS), in which the condition attribute set consists of multiple types of attributes and their domain constitute lattice. Therefore, this study concentrates on the decision-theoretic rough approach in a LvIS. Then, the total decision cost associated with rough regions is addressed and an attribute reduction algorithm will be designed based on minimum decision cost. Finally, a case study on medical diagnosis is conducted to illustrate the decision procedure and attribute reduction approach.