The decision-theoretic rough set, as a special case of probabilistic rough set, mainly adopts Bayesian decision procedure to achieve the thresholds from a given loss function. It provides a novel semantic interpretation for rough regions by utilizing three-way decision approach and has been widely applied in decision making. However, there is a limitation of classical decision-theoretic rough set that it lacks of ability to deal with hybrid data. Where the condition attributes are composed of multiple types, for instance, real-valued, set-valued, interval-valued, fuzzy-valued, intuitionistic fuzzy-valued attribute and so on. These complex data constitute a knowledge representation system named lattice-valued decision information system. In this talk, we develop a decision-theoretic rough set model in a lattice-valued decision information system to study these hybrid data. Then, some essential properties of this model are addressed and decision rules are investigated. Furthermore, we design two heuristic attribute reduction algorithms based on rough entropy and positive region preservation, respectively. Finally, a series of examples based on medical diagnosis are conducted to interpret decision rules and demonstrate these algorithms.
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