Attribute reduction based on interval-set rough sets

As an important extension of the rough set theory, interval-set rough sets provide an effective method to solve the problem that the objective sets cannot be accurately expressed in the rough approximation process and to induce classification rules from incomplete information systems. In practical information systems, the value of an object’s decision attribute may be set-valued due to missing decision information or multiple decision values. However, this situation is not considered by any of the existing rough set models. Therefore, to properly deal with the information system where decision attributes are set-valued, we construct the interval-set rough set model on the information system and study attribute reductions of interval-set rough sets. First, we define the information system where decision attributes are set-valued as an extended set-valued decision information system (ESVDIS) and construct the interval-set rough set model on the ESVDIS. Second, the accuracy and the roughness are extended to the interval-set approximation accuracy and the interval-set approximation roughness, respectively. The two extended measures can be used to measure the uncertainty caused by rough approximations. In addition, the dependency degree of interval-set rough sets called the interval-set dependency degree is defined to estimate the significance of attribute subsets. By adopting the interval-set dependency degree, we propose the definition of attribute reduction based on interval-set rough sets and design a heuristic attribute reduction algorithm. Finally, the effectiveness of the proposed attribute reduction algorithm is demonstrated using 12 public data sets. Experimental results show that the model is applicable to some fields, such as missing decision information and group decision-making.