On generalization reducts in incomplete multi-scale decision tables

In reality, data is always arranged at multiple granularity levels. Multi-scale information tables were introduced from the viewpoint of granular computing to represent such types of data sets. In the present paper, we focus on acquisition of if-then rules in incomplete multi-scale decision tables (IMSDT for short). The notion of generalization reducts is proposed to achieve the desired goal. By firstly considering the generalization reducts of an IMSDT and then calculating the generalization reducts for each object, a collection of optimal decision rules can be thus obtained. During the entire process of generalization reducts, both the number and the generalization ability of the original attribute set are taken into consideration. It is shown that a more general and simple set of decision rules can be obtained by using generalization reducts, compared with the approaches in the literature. Lastly, an explanatory example is employed to show the advantage of our approach, and an experiment is designed for performing a comparative study between different approaches.