Acquisition of representative objects and attribute reductions based on generalized decisions of dominance-based rough set approach

Dominance principles play a pivotal role in decision makings, in which the superior the object performs on criteria, the higher the object will be assigned by decision attributes. In practical issues, the result of decision makers is influenced significantly because of the existence on redundant objects and attributes. However, little work studies the inconsistency of dominance principles caused by redundant objects. The proposed generalized decision aims to intuitively reveal the consistency of dominance principles. Since then, considerable attention has been devoted to accelerating attribute reductions in dominance -based rough sets. But there has been limited discussion on the semantic explanation of generalized decisions. This paper addresses this gap by introducing a graded information granule that not only explains the consistency of dominance principles but also facilitates the partitioning of the universe. Based on this foundation, several theoretical properties are thoroughly investigated. Moreover, we acquire a representative object set by applying a threshold to filter out objects with an extreme imbalance of dominance principles, and a final compact data set is generated with the best threshold by a particular parameter selection mechanism. Additionally, we design an attribute reduction method based on graded information granules using the compact data set. Furthermore, we employ numerical data sets to illustrate the effectiveness and efficiency of our method by running time and importance of reducts performed from the perspective of dominance -based rough sets and machine learning. Finally, the practicability of compact data sets is explained from the viewpoint of decision rules in dominance -based rough set approach.