Two kinds of average approximation accuracy

Rough set theory places great importance on approximation accuracy, which is used to gauge how well a rough set model describes a target concept. However, traditional approximation accuracy has limitations since it varies with changes in the target concept and cannot evaluate the overall descriptive ability of a rough set model. To overcome this, two types of average approximation accuracy that objectively assess a rough set model's ability to approximate all information granules is proposed. The first is the relative average approximation accuracy, which is based on all sets in the universe and has several basic properties. The second is the absolute average approximation accuracy, which is based on undefinable sets and has yielded significant conclusions. We also explore the relationship between these two types of average approximation accuracy. Finally, the average approximation accuracy has practical applications in addressing missing attribute values in incomplete information tables.