Upper and Lower Approximations

Upper and lower approximations are concepts from rough set theory used to handle uncertainty in classification. The **lower approximation** includes all elements that definitely belong to a specific category based on available information. The **upper approximation** covers all elements that possibly belong to that category, even if there's some ambiguity. Think of it like trying to identify a particular fruit: the lower approximation includes only fruits clearly identified as that type, while the upper approximation includes all fruits that could be that type, including some that are uncertain. These tools help manage and analyze vague or imprecise data effectively.