Test cost sensitive multigranulation rough set: Model and minimal cost selection

Multigranulation rough set is an expansion of the classical rough set by using multiple granular structures. Presently, three important multigranulation rough sets have been proposed, they are optimistic, pessimistic and β-multigranulation approaches. However, such three multigranulation rough sets do not take the test cost into consideration, which is an important issue in both data mining and machine learning. To solve such problem, we propose a test cost sensitive multigranulation rough set model in this paper. We show that test cost sensitive multigranulation rough set is a generalization of optimistic, pessimistic and β-multigranulation rough sets. Furthermore, it is found that the traditional heuristic algorithm is not suitable for granular structure selection with lower test cost, we then propose a backtracking algorithm for granular structure selection with minimal test cost. The algorithms are tested on ten UCI (University of California–Irvine) data sets. Experimental results show the effectiveness of backtracking algorithm by comparing with heuristic algorithm. This study suggests potential application areas and new research trends concerning multigranulation rough set theory.