Empirical Risk Minimization for Variable Precision Dominance-Based Rough Set Approach
In this paper, we characterize Variable Precision Dominance-based Rough Set Approach (VP-DRSA) from the viewpoint of empirical risk minimization. VP-DRSA is an extension of the Dominance-based Rough Set Approach (DRSA) that admits some degree of misclassification error. From a definable set, we derive a classification function, which indicates assignment of an object to a decision class. Then, we define an empirical risk associated with the classification function. It is defined as mean hinge loss function. We prove that the classification function minimizing the empirical risk function corresponds to the lower approximation in VP-DRSA.
Keywordsrough sets variable precision dominance-based rough set approach empirical risk minimization
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