Weights Based Ranked Fuzzy Rough Reduction

Fuzzy rough technique is a mathematical tool to deal with fuzzy and rough knowledge, which could reduce the redundant objects and attributes by keeping the information invariant. In the existing researches on fuzzy rough sets, all the attributes are assumed to have the same weights for the decision. Actually different attributes may play different roles on the decision. As a result, we introduce weights into fuzzy rough sets and design weights based ranked attribute reduction in this paper. First, we apply Minkowski distance with attribute weights to define fuzzy rough set and then weights are introduced into fuzzy rough set. And then it is important for weighted fuzzy rough sets to find the optimal weights. By maximizing the weighted discernibility information, we find that the dependency degree of corresponding attributes are the optimal weights. Based on this discovery, we design an algorithm of attribute reduction by ranking the weights. Finally, we compare the classical heuristic reduction algorithm and proposed weight based ranked reduction algorithm. The numerical results shows that the proposed algorithm is more efficiency on the datasets with large number of attributes.