Feature Selection Based on Weighted Fuzzy Rough Sets

Fuzzy rough set approaches have received widespread attention across the disciplines of feature selection and rule extraction. When calculating the fuzzy degree of membership of a sample within a specific class, traditional fuzzy rough sets give precedence to the distance information between the sample and other samples that do not belong to the class, often neglecting the influence of the remoteness of the sample from the specified class. In fact, this calculation strategy limits the discriminability of different samples relative to a given class, which may affect the accuracy and efficiency of feature subset selection. To address the shortcoming, the present study puts forward a new fuzzy rough set approach, weighted fuzzy rough set, which can more accurately measure the correlation and difference between samples relative to the decision class. Based on the distance from a sample to a class, the model first defines the importance of the sample to the class and uses it as a weight to measure the distance between the sample and other samples that do not belong to the class, thereby constructing a more effective fuzzy rough approximation operator. On this basis, a dependency measure between decision variables and conditional attributes is defined to evaluate the importance of candidate features. Then, a concept of discrimination between samples relative to a class is proposed, and the rationality of weighted fuzzy rough set is discussed. Finally, based on weighted fuzzy rough approximation operator, a new algorithm for selecting a subset of features is formulated. Experimental outcomes demonstrate that the algorithm performs well in terms of performance, not only selecting a smaller number of features, but also achieving higher classification accuracy for simplified data, showing its practical application value in feature selection.