Research On Robust Fuzzy Rough Set Models

Fuzzy rough set theory is claimed to be a powerful mathematical tool for dealingwith uncertainty in data analysis. It has attracted much attention from domains of granularcomputing, machine learning and uncertainty reasoning in the past decade. However, theclassical fuzzy rough set model is sensitive to noise, which makes the theory limited inapplication. Now much work is still focusing on the research of robust fuzzy rough setmodels. It is significant to design robust fuzzy rough set models. In this work, we designrobust fuzzy rough set models in the two ways to handling noisy data. Our work is shownas follows:The robustness and limitation of existent rough sets are analyzed. In order to showthe sensitivity of rough set theory to noise, the robustness and limitation of rough setmodels are analyzed, such as Pawlak's rough sets, neighborhood rough sets, fuzzy roughsets, variable precision rough sets, neighborhood consistency, ??-precision fuzzy roughsets, fuzzy variable precision rough sets, variable precision fuzzy rough sets and vaguelyquantified rough sets. And analyzed results are tested with experiments.A soft minimum enclosing ball-based fuzzy rough set model is designed. Soft mini-mum enclosing ball is a state-of-the-art method in novelty detection. It is introduced intofuzzy rough sets to form a robust model, the robustness of which is tested with experi-ments. Moreover, with the proposed model a robust fuzzy rough decision tree model ispresented and tested by experiments.A robust statistics-based fuzzy rough set model is introduced. The classical fuzzyrough set model is defined with minimum and maximum, which results in its sensitivityto noise. In this work, three robust statistics are introduced into fuzzy rough sets to designa robust model. The new model is robust to noise by changing the computational ways oflower and upper approximations. Besides, a robust classification model is designed withthe lower approximation of the robust statistics-based fuzzy rough sets, and is tested withexperiments.A robust fuzzy rough set model named soft fuzzy rough sets is introduced. It isinspired by soft margin support vector machines. The new model makes trade-off betweenmemberships and numbers of overlooked samples. It enlarges the lower approximations or reduces the upper approximations as well as restricting numbers of samples neglected.In order to test the validity and robustness of soft fuzzy rough sets, a feature selectionalgorithm is designed by taking soft fuzzy dependency as feature evaluation measure andclassification accuracies of data sets on selected features as the evaluation measure of thealgorithm and soft fuzzy rough sets.Robust fuzzy rough set models are compared and applied in solar ?are prediction.A case-based prediction model is present. It takes the lower approximation membershipsof robust fuzzy rough sets as theoretical sustainment of case selection and case reasoning.The robustness of the prediction model is tested with experiments.