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Issue No.11 - November (2011 vol.23)

pp: 1649-1667

Qinghua Hu , Harbin Institute of Technology, Harbin and The Hong Kong Polytechnic University, Hong Kong

Daren Yu , Harbin Institute of Technology, Harbin

Witold Pedrycz , University of Alberta, Edmonton and Polish Academy of Sciences, Warsaw

Degang Chen , North China Electric Power University, Beijing

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TKDE.2010.260

ABSTRACT

Kernel machines and rough sets are two classes of commonly exploited learning techniques. Kernel machines enhance traditional learning algorithms by bringing opportunities to deal with nonlinear classification problems, rough sets introduce a human-focused way to deal with uncertainty in learning problems. Granulation and approximation play a pivotal role in rough sets-based learning and reasoning. However, a way how to effectively generate fuzzy granules from data has not been fully studied so far. In this study, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generating fuzzy information granules in the approximation space. Subsequently fuzzy granules are used to approximate the classification based on the concepts of fuzzy lower and upper approximations. Based on the models of kernelized fuzzy rough sets, we extend the measures existing in classical rough sets to evaluate the approximation quality and approximation abilities of the attributes. We discuss the relationship between these measures and feature evaluation function ReliefF, and augment the ReliefF algorithm to enhance the robustness of these proposed measures. Finally, we apply these measures to evaluate and select features for classification problems. The experimental results help quantify the performance of the KFRS.

INDEX TERMS

Rough set, fuzzy rough set, kernel, feature evaluation, feature selection.

CITATION

Qinghua Hu, Daren Yu, Witold Pedrycz, Degang Chen, "Kernelized Fuzzy Rough Sets and Their Applications",

*IEEE Transactions on Knowledge & Data Engineering*, vol.23, no. 11, pp. 1649-1667, November 2011, doi:10.1109/TKDE.2010.260REFERENCES