Condensed fuzzy nearest neighbor methods based on fuzzy rough set technique

As a generalization of K-nearest neighbor (K-NN) algorithm, the fuzzy K-nearest neighbor (fuzzy K-NN) algorithm was originally developed by Keller in 1985 to overcome one of the drawbacks of K-NN (i.e. all of instances are considered equally important in K-NN). However, fuzzy K-NN algorithm still suffers from the problem of large memory requirement same as K-NN. To deal with this problem, based on fuzzy rough set technique, this paper proposed two condensed fuzzy nearest neighbor methods denoted by CFK-NN1 and CFK-NN2 and a modified fuzzy K-NN. The CFK-NN1 and CFK-NN2 both consists of three steps: (1) obtaining a fuzzy attribute reduct based on fuzzy rough set technique, (2) finding two sets of prototypes, the one is selected from fuzzy positive region (corresponding to CFK-NN1) and the other is selected from fuzzy boundary region (corresponding to CFK-NN2), (3) extracting fuzzy classification rules with the modified fuzzy K-NN from the two sets of prototypes. Extensive experiments and statistical analysis are conducted to verify the effectiveness of our proposed method. The experimental results and the statistical analysis of the experimental results both demonstrate that the proposed methods outperform other related methods such as CNN, ENN, and ICF et al.