On strong consistency of the fuzzy generalized nearest neighbor rule

The k nearest neighbor rule (k-NNR) is a well-known nonparametric decision rule in pattern classification. Fuzzy set theory has been widely used to represent the uncertainty of class membership. Several researchers extended conventional k-NNR to fuzzy k-NNR, such as Bezdek et al. (Fuzzy Sets and Systems 18 (1986) 237-256), Keller et al. (IEEE Trans. Syst. Man, and Cybern. 15(4) (1985) 580-585), B6reau and Dubuisson (Fuzzy Sets and Systems 44 (1991) 17-32). In this paper, we describe a fuzzy generalized k-NN algorithm. This algorithm is a unified approach to a variety of fuzzy k-NNR's. Then we create the strong consistency of posterior risk of the fuzzy generalized NNR.

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