On the edited fuzzy K-nearest neighbor rule

Classification of objects is an important area in a variety of fields and applications. In the presence of full knowledge of the underlying joint distributions, Bayes analysis yields an optimal decision procedure and produces optimal error rates. Many different methods are available to make a decision in those cases where information of the underlying joint distributions is not presented. The k nearest neighbor rule (k-NNR) is a well-known nonparametric decision procedure. Many classification rules based on the k-NNR have already been proposed and applied in diverse substantive areas. The edited k-NNR proposed by D.L. Wilson (1972) would be an important one. Fuzzy theory, originated by L.A. Zadeh (1965), is widely used to represent the uncertainty of class membership. The fuzzy k-NNR has been proposed by several investigators. In this paper an edited type of the fuzzy k-NNR is developed. Next, some asymptotic properties of the proposed edited fuzzy k-NNR are created. Moreover, numerical comparisons are made between the proposed edited fuzzy k-NNR and the other fuzzy k-NNR. Those results confirm that the edited fuzzy k-NNR has a better performance than the fuzzy k-NNR.