Nearest Neighbor Tests for Fuzzy Data

A new statistical goodness-of-fit for comparing distributions of two or more populations and based on fuzzy data is proposed. Its idea goes back to the k-nearest neighbor technique applied in pattern recognition, where it simply consists in classifying an object by the majority vote of its neighbors. In our paper we show that by an appropriate test statistic construction which counts the number of nearest neighbors between and within samples it is possible to check whether available fuzzy samples come or not from the same distribution. It is worth underlying that the suggested testing procedure is completely distribution-free which seems to be of extreme importance in statistical reasoning with fuzzy data. Our test proposal is completed with a study of its properties and a case study related to quality assessment.