We present a new generalized version of the fuzzy k-nearest neighbor (FKNN) classifier that uses local mean vectors and utilizes the Bonferroni mean. We call the proposed new method Bonferroni-mean based fuzzy k-nearest neighbor (BM-FKNN) classifier. The BM-FKNN classifier can be easily fitted for various contexts and applications, because the parametric Bonferroni mean allows for problem-based parameter value fitting. The BM-FKNN classifier can perform well also in situations where clear imbalances in class distributions of data are found. The performance of the proposed classifier is tested with six real-world data sets and with one artificial data set. The results are benchmarked with classification results obtained with the classical k-nearest neighbor-, the local mean-based k-nearest neighbor-, the fuzzy k-nearest neighbor- and other three selected classifiers. In addition to this, an enhancement of the local mean-based k-nearest neighbor classifier by using the Bonferroni means is also proposed and tested. The results show that the proposed new BM-FKNN classifier has the potential to outperform the benchmarks in classification accuracy and confirm the usefulness of using the Bonferroni mean in the learning part of classifiers.

我们提出了使用局部均值向量并利用Bonferroni均值的模糊k近邻（FKNN）分类器的新广义版本。我们将所提出的基于Bonferroni-mean的新方法称为模糊k近邻（BM-FKNN）分类器。BM-FKNN分类器可以轻松地适合各种环境和应用，因为参数Bonferroni均值允许基于问题的参数值拟合。BM-FKNN分类器在发现数据的类分布明显不平衡的情况下也可以很好地执行。拟议的分类器的性能已通过六个实际数据集和一个人工数据集进行了测试。该结果以经典k的分类结果为基准-最近邻居-，基于局部均值的k-最近邻居-，模糊k-最近邻居-和其他三个选定分类器。除此之外，还提出并测试了使用Bonferroni手段增强基于局部均值的k近邻分类器的功能。结果表明，所提出的新的BM-FKNN分类器具有优于分类基准的潜力，并证实了在分类器的学习部分使用Bonferroni均值的有用性。