This paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. First of all, a valid fuzzy covering of the universe is constructed on the basis of an appropriate fuzzy similarity relation, which helps capture the structural information and the internal connections of the dataset from the global perspective. Due to the advantages of valid fuzzy covering, we explore the valid fuzzy covering instead of the raw dataset for RFCM algorithm-based three-way clustering. Subsequently, from the perspective of semantic interpretation of balancing the uncertainty changes in fuzzy sets, a method of partition thresholds acquisition combining linear and nonlinear fuzzy entropy theory is proposed. Furthermore, boundary regions in three-way clustering correspond to the abstaining decisions and generate uncertain rules. In order to improve the classification accuracy, the k-nearest neighbor (kNN) algorithm is utilized to reduce the objects in the boundary regions. The experimental results show that the performance of the proposed three-way clustering based on fuzzy covering and kNN-FRFCM algorithm is better than the compared algorithms in most cases.

中文翻译：

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基于模糊覆盖的三向聚类

本文研究了涉及模糊覆盖，阈值获取和边界区域处理的三向聚类。首先，在适当的模糊相似关系的基础上构建有效的宇宙模糊覆盖，这有助于从全局角度捕获结构信息和数据集的内部联系。由于有效模糊覆盖的优点，我们探索了有效模糊覆盖而不是原始数据集，用于基于RFCM算法的三向聚类。随后，从平衡模糊集不确定性变化的语义解释的角度出发，提出了一种结合线性和非线性模糊熵理论的分区阈值获取方法。此外，三向聚类中的边界区域对应于弃权决定并生成不确定规则。为了提高分类的准确性，利用k最近邻算法（kNN）来减少边界区域中的物体。实验结果表明，在大多数情况下，基于模糊覆盖和kNN-FRFCM算法的三向聚类算法的性能优于比较算法。