Abstract
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.
Highlights
Based on the above backgrounds and work in three-way decisions, a novel method for three-way clustering based on fuzzy covering is discussed
We can obtain that the results of clustering based on fuzzy covering are mostly better than the results of clustering with raw data. erefore, the valid fuzzy covering can replace the raw dataset for clustering, and the clustering results are better than the raw dataset. e premise that fuzzy covering can replace the raw dataset for clustering is to select the appropriate fuzzy similarity relation [46]
Because the similarity between fuzzy similarity classes in the valid fuzzy covering can be used to measure the similarity between objects in the raw dataset, each fuzzy similarity class reflects the connection with the whole dataset, so valid fuzzy covering instead of the raw data for clustering can improve the precision of clustering
Summary
College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao 028000, China. Is paper investigates the three-way clustering involving fuzzy covering, thresholds acquisition, and boundary region processing. It is to obtain that if the value of m tends to 1, the memberships are most crisp, as well as the uncertainty of the system is reduced which is suitable for three-way clustering In this circumstance, only objects that are approximately the same distance from each cluster center are divided into boundary regions. The parameter m cannot be assigned with a very large value because as the value increases, the memberships of objects around the center of the cluster will be assigned to 1 and most objects are divided into boundary region which will increase the uncertainty of the system and the error rate of decision-making. E commonly used linear and nonlinear fuzzy entropy functions are listed as follows [41,42,43]:
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