Improving fuzzy clustering algorithm for overlapping elements and its application

This paper proposes an improved fuzzy cluster analysis algorithm for processing overlapping elements. The algorithm employs a novel measure called the H index as the optimal criterion in the fuzzy clustering problem. It aims to capitalize on the advantages of fuzzy relationships, thereby facilitating the processing of overlapping elements. The approach is grounded in compactness and/or separation measures of centroid elements. The calculations of fuzzy information are sufficient to distinguish the geometric structures of clusters with overlapping elements. Moreover, this study develops an algorithm capable of identifying the optimal number of clusters for overlapping elements, providing advantages over the Elbow method. The developed algorithm is tested and implemented through numerical examples using Matlab software. Additionally, it is applied to construct a forecasting model for fuzzy time series. The experimental results demonstrate the superiority of the developed algorithm over certain existing algorithms