Contribution-Factor based Fuzzy Min-Max Neural Network: Order-Dependent Clustering for Fuzzy System Identification

This study addresses the construction of Takagi-Sugeno-Kang (TSK) fuzzy models by means of clustering. A contribution-factor based fuzzy min-max neural network (CFMN) is developed based on Simpson’s well-known fuzzy min-max neural network (FMNN) for clustering. The contribution-factor (CF) is also known as the typical pattern, and the membership threshold above which a pattern can be a CF of a cluster can be specified by the user. The stability issue is addressed and unnecessary overlaps in FMNN can be avoided. Furthermore, two considerations are combined in the clustering process to fully exploit the information in the data: 1) patterns (points) are generated in a sequence, so it’s reasonable to capture the order-dependent information of data, and 2) the clustering process shouldn’t be influenced too much by noisy data or outliers. As a result, CFMN can put most cluster centers in high-density regions of clusters without influence of the low-density regions. This feature is very important when clusters are used as fuzzy rules because the high-density region of some cluster can be interpreted as the most common part of that rule. Simulations are performed to illustrate the clustering behavior of CFMN and identification performance of the resulting fuzzy inference system (CFMN-FIS). It is shown that the proposed algorithm is fast to learn and has good prediction performance.