On the use of the weighted fuzzy c-means in fuzzy modeling

This paper proposes a fuzzy clustering-based algorithm for fuzzy modeling. The algorithm incorporates unsupervised learning with an iterative process into a framework, which is based on the use of the weighted fuzzy c-means. In the first step, the learning vector quantization (LVQ) algorithm is exploited as a data pre-processor unit to group the training data into a number of clusters. Since different clusters may contain different number of objects, the centers of these clusters are assigned weight factors, the values of which are calculated by the respective cluster cardinalities. These centers accompanied with their weights are considered to be a new data set, which is further elaborated by an iterative process. This process consists of applying in sequence the weighted fuzzy c-means and the back-propagation algorithm. The application of the weighted fuzzy c-means ensures that the contribution of each cluster center to the final fuzzy partition is determined by its cardinality, meaning that the real data structure can be easier discovered. The algorithm is successfully applied to three test cases, where the produced fuzzy models prove to be very accurate as well as compact in size. (c) 2005 Elsevier Ltd. All rights reserved.