Constructing ANFIS with Sparse Data through Group-Based Rule Interpolation: An Evolutionary Approach

An adaptive-network-based fuzzy inference system (ANFIS) offers a popular and powerful fuzzy inference mechanism. As with many other advanced data-driven techniques, developing an effective ANFIS typically requires sufficient training data. However, in many real-world applications, it is not always straightforward to obtain a large amount of representative data that cover the entire problem space to accomplish the required training, seriously restricting the performance of a learned ANFIS. This article introduces a new ANFIS learning approach through an evolutionary process, which is able to generate an ANFIS with only a small amount of training data in a certain problem region, by interpolating well-trained ANFISs in the neighboring regions. Such a process works by first producing an initial population of candidate fuzzy rules in the region of data shortage, through interpolating a rule dictionary constructed from trained ANFISs in the neighborhood regions. The crossover and mutation operations over these candidate rules are then executed in an effort to attain candidates of improved performance. When this genetic learning process terminates, the chromosomes in the final population either collectively form or each individually represents a learned ANFIS, depending on whether a single fuzzy rule or a set of fuzzy rules representing an entire ANFIS is implemented with a chromosome within the evolving population. Comparative experimental evaluations on both synthetic and real-world datasets are carried out, demonstrating that in spite of data shortage, the proposed interpolation approach is able to produce ANFIS models that significantly outperform those trained using existing learning mechanisms.