Zero-order fuzzy neural network with adaptive fuzzy partition and its applications on high-dimensional problems

The number of fuzzy rules in a fuzzy neural network usually depends on the grid-type partition or clustering-based partition. However, the number of grids or clusters needs to be set in advance and the initial number of fuzzy sets on each dimension is usually the same. This usually does not fit the real situation (for example, when forecasting the weather, various features such as temperature, humidity, wind direction, wind speed, etc., may have different numbers of fuzzy sets). In this paper, a novel zero-order fuzzy neural network with an adaptive fuzzy partition (AdFPFNN) is proposed, which does not need to preset the number of fuzzy sets and owns various numbers of fuzzy sets on different dimensions. The trick is to use the mean shift algorithm to perform adaptive clustering for each feature individually. For common fuzzy neural networks, dealing with high-dimensional problems is challenging work on account of the "fuzzy rule curse"and "computation underflow". To overcome these issues, an improved version of AdFPFNN is devised to tackle high-dimensional problems, called PaCoAMF-based AdFPFNN. It adopts two techniques to overcome the "fuzzy rule curse"and "computation underflow". One is the construction of a partially combined fuzzy rule base, which can generate rules that are adequate but do not grow exponentially with the number of features. Another is the proposal of an adaptive membership function that can guarantee the elimination of numerical underflow due to the product T-norm. Without feature selection or other dimensional reduction methods, the proposed PaCoAMF-based AdFPFNN can be directly used to solve high-dimensional problems. Simulation results on one constructed dataset and 13 real-world datasets (including 5 high-dimensional problems) confirm the effectiveness of the proposed models.