Hierarchical neuro-fuzzy quadtree models
The authors propose a new hybrid fuzzy model named hierarchical neuro-fuzzy quadtree (HNFQ) which is based on a recursive partitioning method of the input space called quadtree. In this partitioning and contrary to the usual binary partitioning, the \(n\)-dimensional space is successively subdivided in quadrants that, in turn, can be again subdivided in four regions. Thus, the learning capacity of artificial neural networks is maintained, and the theory of fuzzy sets makes it possible to present the information learned in a format which is well interpretable. The article describes the architecture of this new model, presenting its basic cell and its learning algorithm. Further, it is evaluated in three well-known benchmark applications; i.e., the approximation of the function sinc\((x,y)=\sin(x)\sin(y)/(xy)\) -- which yields a shape resembling a Mexican hat --, the Mackey Glass chaotic series forecast and the two spirals problem. When compared to other neuro-fuzzy systems, the HNFQ exhibits competing results with two major advantages: it creates automatically its own structure and it is not limited to few input variables.
scientific article; zbMATH DE number 1864833