This article presents an innovative method for designing fuzzy systems composed of fewer fuzzy rules. The conventional approach to fuzzy-system design usually assumes that there exists no correlation among input variables, therefore, grid-type fuzzy partitions are widely adopted. However, in many cases, it is likely that input variables are highly correlated with one another. To avoid the problem of growth of partitioned grids in some complex system, we used an aggregation of hyperrectangulars with different size and different positions to approximate fuzzy partitions that are arbitrarily shaped. The corresponding parameters defining these hyperrectangulars are selected by using genetic algorithms. Furthermore, the number of fuzzy rules of the constructed system can be automatically minimized by choosing a special fitness function that takes this factor into account. Finally, an inverted pendulum control and nonlinear modeling problems are utilized to illustrate the effectiveness of the proposed method.
