Learning feed-forward and recurrent fuzzy systems: A genetic approach

In this paper, we present a new learning method for rule-based feed-forward and recurrent fuzzy systems. Recurrent fuzzy systems have hidden fuzzy variables and can approximate the temporal relation embedded in dynamic processes of unknown order. The learning method is universal i.e., it selects optimal width and position of Gaussian like membership functions and it selects a minimal set of fuzzy rules as well as the structure of the rules. A genetic algorithm (GA) is used to estimate the fuzzy systems which capture low complexity and minimal rule base. Optimization of the "entropy" of a fuzzy rule base leads to a minimal number of rules, of membership functions and of subpremises together with an optimal input/output (I/O) behavior. Most of the resulting fuzzy systems are comparable to systems designed by an expert but offers a better performance. The approach is compared to others by a standard benchmark (a system identification process). Different results for feed-forward and first-order recurrent fuzzy systems with symmetric and non-symmetric membership functions are presented.