On generating FC3 fuzzy rule systems from data using evolution strategies

Sophisticated fuzzy rule systems are supposed to be flexible, complete, con sistent and compact (FC3). Flexibility, completeness and consistency are es sential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of th e input variables increases. However, the completeness and consistency cond itions are often violated if a fuzzy system is generated from data collecte d from real world applications. In an attempt to develop FC3 fuzzy systems, a systematic design paradigm is proposed using evolution strategies. The structure of the fuzzy rules, whi ch determines the compactness of the fuzzy systems, is evolved along with t he parameters of the fuzzy systems. Special attention has been paid to the completeness and consistency of the rule base. The completeness is guarante ed by checking the completeness of the fuzzy partitioning of input variable s and the completeness of the rule structure. An index of inconsistency is suggested with the help of a fuzzy similarity measure, which can prevent th e algorithm from generating rules that seriously contradict with each other or with the heuristic knowledge. In addition, soft T-norm and BADD defuzzi fication are introduced and optimized to increase the flexibility of the fu zzy system. The proposed approach is applied to the design of distance cont roller for cars. It is verified that a FC3 fuzzy system works very well bot h for training and test driving situations, especially when the training da ta are insufficient.