document: Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule This paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the IF-parts , but used only in the THEN-parts of the fuzzy rules of the current layer . The proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier . From the simulation of ball and beam control system , it is demonstrated that the proposed scheme approximates with good accuracy the model nonlinear controller with fewer fuzzy rules than the centralized fuzzy system and its control performance is comparable to that of the nonlinear controller
doc_bio_tags: O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O
extractive_keyphrases: hierarchical fuzzy system fuzzy rules universal approximator continuous function ball and beam control system
abstractive_keyphrases: hierarchical fuzzy logic stone-weierstrass theorem