A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators

Universal approximation is the basis of theoretical research and practical applications of fuzzy systems. Studies on the universal approximation capab ility of fuzzy systems have achieved great progress in recent years. In thi s paper, linear Takagi-Sugeno (TS) fuzzy systems that use linear functions of input variables as rule consequent and their special case named simplifi ed fuzzy systems that use fuzzy singletons as rule consequent are investiga ted, On condition that overlapped fuzzy sets are employed, new sufficient c onditions for simplified fuzzy systems and linear TS fuzzy systems as unive rsal approximators are given, respectively. Then, a comparative study on ex isting sufficient conditions is carried out with numeric examples.