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 capability of fuzzy systems have achieved great progress in recent years. In this paper, linear Takagi-Sugeno (TS) fuzzy systems that use linear functions of input variables as rule consequent and their special case, named simplified fuzzy systems that use fuzzy singletons as rule consequent, are investigated. On condition that overlapped fuzzy sets are employed, new sufficient conditions for simplified fuzzy systems and linear TS fuzzy systems as universal approximators are given, respectively. Then, a comparative study on existing sufficient conditions is carried out with numeric examples