This paper is devoted to investigating the approximation problem of fuzzy systems based on different fuzzy basis func-tions.Firstly,the multi-dimensional regular vague partitions are established based on one-dimensional regular vague partitions and overlap functions,and the fuzzy systems are designed by taking the elements in the partition as the fuzzy basis functions.With the help of the Weierstrass approximation theorem,the conclusion that the fuzzy systems are universal approximators is obtained,and the corresponding approximation error bounds are presented.Secondly,this paper proposes the polynomial,exponential and loga-rithmic fuzzy systems,and gives their approximation error bounds with the parameters of membership functions.Finally,experi-ments are designed to compare the approximation capability of different fuzzy systems.Experimental results further verify the correctness of the theoretical analysis.
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