Computer Science ›› 2024, Vol. 51 ›› Issue (2): 79-86.doi: 10.11896/jsjkx.221100229

• Database & Big Data & Data Science • Previous Articles     Next Articles

Fuzzy Systems Based on Regular Vague Partitions and Their Approximation Properties

PENG Xiaoyu, PAN Xiaodong, SHEN Hanhan, HE Hongmei   

  1. School of Mathematics,Southwest Jiaotong University,Chengdu,611756,China
  • Received:2022-11-28 Revised:2023-03-23 Online:2024-02-15 Published:2024-02-22
  • About author:PENG Xiaoyu,born in 1998,postgra-duate.Her main research interests include fuzzy system and so on.PAN Xiaodong,born in 1979,associate professor.His main research interests include mathematical basic theory of fuzzy information processing and so on.
  • Supported by:
    National Natural Science Fundation of China(61673320,61976130) and Sichuan Applied Basic Research Program(2020YJ0270).

Abstract: This paper is devoted to investigating the approximation problem of fuzzy systems based on different fuzzy basis functions.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 logarithmic fuzzy systems,and gives their approximation error bounds with the parameters of membership functions.Finally,experiments are designed to compare the approximation capability of different fuzzy systems.Experimental results further verify the correctness of the theoretical analysis.

Key words: Fuzzy systems, Regular vague partitions, Fuzzy basis functions, Overlap functions, Approximation error bounds

CLC Number: 

  • TP273.4
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