A new type of fuzzy systems in terms of vague partitions

Article type: Research Article

Authors: Shen, Hanhan^{a; *} | Pan, Xiaodong^a | Peng, Xiaoyu^a | Dan, Yexing^a | Qiao, Junsheng^b

Affiliations: [a] School of Mathematics, Southwest Jiaotong University, Chengdu, PR China | [b] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China

Correspondence: [*] Corresponding author. Hanhan Shen, School of Mathematics,Southwest Jiaotong University, Chengdu, 610000, PR China. E-mail: 20123645@my.swjtu.edu.cn.

Abstract: This paper focuses on simplifying the structure of fuzzy systems and improving the precision. By regarding the fuzzy rule base as a mapping from the vague partition on the input universe to the vague partition on the output universe, we first design a new type of fuzzy system using the complete and continuous fuzzy rule base in terms of vague partitions. We then exploit Weierstrass’s approximation theorem to show that this new type of fuzzy system can approximate any real continuous function on a closed interval to arbitrary accuracy and provide the corresponding approximation accuracy with respect to infinite norms. We also provide two numerical examples to illustrate the effectiveness of this new type of fuzzy system. Both theoretical and numerical results show that this new type of fuzzy system achieves the quite approximation effect with a few fuzzy rules.

Keywords: Vague partition, Fuzzy system, Fuzzy rule base, Approximation

DOI: 10.3233/JIFS-223542

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 6, pp. 9545-9563, 2023