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Interval type-2 fuzzy systems on the basis of vague partitions and their approximation properties

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Abstract

This article mainly focuses on simplifying the structure of interval type-2 (IT2) fuzzy system and studying its approximation properties. First of all, we construct the interval type-2 vague partitions (IT2-VPs) on input universe by overlap functions and vague partition of each attribute, and their properties are characterized. On the basis of these, we give the model of IT2 fuzzy system based on IT2-VPs, which mainly consists of the fuzzy rule base and center-of-sets type-reduction (TR). Next, we investigate its universal approximation property and approximation accuracy by error remainder term and auxiliary function method in numerical analysis. Finally, two comparative experiments indicate that the approximation performance of the proposed IT2 fuzzy systems can achieve better than the typical type-1 (T1) and IT2 fuzzy systems.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61673320).

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  1. Xiaoyu Peng and Xiaodong Pan have contributed equally to this work.

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  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 611756, Sichuan, China

    Xiaoyu Peng & Xiaodong Pan

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  1. Xiaoyu Peng
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  2. Xiaodong Pan
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Correspondence to Xiaoyu Peng.

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Peng, X., Pan, X. Interval type-2 fuzzy systems on the basis of vague partitions and their approximation properties. Comp. Appl. Math. 43, 119 (2024). https://doi.org/10.1007/s40314-024-02629-2

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