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Fuzzy rule-based models via space partition and information granulation

  • S.I. : NCAA 2021
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Fuzzy rule-based model (FRBM) has attracted significant attention in various fields due to its accuracy and high level of interpretability. In this study, two granular Takagi–Sugeno (T–S) FRBMs are designed by employing fuzzy space partition and the principle of allocation of information granularity. The designed models considering different abstraction levels concentrate on the balance of interpretability and accuracy and reflect the rational granularity of rules’ output. According to the layered partition results, the granular T–S FRBMs are generated under two different granularity allocation strategies: uniformly and non-uniformly allocation of information granularity to the T–S FRBM’s parameters. Meanwhile, a unified index incorporating the principle of justifiable granularity is introduced for serving as examining the performance of the granular T–S FRBM and judging whether the obtained partitions need to be further divided in the next layer. The designed models with different types of allocating information granularity are compared with state-of-the-art granular rule modeling way on synthetic datasets and publicly available datasets to illustrate the study’s effectiveness. Under the same information granularity allocation strategy, the designed models in this study can achieve prediction intervals with sound robustness and granular performance. As an application example, a real-world dataset is analyzed to exhibit the potential practicality of the designed models.

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Abbreviations

FRBM:

Fuzzy rule-based model

T–S:

Takagi–Sugeno

FCM:

Fuzzy C-means

GrC:

Granular computing

WLS:

Weighted least square

PSO:

Particle swarm optimization

HiPCA:

Hierarchical fuzzy model learning method based on principal component analysis

r :

Number of possible splitting hyperplanes

c :

Number of clusters

d :

Instability index

\(\varepsilon\) :

Information granularity

m :

Fuzzification coefficient

\(a_{i}\) :

Parameter matrix of the i-th local linear model

\(w_{i}\) :

Mean of the i-th output subspace

\(v_{i}\) :

Mean of the i-th input subspace

\(\gamma\) :

The cumulative variance contribution rate

\(\delta\) :

Stop threshold for data partition

A :

Eigenvalue matrix

P :

Eigenvector matrix

Q :

Evaluation index of granular model

\(\Sigma\) :

Covariance matrix

D i :

The i-th dataset

B(x):

Membership function

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Acknowledgements

This work was supported by the Natural Science Foundation of China (No. 62173053).

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Authors and Affiliations

  1. School of Science, Dalian Maritime University, Dalian, 116026, Liaoning, China

    Yunhui Pang, Lidong Wang, Yifei Liu & Jiayi Guo

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  1. Yunhui Pang
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Correspondence to Lidong Wang.

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Pang, Y., Wang, L., Liu, Y. et al. Fuzzy rule-based models via space partition and information granulation. Neural Comput & Applic 34, 16199–16211 (2022). https://doi.org/10.1007/s00521-022-06974-3

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