Multiple kernel learning-based rule reduction method for fuzzy modeling

As a model for complex processes, the Takagi-Sugeno fuzzy model (T-S fuzzy model) usually requires numerous rules, often leading to dimension disaster. To mitigate this problem while preserving modeling accuracy, a multiple kernel learning-based rule reduction method (MKLRR) is proposed here. First, several fuzzy sets in the original T-S fuzzy model are merged into a larger single set. Dynamic behavior in these big fuzzy sets is strongly nonlinear, and that between sets is often completely different, rendering ineffective the local linear model structure of traditional T-S fuzzy modeling. To solve this difficulty, we develop a multiple kernel learning strategy to project each big fuzzy set from a low-dimensional space into a high-dimensional space using the corresponding projection function. In each high-dimensional space, data has a linear relation which is easily represented by a linear model. The final model is constructed through fuzzy inference by combining all linear models from these high-dimensional spaces, greatly reducing the rule number and preserving modeling accuracy due to the good approximating ability of multiple kernel learning. Two solving strategies are developed to subsequently train the model. Additional analysis and proofs state the effectiveness of the proposed method. Case study indicates that the constructed model performs better with a fewer number of rules than the other methods with a greater number of rules, which effectively solves the problem of dimension disaster.(c) 2023 Elsevier B.V. All reserved.

Automated summary

In order to address the problems of excessive rule numbers and dimension disaster in the T-S fuzzy model, this study proposes a rule reduction method based on multiple kernel learning (MKLRR). By merging multiple fuzzy sets into larger sets and applying multiple kernel learning to project them from a low-dimensional space to a high-dimensional space, the final model is constructed through fuzzy inference, reducing the rule number while maintaining modeling accuracy.