How to Vary the Input Space of a T-S Fuzzy Model: A TP Model Transformation-Based Approach

The motivation behind 15 years of continuous development within the topic of the tensor product (TP) model transformation is that the greater the number of parameters or components of the Takagi-Sugeno (T-S) fuzzy model one can manipulate, the larger complexity reduction or control optimization one can achieve. This article proposes a radically new type of extension to the TP model transformation. While earlier variants of the TP model transformation focused on how the antecedent-consequent fuzzy set system of a given T-S fuzzy model could be varied, this article, in contrast, focuses on how the number of inputs to a given T-S fuzzy model can be manipulated. The proposed extension is capable of changing the number of inputs or transforming the nonlinearity between the fuzzy rules and the input dimensions. These new features considerably increase the modeling power of the TP model transformation, allowing for further complexity reduction and more powerful control optimization to be achieved. This article provides two examples to show how the proposed extension can be used in a routine-like fashion.