A new approach to an exact inversion of TSK fuzzy systems

In this study, a new approach to an exact analytical inversion of Takagi-Sugeno-Kang (TSK) fuzzy systems with singleton consequents is presented. Here, the inversion variable is represented by piecewise linear membership functions (PWLMFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed approach, linear equations of PWL-MFs which determine membership degrees are directly used in the analytical formulation of TSK fuzzy system. This provides us to express the fuzzy system output in a unique linear form in terms of the inversion variable for any region where only the parameters of the appropriate linear equations of PWL-MFs are embedded. Thus, finding the inverse solutions for any region is transformed to solve the linear equations which is relatively easy. The proposed method has been tested on an illustrative example.