Exact inversion of TSK fuzzy systems with linear consequents

In literature, there is no exact inversion method for TSK fuzzy systems with linear consequents. In this study, an analytical method is proposed for the exact inversion of TSK fuzzy systems with linear consequents of which input variables are described using strong triangular partitions. When strong triangular partitions are used, the universes of discourse of input variables are divided into specific regions. In the proposed method, linear equations of triangular membership functions of inversion variable and the rule consequents are directly used in the analytical formulation of TSK fuzzy system output. In this way, the output of the TSK fuzzy system can be expressed in a unique quadratic form in terms of the inversion variable for any region where only the parameters of the appropriate equations of triangular membership functions are embedded. Thus, the inverse solution is easily obtained for any region by using explicit solution of the quadratic equation. An illustrative example has been given to validate the proposed method.