Exact inversion of decomposable interval type-2 fuzzy logic systems

It has been demonstrated that type-2 fuzzy logic systems are much more powerful tools than ordinary (type-1) fuzzy logic systems to represent highly nonlinear and/or uncertain systems. As a consequence, type-2 fuzzy logic systems have been applied in various areas especially in control system design and modelling. In this study, an exact inversion methodology is developed for decomposable interval type-2 fuzzy logic system. In this context, the decomposition property is extended and generalized to interval type-2 fuzzy logic sets. Based on this property, the interval type-2 fuzzy logic system is decomposed into several interval type-2 fuzzy logic subsystems under a certain condition on the input space of the fuzzy logic system. Then, the analytical formulation of the inverse interval type-2 fuzzy logic subsystem output is explicitly driven for certain switching points of the Karnik–Mendel type reduction method. The proposed exact inversion methodology driven for the interval type-2 fuzzy logic subsystem is generalized to the overall interval type-2 fuzzy logic system via the decomposition property. In order to demonstrate the feasibility of the proposed methodology, a simulation study is given where the beneficial sides of the proposed exact inversion methodology are shown clearly.

► An analytical methodology is developed for interval type-2 fuzzy logic system inversion. ► The decomposition property is extended and generalized to interval type-2 fuzzy logic systems. ► The interval type-2 fuzzy logic system is decomposed into several interval type-2 fuzzy logic subsystems. ► The analytical formulation of the type-2 fuzzy subsystem output is tried to be reached to find the inverse solution. ► The exact inverse interval type-2 fuzzy logic system is obtained through inversion of each type-2 fuzzy subsystem.