In this paper, the interval type-2 fuzzy proportional–integral–derivative controller (IT2F-PID)
is proposed for controlling an inverted pendulum on a cart system with an uncertain model.
The proposed controller is designed using a new method of type-reduction that we have
proposed, which is called the simplified type-reduction method. The proposed IT2F-PID
controller is able to handle the effect of structure uncertainties due to the structure of the
interval type-2 fuzzy logic system (IT2-FLS). The results of the proposed IT2F-PID controller …

In this paper, we derive the analytical structure of a class of the interval type-2 fuzzy
proportional–integral–derivative (IT2F-PID) controller. In the proposed IT2F-PID controller
structure, a rule-based Mamdani-type-2 fuzzy system is used to select the gains of the
classical PID controller. The mathematical input–output relationships for the IT2F-PID
controller are derived by dividing the input space and identifying the input–output
relationship for each region. The IT2F-PID controller uses the following identical elements …