Closed-Form Mathematical Representations of Interval Type-2 Fuzzy Logic Systems with Application to Inverted Pendulum Stabilization

Interval type-2 fuzzy logic systems (IT2 FLSs) have a wide range of applications due to their ability to handle uncertainties. A drawback of IT2 FLSs is that their different representations generally suffer from high computational complexity. This paper discusses the representation of IT2 FLSs in closed mathematical form. The proposed form provides an easy, computationally efficient method to implement IT2 FLSs. Additionally, the closed-form is preferred in control systems. We also discuss the use of the proposed method in balancing an inverted pendulum on a cart, a common problem in control theory. Simulation results are provided to compare the performance of the proposed closed-form systems against the performance of other IT2 FLSs. The results confirm that the introduced IT2 representations perform closely to their more computationally complex counterparts.