A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems

This paper presents a comparative study of type-2 fuzzy logic systems with respect to interval type-2 and type-1 fuzzy logic systems to show the efficiency and performance of a generalized type-2 fuzzy logic controller (GT2FLC). We used different types of fuzzy logic systems for designing the fuzzy controllers of complex non-linear plants. The theory of alpha planes is used for approximating generalized type-2 fuzzy logic in fuzzy controllers. In the defuzzification process, the Karnik and Mendel Algorithm is used. Simulation results with a type-1 fuzzy logic controller (T1FLC), an interval type-2 fuzzy logic controller (IT2FLC) and with a generalized type-2 fuzzy logic controller (GT2FLC) for benchmark plants are presented. The advantage of using generalized type-2 fuzzy logic in fuzzy controllers is verified with four benchmark problems. We considered different levels of noise, number of alpha planes and four types of membership functions in the simulations for comparison and to analyze the approach of generalized type-2 fuzzy logic systems when applied in fuzzy control.