Vertical Slice Based General Type-2 Fuzzy Reasoning and Defuzzification for Control Applications

Two well-known representations of Generalized Type-2 Fuzzy sets, such as the z-slice and the vertical slice, are prevalent in the literature. While the z-slice based model has shown promising performance in reasoning and control applications, the vertical slice based model, until this date, is restrictedly being used for reasoning with rules containing General type-2 propositions in the antecedent and Interval type-2 propositions in the consequent. This paper attempts to overcome this restriction by proposing a general framework for automated reasoning with rules containing Vertical Slice based General Type-2 propositions in both the antecedent and the consequent. Naturally, the inference is a Vertically Sliced General type-2 fuzzy set, which is type-reduced and then (type-1) defuzzified by a simple but elegant approach. The proposed Vertical slice based defuzzification is time-efficient in comparison to its z-slice based counterpart as the former requires type-1 centroidal defuzzification only in mu-mu plane, while the latter requires Karnik-Mendel defuzzfication over each z-slice. The proposed vertical slice based reasoning and defuzzification has successfully been applied in angular position control of an inverted pendulum system. Experiments undertaken confirms that the proposed vertical slice based controller outperforms the existing z-slice, Interval type-2 plus KM/CKM defuzzification, and other control strategies with respect to the settling time, peak-overshoot, and root-mean square error.