A method for deriving the analytical structure of the TS fuzzy controllers with two linear interval Type-2 fuzzy sets for each input variable

Type-2 fuzzy controllers have been mostly viewed and treated as black boxes in that their input-output mathematical mappings (i.e., analytical structures) are unknown. In contrast, this is never the case for any conventional controller. In this paper, we show an innovative analytical structure derivation technique for the interval Type-2 TS fuzzy controllers whose configurations are as follows: two input variables, two linear input fuzzy sets for each input variable, linear TS fuzzy rules, Zadeh AND operator, the Karnik-Mendel center-of-sets type reducer, and the centroid defuzzifier. Revealing the analytical structure of any Type-2 fuzzy controller, this one included, is important as it can lead to better understanding of the controller and more productive analysis and design of the Type-2 fuzzy control system.