LAUSR

In this paper, the main concepts of interval type-2 (IT2), generalized type-2 (GT2), and interval type-3 (IT3) fuzzy logic systems (FLSs) are mathematically and graphically studied. In representation approaches of fuzzy sets (FSs), the main differences between IT2, GT2, and IT3 fuzzy sets were investigated. For the first time, the simple Matlab Simulink and M-files by illustrative examples and symmetrical FSs are presented for the practical use of IT3-FLSs. The computations were simplified for the practical use of IT3-FLSs. By the use of various examples, such as online identification, offline time series modeling, and a robotic control system, the design of IT3-FLSs is elaborated. The required derivative equations are also presented to design the adaptation laws for the rule parameters easily in other learning schemes. Some simulation examples show that the designed M-files and Simulink work well and result in a good performance.