A Simplified Method of FOU Design Utilising Simulated Annealing

The main feature of type-2 fuzzy sets is their ability to represent uncertainties within a system. These uncertainties are captured in the Footprint Of Uncertainty (FOU) of a type 2 membership function which can be described by the upper and the lower membership function. One of the challenges in modelling a type-2 fuzzy logic system is the problem of defining the membership function parameters and their FOUs, given noisy data or imperfect measurements. This challenge is increased by the complexity which arises from the increase in the number of parameters of IT2 MFs to be tuned. This paper presents a novel method for designing interval type-2 fuzzy logic systems, in which the FOU creation method presented in [1] is adopted, and then the design parameters are tuned through simulated annealing. The novelty of this approach is that it has fewer parameters to be tuned than the conventional approach, as only a single extra parameter is used to define the IT2 MFs. We demonstrate the approach through application to the Mackey-Glass time series prediction problem, using training data sets corrupted with different levels of noise. By doing so, we demonstrate that this approach is an efficient FOU selection mechanism that produces IT2 FLSs with good performance using less computational time than the conventional approach.