Automatic generation of type-1 and interval type-2 membership functions for prediction of time series data

Abstract

The use of type-1 or type-2 membership functions in fuzzy systems offers a wide range of research opportunities. In this aspect, there are neither formal recommendations, methods that can help to decide which type of membership function should be chosen nor has the process of generating these membership functions been formalized. Against this background, this paper describes a study comparing the results of employing both a Genetic Algorithm and a Simulated Annealing for automatic generation of type-1 and interval type-2 membership functions. The paper also describes tests with different degrees of uncertainty inherent both to the input data and the fuzzy system rules. Experiments were conducted to predict the Mackey-Glass time series and the results were verified using statistical tests. The data obtained from statistical analysis can be used to determine which type of membership function is most appropriate for the problem.