Multi-Objective Optimisation for Fuzzy Modelling using Interval Type-2 Fuzzy Sets

This paper reports on a new Mamdani data-driven fuzzy modelling approach, which makes use of interval type-2 fuzzy sets and employs a multi-objective evolutionary algorithm to optimise the structure and parameters of interval type-2 fuzzy models with respect to the predictive accuracy and the complexity of fuzzy models. In order to reduce the computational burden of the interval type-2 fuzzy modelling, a computationally efficient type-reduction technique is developed based on the center-of-sums defuzzifier. As the clustering-based method is utilised to elicit the initial fuzzy model, a new objective function is also introduced to improve the distribution of membership functions in each variable domain. The proposed modelling approach is then tested on a benchmark problem, where it is shown to be able to conduct an interpretable interval type-2 fuzzy model while maintaining a good predictive accuracy. This approach is also applied to the problem of prediction of the mechanical properties of alloy steels, and is shown to perform well.