A hybrid method for IT2 TSK formation based on the principle of justifiable granularity and PSO for spread optimization

In this paper, a new hybrid method for forming interval type 2 fuzzy inference systems (IT2 FIS) is shown. This methodology builds upon an existing type 1 fuzzy inference system (T1 FIS) or from the output centers from any clustering algorithm, calculating the footprint of uncertainty (FOU) based on the implementation of the principle of justifiable granularity, and finally a particle swarm optimization algorithm (PSO) optimizes the spreads from First Order Takagi-Sugeno-Kang (TSK) type consequents to improve the coverage of the FOU. Focusing mainly in the coverage of the FOU, two datasets are used to demonstrate the effectiveness of FOU coverage in environments with noise, especially when the noise is on the outputs. These two datasets are a simple Fifth Order curve, and the iris benchmark dataset.