Multi-species PSO and fuzzy systems of Takagi–Sugeno–Kang type

We study a method by using the Hierarchical Cluster-based Multi-Species Particle Swarm Optimization (HCMSPSO) algorithm to generate a Tagaki–Sugeno–Kang (TSK-) fuzzy system implemented in a spatial analysis problem. Precisely we consider an area of study divided in subzones: from the data measured in each subzone a TSK-fuzzy system is extracted and hence we associate an opportune Root Means Square Error (RMSE). If the hth and kth subzones have a defined suitably similarity index Shk greater or equal than a specific threshold Sthreshold, then they are merged in a new subzone and the corresponding datasets are grouped together in a single dataset, thus we restart the HCMSPSO algorithm for generating the TSK-fuzzy system of the new subzone. This process is iterated until we have that Shk < Sthreshold for all hth and kth adjacent subzones. Since we are interested to analyze whether or not the distribution of the pattern data in the final subzones is approximately uniform, a thematic map is produced in which these subzones are classified in accordance to of the Normalized Root Mean Square Error (NRMSE) or the Coefficient of Variation of the RMSE error (CVRMSE).