Error Optimization of Fuzzy Transform Using Evolution Algorithms
František Huňka, Viktor Pavliska · 2008
Fuzzy transform is a transform that considerably simplifles solution of difierential or integral-difierential equations, by transforming them into a n-dimensional vectors that are easier to solve. The inverse fuzzy transform transforms the achieved results back into the original domain creating thus an approximated function of the original one. As the other approximations it also works with some level of error. With the F-transform the level of error is mainly caused by the distribution of the nodes in the searching area. Before the fuzzy transform starts, the universe has to be partitioned by the nodes. The main aim of the article is to propose and verify optimization of node distribution with respect to objective functions such that the difierence between original and approximated function would be minimal. The article further discusses other possibilities of the distribution of the nodes as well as difierent heuristics, which may be used in flnding the best distribution of the nodes so as the approximation error would be minimal. By this way the approximated function would be more closer to the original one.