Optimization method for membership functions of type-2 fuzzy systems based on the level of uncertainty applied to the response integration of modular neural network for multimodal biometrics

This research proposes a method for optimizing the membership functions of type-2 fuzzy systems based on their level of uncertainty. The proposed new method of optimization considers three different cases of uncertainty (Footprint of Uncertainty) and obtains an optimal type-2 fuzzy system. Such cases have been called Case 1, Case 2 and Case 3. The first case is distinguished by having the same footprint of uncertainty for all existing membership functions of the fuzzy system inputs. The second case has a different footprint of uncertainty for the different inputs. And finally, the third case, which has a different footprint of uncertainty for each membership function of each input. The experimental results were tested in modular neural networks for multimodal biometry.