Adaptive non-additive generalized fuzzy systems

An adaptive non-additive generalized fuzzy model (GFM) is presented in this paper using the framework of Gaussian mixture model (GMM) which provides the membership functions for the input fuzzy sets. By replacing the consequent part of the additive GFM rule by a non-additive function, we obtain the non-additive GFM. The coefficients of the non-additive function then become the fuzzy measures. The defuzzified output constructed from both the premise and consequent parts of the modified GFM rules in the wake of non-additiveness takes the form of Choquet fuzzy integral. The parameters of the premise and the consequent parts of the non-additive fuzzy rules are updated based on the estimation error on the arrival of each online data to make the system adaptive. The resulting adaptive non-additive fuzzy model is applied on two benchmark applications and the results demonstrate the advantage of the adaptive feature.