From a Gaussian Mixture Model to Nonadditive Fuzzy Systems

This paper presents the formulation of nonadditive generalized fuzzy model (GFM) by using the framework of the Gaussian mixture model, which provides the membership functions for the input fuzzy sets. By treating the consequent part as a function of fuzzy measures, we derive its coefficients. The defuzzified output constructed from both the premise and consequent parts of the GFM rules takes the form of Choquet integral. The computational burden involved with the solution of lambda-measure is mitigated using Q-measure. This nonadditive fuzzy model is applied on two benchmark applications, and the results are found to be better than those obtained from the additive fuzzy models.