Generalization of adaptive neuro-fuzzy inference systems

The adaptive network-based fuzzy inference systems (ANFIS) of Jang (1993) is extended to the generalized ANFIS (GANFIS) by proposing a generalized fuzzy model (GFM) and considering a generalized radial basis function (GRBF) network. The GFM encompasses both the Takagi-Sugeno (TS)-model and the compositional rule of inference (CRI) model. The conditions by which the proposed GFM converts to TS-model or the CRI-model are presented. The basis function in GRBF is a generalized Gaussian function of three parameters. The architecture of the GRBF network is devised to learn the parameters of GFM, where the GRBF network and GFM have been proved to be functionally equivalent. It Is shown that GRBF network can be reduced to either the standard RBF or the Hunt´s RBF network. The issue of the normalized versus the non-normalized GRBF networks is investigated in the context of GANFIS. An interesting property of symmetry on the error surface of GRBF network is investigated. The proposed GANFIS is applied to the modeling of a multivariable system like stock market.