Generalization of adaptive neuro-fuzzy inference systems

The paper aims at several objectives. The adaptive network-based fuzzy inference systems (ANFIS) of Jang 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. A local model, a property of TS-model, and the index of fuzziness, a property of CRI-model define the consequent part of a rule of GFM. 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, since it has been proved in this paper that GRBF network and GFM are 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 nonnormalized GRBF networks is investigated in the context of GANFIS. An interesting property of symmetry on the error surface of GRBF network is investigated in the present work. The proposed GANFIS is applied for the modeling of a multivariable system like stock market.