Generalization of adaptive neuro-fuzzy inference systems

The paper aims at several objectives, The adaptive network-based fuzzy infe rence 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 lo cal model, a property of TS-model, and the index of fuzziness, a property o f 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 par ameters. The architecture of the GRBF network is devised to learn the param eters 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 reduc ed to either the standard RBF or the Hunt's RBF network. The issue of the n ormalized versus the nonnormalized GRBF networks is investigated in the con test of GANFIS, An interesting property of symmetry on the error surface of GRBF network is investigated in the present work, The proposed GANFIS is a pplied for the modeling of a multivariable system like stock market.