Fuzzy Neural Tree for Knowledge Modeling: a Probabilistic Possibilistic Framework

A novel fuzzy-neural tree (FNT) is presented, where each tree node uses a Gaussian as a fuzzy membership or possibility distribution in place of sigmoidal function in conventional neural networks. Although neural networks with Gaussian activation functions as well as different types of cooperative neuro-fuzzy systems have been extensively described in the literature, the FNT presented in this paper implies a novel type of cooperation between fuzzy logic and neural structure. The neurons of the neural tree perform fuzzy logic operations, and in contrast to existing neural systems, the parameters of the operations are established not by training from measured data, but by conditioning the neuron with the consistency condition of possibility theory being entirely independent of data. Therefore the FNT uniquely performs transparent knowledge-driven modeling of systems with arbitrary complexity, which is in contrast to data-driven modeling in the existing neural network and neuro-fuzzy systems cases, as well as the transparent knowledge-driven modeling of systems with restricted complexity in the case of the existing fuzzy logic applications. The novel FNT is described in detail pointing out its various potential utilizations, and exemplifying them by means of three computer experiments.