Neurons and Neural Fuzzy Networks Based on Nullnorms

This paper suggests a new type of elementary unit for neural fuzzy networks based on the concept of nullnorm. A nullnorm is a category of fuzzy set-oriented operators that generalizes triangular norms and conorms. The new unit, called nullneuron, is a generalization of and or logic-based neurons parametrized by an element u, called the absorbing element. If the absorbing element u = 0, then the nullneuron becomes an and neuron and if u = 1, then the nullneuron becomes a dual or neuron. The paper also addresses two learning schemes for a class of hybrid neural fuzzy networks with nullneurons. The first scheme uses the gradient descent technique and the second reinforcement learning. Both learning schemes adjust not only the weights associated with the inputs of the nullneurons, but also the role of the nullneuron in the network (and or or) by individually adjusting the parameter u of each nullneuron. The neurofuzzy network presented here is more general than alternative approaches discussed in the literature because they allow different triangular norms in the same network structure. Experimental results show that nullneuron-based networks provide accurate results with low computational effort.