Sum of Certainties with the Product of Reasons: Neural Network with Fuzzy Aggregators

The paper attempts to bridge the gap between widely accepted models of biological systems based on the Tsetlin automata acting in random environment and traditional artificial neural networks that consist of the McCalloch and Pitts neurons. Using recently developed algebra with uninorm and absorbing norm aggregators, we consider the neurons as extended Tsetlin automata that implement multi-valued not-xor operator applied to the aggregated inputs and internal states, and then construct the network using these neurons. The inputs of the neurons are specified by the synapses that implement multi-valued joined and and or operations. We demonstrate that for favorable (in the sense of learning) states the suggested neurons act similarly to the traditional neurons, while for unfavorable states they immediately change their activity to the reverse one. Such properties of the neurons both results in the correct activity of the network and demonstrates better correspondence with the logics of natural neural networks.