OR/AND Neuron in Modeling Fuzzy Set Connectives

The paper introduces a neural network-based model of logical connectives. The basic processing unit consists of two types of generic OR and AND neurons structured into a three layer topology. Due to the functional integrity we will be referring to it as an OR/AND neuron. The specificity of the logical connectives is captured by the OR/AND neuron within its supervised learning. Further analysis of the connections of the neuron obtained in this way provides a better insight into the nature of the connectives applied in fuzzy sets by emphasizing their features of “locality” and interactivity. Afterward, we will study several architectures of neural networks comprising these neurons treated as their basic functional components. The numerical studies embrace both the structures formed by single OR/AND neurons and aimed at modeling logical connectives (including the Zimmermann-Zysno data set) and the networks representing various decision-making architectures. We will also propose a realization of a pseudo median filter in which the OR/AND neurons play an ultimate role.