3W-SLP: A Conceptual Model of Three-Way Single Layer Perceptrons

This study introduces a novel conceptual model, the three-way single layer perceptron (3W-SLP), positioned as fundamental components of artificial neural networks. Existing commonly-used perceptrons yield either two-valued outputs with hard limiting thresholding functions or continuous outputs with sigmoid and logistic functions. While the former facilitates straightforward interpretation, it confines single perceptrons to linearly separable datasets and lacks a mechanism for expressing uncertainty. Conversely, continuous outputs enhance capabilities of single perceptrons but increase complexity in interpretation. This work proposes an intermediate solution, the 3W-SLP, where three-valued outputs are generated by incorporating two thresholds into the activation functions. In comparison to two-valued outputs, the addition of a third value provides a means to represent uncertainty without significantly increasing the interpretation complexity. Moreover, this third value enables 3W-SLP to handle linearly separable datasets. This work focuses on the conceptualization of 3W-SLP, including its formulation and learning processes. This groundwork establishes a foundation for subsequent experimental analyses, laying the path for future explorations and applications.