Fuzzy decision mapping for explainable artificial intelligence: a mathematical model

Abstract

In this work, a mathematical model is developed to represent decision-making processes in Artificial Intelligence systems using Fuzzy Set Theory. The work addresses the challenge of uncertainty and imprecision in real-world decision parameters and aims to enhance the interpretability of Artificial Intelligence reasoning in complex environments. The proposed approach integrates fuzzy inference mechanisms into AI architectures, allowing linguistic concepts such as reliability, priority, and risk to be translated into quantitative decision weights. The model formulation includes the construction of membership functions and fuzzy rules that reflect human-like reasoning patterns. Experimental evaluation shows that the fuzzy-based framework provides more stable and interpretable decision outputs compared to traditional crisp algorithms, especially when input data are incomplete or ambiguous. The findings indicate that fuzzy mathematical structures can effectively support Artificial Intelligence systems in producing transparent and robust decisions. These results suggest that the model is suitable for Artificial Intelligence-driven decision support applications where interpretability under uncertainty is a fundamental requirement.