Quantum-Inspired Mathematical Models for Complex Decision Systems

Page No.:15-29

Abstract

The increasing complexity of modern decision-making environments has challenged the effectiveness of classical mathematical models. Traditional probabilistic frameworks often struggle to represent uncertainty, ambiguity, contextual dependence, and nonlinear interactions among decision variables. Quantum-inspired mathematical models have emerged as a promising interdisciplinary approach that leverages mathematical principles derived from quantum theory without requiring quantum computing hardware. These models utilize concepts such as superposition, interference, entanglement, and contextuality to represent complex decision processes more accurately. This paper explores the theoretical foundations, mathematical structures, and applications of quantum-inspired decision models in complex systems. The study examines how quantum probability theory provides a more flexible representation of human cognition, organizational decision-making, financial forecasting, and artificial intelligence systems. Furthermore, the paper discusses mathematical formulations, implementation strategies, advantages, challenges, and future research directions. The findings suggest that quantum-inspired models offer significant potential for addressing uncertainty and dynamic interactions in complex decision environments, thereby contributing to the advancement of intelligent decision support systems.