Linear Equation Systems Under Uncertainty: Applications to Multiproduct Market Equilibrium

Market equilibrium models are essential tools within classical economic theory for analyzing the interaction between supply and demand. However, traditional formulations are often based on deterministic relationships and assume the existence of perfect information, an assumption that diverges from real-world conditions, which are characterized by ambiguity and uncertainty. This article addresses the modeling of multiproduct supply and demand equilibrium under uncertainty, using systems of linear equations with fuzzy coefficients and/or variables. By applying fuzzy set theory, the model incorporates the inherent vagueness of supply and demand functions, enabling a more flexible and realistic representation of market behavior. The proposed methodology involves reformulating the equilibrium conditions through fuzzy arithmetic and examining the existence and nature of fuzzy solutions. The theoretical proposals are illustrated through a simplified real-world case involving a Colombian multinational company, demonstrating their applicability and effectiveness.