Controlled Fuzzy 2-Metric Spaces: A Soft Computing Framework with Dynamic Applications

In this article, we introduce the concept of a controlled fuzzy 2-metric space, formulated by incorporating three control functions that flexibly regulate the fuzzy distance relationships among triplets of points. This structure provides a flexible analytical tool for modeling systems influenced by uncertainty, interdependence, and approximate reasoning. We establish several fundamental properties of this structure and derive fixed-point results. To demonstrate its practical relevance, we apply the proposed framework to a dynamic market-equilibrium problem, in which agents’ interactions are governed by fuzzy relations and control-dependent adjustments. The study also discusses implications for soft computing and decision-making systems, highlighting the framework’s potential in modeling adaptive and uncertain environments.