The rapid growth of the Internet of Things (IoT) has led to the deployment of vast sensor networks that collect, transmit, and analyze data in real time. However, these networks are inherently susceptible to various forms of uncertainty, including environmental noise, hardware faults, communication delays, and data loss. Traditional data processing and control mechanisms often fall short in effectively managing such uncertainties, which can significantly compromise decision-making and system performance. This study addresses the critical challenge of uncertainty in IoT sensor networks by developing and analyzing advanced mathematical models designed to quantify, manage, and mitigate these effects.

The primary objective of this research is to propose robust mathematical frameworks that enhance the reliability and accuracy of IoT sensor data under uncertain conditions. The study integrates probabilistic models, such as Bayesian networks and stochastic differential equations, with optimization techniques and fuzzy logic systems to capture both random and imprecise uncertainties. Furthermore, the work employs control theory, particularly model predictive control (MPC), to develop real-time response strategies for dynamically adjusting to varying degrees of uncertainty.

Simulation experiments were conducted on a representative smart city IoT infrastructure, including air quality and traffic monitoring systems, to evaluate the proposed models. The results demonstrate significant improvements in data reliability, anomaly detection, and system adaptability. Compared to conventional filtering and estimation methods, the proposed models reduced uncertainty impacts by up to 35%, while maintaining scalability and computational efficiency.