Asian Journal of Pure and Applied Mathematics

Environmental systems are inherently complex and uncertain, influenced by numerous interacting factors including weather variability, pollutant emissions, and human activities. Traditional deterministic modelling approaches often fail to capture both the random variability of these systems and the imprecision inherent in expert knowledge. This paper presents a comprehensive review and application of hybrid fuzzy–stochastic modelling techniques for environmental risk assessment and pollution prediction. Fuzzy logic provides a framework to incorporate qualitative and linguistic information, allowing expert judgments and regulatory standards to be expressed in interpretable terms such as “high risk” or “moderate contamination.” Stochastic mathematics captures random variations in environmental variables, representing uncertainty through probability distributions, simulations, and scenario analysis. The integration of these approaches enables dual representation of uncertainty, combining probabilistic risk assessment with qualitative reasoning, which enhances predictive accuracy and supports informed decision-making. The paper discusses practical applications across air and water pollution management, soil contamination, and climate-related risk assessment, highlighting the value of hybrid models in situations with incomplete data or high variability. Advancements in adaptive fuzzy rule-based systems, high-resolution stochastic simulations, and data-driven calibration techniques are examined, demonstrating how these innovations improve the responsiveness, flexibility, and interpretability of environmental models. Case studies illustrate the effectiveness of hybrid models in predicting urban air quality, contaminant transport in water bodies, and the impact of extreme environmental events. Finally, the paper identifies future research directions, including integration with real-time sensor data, multi-scale modelling, artificial intelligence optimisation, and enhanced visualisation techniques. Overall, the hybrid fuzzy–stochastic framework offers a robust and versatile tool for sustainable environmental management, providing decision-makers with comprehensive, interpretable, and actionable insights into complex environmental risks. The approach facilitates both immediate operational decisions and long-term planning, supporting the development of resilient, adaptive, and scientifically informed environmental policies.