ABSTRACT

This presentation explores the dynamic fusion of AI, Applied Mathematics, and Granular Computing to address complex challenges. Key projects illustrate the foundational role of rough set theory (RST) in big data analytics, with granular computing leveraging both RST and fuzzy set theory for precise topological and computational analyses. By addressing inconsistencies in classical models, we propose predictive intelligence as an effective solution for informed decision-making and forecasting, made more robust through neurowavelet methods that combine neural networks and wavelet analysis to accurately capture time-series dynamics in the time-frequency domain. We present several practical applications, including an AI-driven algorithm for analyzing earthquake events in China, underscore this approach’s impact. This algorithm, which blends finite element and framelet collocation methods, categorizes seismic events and provides a stable framework for earthquake prediction. We also introduce an innovative approach by integrating Granular Computing (GRC) and Topology-Based Approximate Arithmetic, inspired by human cognition’s hierarchical processing. This approach mitigates challenges in numerical computing, such as rounding errors, through granular operations and semi-group structures, thus enhancing precision in data handling. Finally, we highlight future research directions aimed at refining GRC structures and granular arithmetic models, fostering interdisciplinary collaboration to drive advancements across multiple fields.