The rapid growth of Internet of Things (IoT) technologies has made real-time data processing a critical component for efficient monitoring, analysis, and intelligent decision-making in dynamic and large-scale environments. IoT systems continuously generate massive volumes of heterogeneous data that must be processed with minimal latency to ensure timely responses and reliable system performance. Effective real-time data processing enables IoT applications to adapt to changing conditions, enhance operational efficiency, improve safety and reliability, and support time-sensitive services in domains such as smart cities, healthcare monitoring, industrial automation, and intelligent transportation systems. This study presents a comprehensive mathematical framework for the analysis of real-time data processing methods for IoT applications based on hesitant bipolar fuzzy (HBF) Dombi power operators. The proposed model is designed to effectively capture uncertainty, hesitation, and bipolar information that naturally arise in real-world IoT environments due to incomplete, imprecise, and conflicting data sources. By incorporating a multi-criteria decision-making (MCDM) approach, multiple real-time data processing techniques are systematically evaluated and prioritized with respect to several performance-related attributes. The proposed HBF Dombi power-based framework offers a reliable and transparent mechanism for comparing competing real-time data processing strategies and selecting the most suitable method for specific IoT scenarios. The results indicate that the proposed approach improves decision accuracy and supports better alignment between data processing methods and the complex operational requirements of modern IoT systems. This work contributes both theoretical insights and practical guidance for the design and evaluation of efficient, adaptive, and intelligent real-time IoT data processing architectures.