This work proposes a hybrid decision making model for dynamic and irregularly connected communication systems called Delay-Tolerant Networks (DTNs). A resilient and adaptable network allows for communication in an environment where traditional networks may fail to operate effectively. The main significance of this system is that it is commonly utilized in such scenarios where traditional networks are impractical, such as remote areas, disaster-stricken regions, space missions, and military operations. The proposed model includes the “Multi-Attributive Border Approximation Area Comparison” (MABAC) method, together with Bipolar Complex Fuzzy Dombi Heronian Mean (BCFDHM) operators. To take the positive as well as negative attributes’ evaluations into consideration in complicated fuzzy environments, we use an enriched aggregation structure for the criteria, which incorporates the relationship between criteria through the Heronian mean function. Due to this, the MABAC technique within BCF information is more advanced and better than classical MABAC techniques in various models. After that, with the help of these enriched aggregation structures, we successfully identify and rank alternatives for DTN in an uncertain, imprecise, and bipolar condition. By employing the MABAC technique for the DTN system, we find the best and better alternative to the DTN system, which is Ã4 as mentioned below in section 4. At last, we compare our initiated work with many existing theories to prove the authenticity of the suggested work.

The current definition of the Complex Hesitant Fuzzy Set (CHFS), derived from the Ramot form of complex numbers, cannot process information as in Tamir’s complex fuzzy form. We have data with uncertainty and extra information that cannot be described by any other structure than Tamir’s complex fuzzy form. Hence, in this article, we initiated the idea of CHFS based on Tamir’s complex fuzzy form and established its operational laws. Since Decision-Making (DM) theory is central to nearly all disciplines, we have proposed a novel complex hesitant fuzzy Multi-Criterion Decision-Making (MCDM) model. This method can handle all sorts of real-life MCDM problems, where the data contains uncertainty, hesitancy, and extra fuzzy information. While developing this method, we also develop and apply Dombi aggregation operators in this manuscript. After that, we discussed a case study that concerns energy storage system selection for AI-controlled microgrids and discussed how the theory we have developed can be applied to real-world challenges. Last, we conferred on how this proposed theory is superior to other theories and why it should be adopted.

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.