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.