Multi-criteria group decision-making (MCGDM) approaches have a substantial effect on decision-making in a range of critical sectors, including science, business, and real-life research. These strategies also efficiently assist researchers in resolving challenges that may arise throughout their study activity. The current work's major purpose is to research and develop the combinative distance-based assessment (CODAS) approach by employing 2-tuple linguistic $q$-rung picture fuzzy sets (2TL $q$-RPFSs) as a background. The CODAS technique computes the distances from the negative ideal solutions and ranks the alternatives in increasing order. To compute the normal weights of attributes, the entropy weighting information process is used. Furthermore, two aggregation operators, namely the 2-tuple linguistic $q$-rung picture fuzzy Einstein weighted average and the 2-tuple linguistic $q$-rung picture fuzzy Einstein order weighted average, are introduced. Our inspiration for employing the notion of 2TL $q$-RPFSs is the ability of $q$-RPFSs to support a wide range of information and the significant qualities of 2-tuple linguistic term sets to handle qualitative data. Congested transportation networks may be made more efficient by leveraging digital transformation. Real-time traffic management is one solution to the problem of road congestion. As a result of connected autonomous vehicle (CAV) advances, the benefits of real-time traffic management systems have grown dramatically. CAVs can help manage traffic by acting as enforcers. To complement the extended approach, the proposed technique is used to select the best alternative for a real-time traffic management system. The performance of the suggested technique is validated using scenario analysis. The results show that the suggested strategy is efficient and relevant to real-world situations.

A directed rough fuzzy graph (DRFG) is a unique and innovative hybrid model because it deals with more complex problems of uncertainty in the presence of incomplete data information or rough universe. A DRFG can be obtained from two given DRFGs by union, Cartesian product and composition. When we study operations for DRFGs with a large number of vertices, the degree of vertices in a DRFG presents a confusing picture. Therefore, a mechanism for determining the degree of vertices for DRFG operations is needed. The main objective of this study is to analyze and investigate the degree of vertices in DRFGs formed by certain operations, which will provide clear explanations of operations on DRFGs and their effects on vertex degrees with examples. In this paper, we find the degree of a vertex in DRFGs formed by these operations in terms of the degree of vertices in the given DRFGs in some special cases. We explain these operations with some examples. In addition, we provide an application to the corporate merger problem to test our approach and obtain an optimal result. We have developed two algorithms to elaborate the procedure for our application. Finally, we created a comparison table comparing our results for Algorithms 1 and 2 for the same enterprise merger network.