The selection of an optimal supplier is a critical and open challenge in supply chain management. While experts' assessments significantly influence the supplier selection process, their subjective interactions can introduce unpredictable uncertainty. Existing methods have limitations in effectively representing and handling this uncertainty. The paper aims to address these challenges by proposing a novel approach that leverages q-rung orthopair fuzzy sets (q-ROFSs). The novelty of the proposed approach lies in its ability to accurately capture experts' preferences through the use of q-ROFSs, which offer membership and non-membership degrees, providing a broader expression space compared to conventional fuzzy sets. Additionally, it incorporates social network analysis (SNA) to effectively consider the trust relationships among experts. The proposed approach is divided into three stages. The first stage, presents a novel method to determine experts' weights by combining SNA, the Bayesian formula, and the maximum entropy principle. This approach allows for a more precise representation of varying levels of expertise and influence among experts, addressing the uncertainty arising from subjective interactions. The second stage introduces a hybrid weight determination method to determine criteria weights within the context of q-ROFSs. Entropy plays a crucial role in capturing fuzziness and uncertainty in q-ROFSs, while the projection measure simultaneously provides information about the distance and angle between alternatives. By employing both objective weights estimated using entropy and normalized projection measure and subjective weights derived using an aggregation operator and a score function, the presented approach achieves a comprehensive assessment of criteria importance. To incorporate both subjective and objective weights effectively, game theory is applied which allows us to align decision-making with both quantitative and qualitative aspects, making the method more versatile and applicable. The third stage redefines the traditional Combined Compromise Solution (CoCoSo) method using Bonferroni mean operators which captures interrelationships among arguments to be aggregated. Furthermore, in recognition of the importance of an expert risk preferences and psychological behaviors, we apply regret theory, ensuring that the chosen solutions align more effectively with their underlying preferences and aspirations. The applicability and effectiveness of the proposed approach are demonstrated through a numerical example of green supplier selection. The comparative analysis illustrates the practicality and real-world relevance while the sensitivity analysis, confirms the stability and robustness of the proposed approach.

Uncertainty is an important factor in the decision-making process. Hesitant Pythagorean fuzzy sets (HPFS), a combination of Pythagorean and hesitant fuzzy sets, proved as a significant tool to handle uncertainty. Well-defined operational laws and attribute weights play an important role in decision-making. Thus, the paper aims to develop new Trigonometric Operational Laws, a weight determination method, and a novel score function for group decision-making (GDM) problems in the HPF environment. The approach is presented in three phases. The first phase defines new operational laws with sine trigonometric function incorporating its special properties like periodicity, symmetricity, and restricted range hence compared with previously defined aggregation operators they are more likely to satisfy the decision maker preferences. Properties of trigonometric operational laws (TOL) are studied and various aggregation operators are defined. To measure the relationship between arguments, the operators are combined with the Generalized Heronian Mean operator. The flexibility of operators is increased by the use of a real parameter λ to express the risk preference of experts. The second phase defines a novel weight determination method, which separately considers the membership and non-membership degrees hence reducing the information loss and the third phase conquers the shortcomings of previously defined score functions by defining a novel score function in HPFS. To further increase the flexibility of defined operators they are extended in the environment with unknown or incomplete attribute weights. The effectiveness of the GDM model is verified with the help of a supplier selection problem. A detailed comparative analysis demonstrates the superiority, and sensitivity analysis verifies the stability of the proposed approach.