A q-rung orthopair fuzzy decision-making framework considering experts trust relationships and psychological behavior: An application to green supplier selection

Theselection of an optimal supplier is a critical and open challenge in supplychain management. While experts' assessments significantly influence thesupplier selection process, their subjective interactions can introduceunpredictable uncertainty. Existing methods have limitations in effectivelyrepresenting and handling this uncertainty. The paper aims to address thesechallenges by proposing a novel approach that leverages q-rung orthopair fuzzysets (q-ROFSs). The novelty of the proposed approach lies in its ability toaccurately capture experts' preferences through the use of q-ROFSs, which offermembership and non-membership degrees, providing a broader expression spacecompared to conventional fuzzy sets. Additionally, it incorporates social networkanalysis (SNA) to effectively consider the trust relationships among experts.The proposed approach is divided into three stages. The first stage presents anovel method to determine experts' weights by combining SNA, the Bayesianformula, and the maximum entropy principle. This approach allows for a moreprecise representation of varying levels of expertise and influence amongexperts, addressing the uncertainty arising from subjective interactions. Thesecond stage introduces a hybrid weight determination method to determinecriteria weights within the context of q-ROFSs. Entropy plays a crucial role incapturing fuzziness and uncertainty in q-ROFSs, while the projection measuresimultaneously provides information about the distance and angle between alternatives.By employing both objective weights estimated using entropy and normalizedprojection measure and subjective weights derived using an aggregation operatorand a score function, the presented approach achieves a comprehensiveassessment of criteria importance. To incorporate both subjective and objectiveweights effectively, game theory is applied which allows us to aligndecision-making with both quantitative and qualitative aspects, making themethod more versatile and applicable. The third stage redefines thetraditional Combined Compromise Solution (CoCoSo) method using Bonferroni meanoperators which captures interrelationships among arguments to be aggregated. Furthermore, in recognition of theimportance of an expert risk preferences and psychological behaviors, we applyregret theory, ensuring that the chosen solutions align more effectively withtheir underlying preferences and aspirations. The applicability andeffectiveness of the proposed approach are demonstrated through a numericalexample of green supplier selection. The comparative analysis illustrates thepracticality and real-world relevance while the sensitivity analysis confirmsthe stability and robustness of the proposed approach.