Multi-Attribute Decision-Making Based on Consistent Bidirectional Projection Measures of Triangular Dual Hesitant Fuzzy Set

To solve complex multi-attribute decision-making (MADM) problems within a triangular dual hesitant fuzzy (TDHF) environment where the attribute weights (Aws) are either fully or partially known, a novel bidirectional projection method is proposed, named multi-attribute decision-making and based on the consistent bidirectional projection measures of triangular dual hesitant fuzzy sets (TDHFSs). First, some notions are developed, such as the operation laws, score and accuracy functions, negative ideal points (NIPs), and positive ideal points (PIPs) of TDHFSs. The correlation coefficients and the cosine of the angle between the vectors of each alternative and the triangular dual hesitant fuzzy (TDHF) points are introduced. Then, the consistent bidirectional projection decision-making method based on the TDHFSs’ correlation coefficients is proposed. Additionally, an optimization model is established via maximizing the consistent coefficient to determine the Aws. Furthermore, some approaches are investigated based on the proposed approaches concerning the MADM issues with attribute values represented by triangular dual hesitant fuzzy elements (TDHFEs). Finally, a supply chain management (SCM) problem is illustrated, and comparative analyses are implemented to demonstrate the presented approach’s feasibility and efficiency.