An enhanced fuzzy credibility bidirectional projection based multi-attribute group decision making and its application in sports equipment supplier selection.

This study proposes an enhanced fuzzy credibility bidirectional projection (FC-BP) approach for multi-attribute group decision-making (MAGDM), with a practical application to sports equipment supplier selection (SSES). First, the fundamental definitions and operational rules of fuzzy credibility numbers (FCNs) are reviewed and extended, introducing the concepts of information energy and module to establish a bidirectional projection measure tailored to FCNs. Second, a combined weighting mechanism is developed by integrating subjective weights with objective weights derived from both the entropy method and the Method based on the Removal Effects of Criteria (MEREC), guided by the Minimum Identification Information Principle (MIIP). Additionally, cumulative prospect theory (CPT) is incorporated to reflect decision-makers' psychological preferences, thereby enhancing the behavioral rationality of the model. Compared with existing approaches (e.g., FCNWAA, FCNWGA, FCDWG), the proposed method demonstrates significant advantages in modeling credibility, capturing behavioral biases, and ensuring ranking robustness. Finally, an empirical example involving SSES is presented to validate the effectiveness and practical applicability of the proposed MAGDM technique under uncertain information and group behavior scenarios.