An Enhanced Bidirectional Projection Approach for Fuzzy Credibility Multi-Attribute Group Decision Making: Application in Sports Equipment Supplier Selection

This article will introduce the fuzzy credibility bidirectional projection (BP) method and some important basic theories of fuzzy credibility set (FCS). Firstly, we reviewed the definition, operation rules, score function, and comparison methods of fuzzy credibility numbers (FCNs). In addition, in order to better integrate the fuzzy credibility evaluation information of multiple experts, we introduced two aggregation operators, such as FCNWAA and FCNWGA. Then, we proposed the concept of the module of FCS and introduced it into the BP method. Incorporating bounded rationality of decision-makers, we applied cumulative prospect theory (CPT) to this multi-attribute group decision-making (MAGDM) method. We employed the minimum identification information principle (MIIP) to integrate the entropy weight method with the method based on the removal effects of criteria (MEREC), alongside subjective weights, to determine decision attribute weights. This approach balances the subjective input of decision-makers with the significance of objective data, making it more applicable to real-world scenarios. Detailed calculation steps for this MAGDM technique are provided. Finally, we propose the MAGDM technique based on fuzzy credibility bidirectional projection method to selection of sports equipment suppliers (SSES) issue with fuzzy credibility information. This paper evaluates the effectiveness of the MAGDM technique by comparing it with the FCNWAA, FCNWGA, and FCDWG operators.