基于GRA-GCRITIC和改进加权双向投影的区间Fermatean模糊多属性群决策方法

针对司法案件决策环境的复杂性及评价信息的模糊性，提出一种基于GRA-GCRITIC（grey relational analysis-group criteria importance through intercriteria correlation）和改进加权双向投影的区间Fermatean模糊Hamacher-TODIM多属性群决策方法。首先考虑到各位专家对各评价方案下各指标评价信息的差异性，提出一种GRA-GCRITIC方法，该方法将灰色关联融入到CRITIC中，以确定指标综合权重比单一获取的指标权重更加客观可靠。其次，结合信任关系对加权双向投影法进行改进，兼顾主客观关系，利用专家个体与群体评价信息的隶属度及非隶属度矩阵间的相似度得到专家权重。最后，考虑到决策者的损失规避心理，将融合了Hamacher算子的TODIM方法拓展至区间Fermatean模糊环境中，通过具体算例可得到其综合优势度及排序，验证了所提方法的可行性及灵活性。

Interval-valued Fermatean fuzzy multi-attribute group decision-making method based on GRA-GCRITIC and improved weighted bidirectional projection

Aiming at the complexity of the judicial case decision-making environment and the fuzziness of evaluation information, this paper proposed an interval-valued Fermatean fuzzy Hamacher-TODIM multi-attribute group decision-making method based on GRA-GCRITIC and improved weighted bidirectional projection. Firstly, considering the differences in evaluation information of each index under each evaluation scheme by experts, this paper proposed a GRA-GCRITIC method, which integrated grey relation into CRITIC to determine the comprehensive weight of indicators more objectively and reliably than obtaining a single indicator weight. Secondly, considering the subjective and objective relationship, this paper used the trust relationship to improve the weighted bidirectional projection method. The approach utilized the similarity between the membership and non-membership degree matrices of expert individual and group evaluation information to obtain expert weights. Finally, considering the decision-maker''s loss aversion psychology, this paper extended the TODIM method, which incorporates the Hamacher operator, to an interval-valued Fermatean fuzzy environment. And a specific case used this method to obtain the comprehensive advantage and ranking. It verifies the feasibility and flexibility of the proposed method.