The hesitant fuzzy group decision matrix.

Probabilistic hesitant fuzzy sets (PHFSs) are superior to hesitant fuzzy sets (HFSs) in avoiding the problem of preference information loss among decision makers (DMs). Owing to this benefit, PHFSs have been extensively investigated. In probabilistic hesitant fuzzy environments, the correlation coefficients have become a focal point of research. As research progresses, we discovered that there are still a few unresolved issues concerning the correlation coefficients of PHFSs. To overcome the limitations of existing correlation coefficients for PHFSs, we propose new correlation coefficients in this study. In addition, we present a multi-criteria group decision-making (MCGDM) method under unknown weights based on the newly proposed correlation coefficients. In addition, considering the limitations of DMs’ propensity to use language variables for expression in the evaluation process, we propose a method for transforming the evaluation information of the DMs’ linguistic variables into probabilistic hesitant fuzzy information in the newly proposed MCGDM method. To demonstrate the applicability of the proposed correlation coefficients and MCGDM method, we applied them to a comprehensive clinical evaluation of orphan drugs. Finally, the reliability, feasibility and efficacy of the newly proposed correlation coefficients and MCGDM method were validated.

概率犹豫模糊集（Probabilistic hesitant fuzzy sets, PHFSs）在避免决策者（decision makers, DMs）间偏好信息丢失问题上，相较于犹豫模糊集（Hesitant fuzzy sets, HFSs）更具优势。正因具备这一优势，PHFSs已得到广泛研究。在概率犹豫模糊环境下，相关系数成为研究热点。随着研究的不断推进，我们发现当前针对PHFSs相关系数的研究仍存在若干未解决的局限。为克服现有PHFSs相关系数的缺陷，本文提出了新型相关系数。此外，基于所提新型相关系数，我们构建了一种权重未知的多准则群决策（multi-criteria group decision-making, MCGDM）方法。考虑到决策者在评估过程中倾向于使用语言变量进行表达的局限，我们在上述新型MCGDM方法中提出了一种将决策者语言变量评估信息转换为概率犹豫模糊信息的方法。为验证所提相关系数与MCGDM方法的适用性，我们将其应用于罕见病药物的综合临床评估场景。最终，验证了所提相关系数与MCGDM方法的可靠性、可行性与有效性。