A certain flexibility of decision makers (DMs) is usually requisite for reaching the consensus in group decision making (GDM). When the judgments of DMs are expressed as fuzzy-valued quantities, the required flexibility has been shown. In this paper, we report a quantification approach to flexibility degrees (FDs) of fuzzy numbers and a consensus model in GDM with fuzzy-valued judgments. First, an axiomatic definition of FDs is proposed for fuzzy numbers. Based on a bounded positive scale, the novel formulae are constructed for quantifying the FDs of interval numbers, triangular fuzzy numbers (TFNs), and trapezoidal fuzzy numbers (TPFNs), respectively. The effects of the prototypical values of TFNs and TPFNs on the FDs are addressed. Second, by considering confidence levels and multiplicative reciprocity, the FD of triangular fuzzy multiplicative reciprocal preference relations (TFMRPRs) is calculated. A flexibility-degree-driven operator is provided to aggregate individual TFMRPRs. Third, the consensus degree of DMs is defined and a nonlinear optimization model is constructed to achieve the largest consensus degree. A new algorithm for the consensus model in GDM is elaborated on and the case study is made to illustrate the proposed method. Finally, the sensitivity of the centroid of TFNs on the final solution of a GDM problem is analyzed by numerical examples. The observations reveal that the position of the centroid plays a great role on the FD of TFNs.

决策者 (DM) 的一定灵活性通常是在群体决策 (GDM) 中达成共识所必需的。当 DM 的判断被表示为模糊值时，就显示了所需的灵活性。在本文中，我们报告了模糊数的灵活度 (FD) 的量化方法和具有模糊值判断的 GDM 中的共识模型。首先，提出了模糊数的 FD 的公理定义。基于有界正尺度，分别构建了用于量化区间数、三角模糊数 (TFN) 和梯形模糊数 (TPFN) 的 FD 的新公式。讨论了 TFN 和 TPFN 的原型值对 FD 的影响。其次，通过考虑置信水平和乘法互惠，计算三角模糊乘法互惠偏好关系（TFMRPRs）的FD。提供了一个灵活度驱动的运算符来聚合单个 TFMRPR。第三，定义DMs的共识度，构建非线性优化模型，实现最大的共识度。详细阐述了一种新的 GDM 共识模型算法，并通过案例研究来说明所提出的方法。最后，通过数值例子分析了 TFN 质心对 GDM 问题最终解的敏感性。观察结果表明，质心的位置对 TFN 的 FD 起着重要作用。定义DMs的共识度，构建非线性优化模型以达到最大的共识度。详细阐述了一种新的 GDM 共识模型算法，并通过案例研究来说明所提出的方法。最后，通过数值例子分析了 TFN 质心对 GDM 问题最终解的敏感性。观察结果表明，质心的位置对 TFN 的 FD 起着重要作用。定义DMs的共识度，构建非线性优化模型以达到最大的共识度。详细阐述了一种新的 GDM 共识模型算法，并通过案例研究来说明所提出的方法。最后，通过数值例子分析了 TFN 质心对 GDM 问题最终解的敏感性。观察结果表明，质心的位置对 TFN 的 FD 起着重要作用。