In fuzzy decision-making problems, existing fuzzy decision-making methods only indicate fuzzy assessment values but lack the degrees/levels of credibility regarding the fuzzy assessment values in alternatives over attributes due to the vagueness and uncertainty of human cognitions/judgments for complicated decision-making problems. Therefore, the credibility degree of the fuzzy assessment value shows its importance and necessity in the fuzzy decision-making problem. To enhance the credibility degrees/levels of fuzzy assessment values, the fuzzy assessment values should be closely related to their credibility measures, which make the assessment information more abundant and more credible. Hence, this study proposes the concept of a fuzzy credibility number (FCN) as a new extension of the fuzzy concept, where both a fuzzy value and a credibility degree are expressed by a pair of fuzzy values. Then, we present operations of FCNs, a score function of FCN, a FCN weighted arithmetic averaging (FCNWAA) operator, and a FCN weighted geometric averaging (FCNWGA) operator. Next, a multi-attribute decision-making (MADM) approach using the FCNWAA or FCNWGA operator is established to deal with MADM problems in the setting of FCNs. Eventually, the established MADM approach is used for a decision-making example on selecting a suitable slope design scheme for an open pit mine in the setting of FCNs to reflect the usability and effectiveness of the established decision-making approach. Compared with the classical fuzzy MADM approach, the established MADM approach makes the assessment information more abundant and more credible, then the sensitivity analysis indicates the importance and efficiency of credibility measures in the ranking order of alternatives, which reflect main advantages of the established MADM approach in the environment of FCNs. However, this study reflects the novelty and new contribution of the proposed information expression and aggregation operations and decision-making method in fuzzy decision theory and methods.

在模糊决策问题中，由于人类对复杂决策的认知/判断的模糊性和不确定性，现有的模糊决策方法仅指示模糊评估值，而缺乏对属性备选方案中模糊评估值的可信度/水平。制造问题。因此，模糊评估值的可信度说明其在模糊决策问题中的重要性和必要性。为了提高模糊评估值的可信度/水平，模糊评估值应与其可信度度量紧密相关，从而使评估信息更加丰富和可信。因此，本研究提出了模糊可信度数（FCN）的概念，作为模糊概念的新扩展，其中模糊值和可信度均由一对模糊值表示。然后，我们介绍了 FCN 的操作、FCN 的评分函数、FCN 加权算术平均 (FCNWAA) 算子和 FCN 加权几何平均 (FCNWGA) 算子。接下来，建立使用 FCNWAA 或 FCNWGA 算子的多属性决策（MADM）方法来处理 FCN 设置中的 MADM 问题。最后，将已建立的 MADM 方法用于在 FCN 设置中为露天矿选择合适的边坡设计方案的决策示例，以反映已建立的决策方法的可用性和有效性。与经典的模糊 MADM 方法相比，建立的 MADM 方法使评估信息更加丰富和可信，然后敏感性分析表明可信度措施在备选方案的排名顺序中的重要性和效率，这反映了已建立的 MADM 方法在 FCN 环境中的主要优势。然而，这项研究反映了所提出的信息表达和聚合操作以及模糊决策理论和方法中的决策方法的新颖性和新贡献。