To solve the problem of choosing the appropriate cloud computing vendors in small and medium-sized enterprises (SMEs), this paper boils it down to a group decision making (GDM) problem. To facilitate the judgment, this paper uses preference relation as the decision making technology. Considering the situation where uncertain positive and negative judgments exist simultaneously, interval-valued intuitionistic fuzzy preference relations (IVIFPRs) are employed to express the decision makers’ judgments. In view of the multiplicative consistency and consensus analysis, a new GDM algorithm with IVIFPRs is offered. To accomplish this goal, a new multiplicative consistency is first defined, which can avoid the limitations of the previous ones. Then, a programming model is built to check the consistency of IVIFPRs. To deal with incomplete IVIFPRs, two programming models are constructed to determine the missing values with the goal of maximizing the level of multiplicative consistency and minimizing the total uncertainty. To achieve the minimum adjustment of original preference information, a programming model is established to repair inconsistent IVIFPRs. In addition, programming models for getting the decision makers (DMs)’ weights and improving the consensus degree are offered. Finally, a practical decision making example is given to illustrate the effectiveness of the proposed method and to compare it with previous methods.

中文翻译：

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具有区间值直觉模糊偏好关系的群决策方法及其在中小企业云计算供应商选择中的应用

为了解决中小企业（SME）选择合适的云计算供应商的问题，本文将其归结为一个群体决策（GDM）问题。为便于判断，本文采用偏好关系作为决策技术。考虑到不确定的正负判断同时存在的情况，采用区间值直觉模糊偏好关系（IVIFPRs）来表达决策者的判断。针对乘法一致性和一致性分析，提出了一种新的带有IVIFPR的GDM算法。为了实现这个目标，首先定义了一个新的乘法一致性，它可以避免以前的限制。然后，建立一个编程模型来检查 IVIFPR 的一致性。为了处理不完整的 IVIFPR，构建了两个编程模型来确定缺失值，目标是最大化乘法一致性水平并最小化总不确定性。为了实现对原始偏好信息的最小调整，建立了一个编程模型来修复不一致的IVIFPR。此外，还提供了用于获取决策者（DM）权重和提高共识度的编程模型。最后，给出了一个实际的决策例子来说明所提出方法的有效性，并与以前的方法进行比较。建立了一个编程模型来修复不一致的 IVIFPR。此外，还提供了用于获取决策者（DM）权重和提高共识度的编程模型。最后，给出了一个实际的决策例子来说明所提出方法的有效性，并与以前的方法进行比较。建立了一个编程模型来修复不一致的 IVIFPR。此外，还提供了用于获取决策者（DM）权重和提高共识度的编程模型。最后，给出了一个实际的决策例子来说明所提出方法的有效性，并与以前的方法进行比较。