The hybrid of AHP and TOPSIS has led researchers to integrate the combination with different extensions of fuzzy sets. The recently developed three-dimensional spherical fuzzy set is an extension of the fuzzy set, which is effective in handling uncertainty and quantifying expert judgements. In this paper, a novel framework is elaborated which combines AHP and TOPSIS with a spherical fuzzy set. Spherical fuzzy AHP is used to calculate the spherical fuzzy weights of the criteria, while spherical fuzzy TOPSIS is used to find the final rank of the alternatives. A new spherical fuzzy geometric mean formula is proposed for calculating the spherical fuzzy criteria weights. A new eleven-point spherical fuzzy linguistic term scale is presented, which can be used by the experts to quantify the preference. The proposed framework is applied to an advanced manufacturing system selection problem with six evaluation criteria and four alternatives. It is found that spherical fuzzy AHP-TOPSIS is effective in handling uncertainty in decision making and leads to robust and competitive results compared with state-of-the-art multi-criteria decision-making (MCDM) approaches.

AHP和TOPSIS的混合使研究人员将组合与模糊集的不同扩展集成在一起。最近开发的三维球形模糊集是模糊集的扩展，可以有效地处理不确定性和量化专家判断。本文提出了一种新颖的框架，该框架将AHP和TOPSIS与球形模糊集相结合。球形模糊AHP用于计算标准的球形模糊权重，而球形模糊TOPSIS用于查找备选方案的最终等级。提出了一种新的球形模糊几何均值公式，用于计算球形模糊准则权重。提出了一种新的十一点球形模糊语言术语量表，专家可以使用它来量化偏好。所提出的框架应用于具有六个评估标准和四个替代方案的高级制造系统选择问题。研究发现，与最新的多准则决策方法相比，球形模糊AHP-TOPSIS可有效地处理决策中的不确定性，并能获得强大且具有竞争力的结果。