The material handling equipment (MHE) has a close connection with layout of machinery and plays the important role in productivity of servicing or manufacturing systems. Since each of MHE has distinct characteristics than the others with respect to conflicting criteria and design experts may state the different subjective judgments with respect to qualitative criteria, the material handling equipment selection problem (MHESP) can be taken into account as a group multi-criteria decision-making (GMCDM) problem. In this paper, a version of type-2 fuzzy sets (T2FSs), named Gaussian interval type-2 fuzzy sets (GIT2FSs), is first used as an alternative to the traditional triangular membership functions (MFs) to weight criteria and sub-criteria and also evaluate of alternatives with respect to sub-criteria. The synthetic value method of GIT2FSs is then carried out to convert the assessments stated as GIT2FSs for each alternative with respect to each sub-criterion and also weights of criteria (sub-criteria) into the single fuzzy rating and weight, respectively. Then, the fuzzy weighted average (FWA) approach is adopted to integrate the single fuzzy ratings of each alternative with respect to sub-criteria and the single fuzzy weights of sub-criteria under each criterion with the aggregated weighted ratings. In next stage, ELECTRE III (ELimination Et Choix Traduisant la Realite´—elimination and choice translation reality) is generalized with GIT2FSs to select the optimal MHE through a new ranking approach. Moreover, some arithmetic operations and properties are extended to GIT2FSs. In addition, to demonstrate its potential applications, the proposed methodology is implemented in a real case study and an illustrative example, and then, the ranking results are compared with those of the others in the literature. Finally, the sensitivity analysis is carried out to show robustness and stability of the obtained results.

物料搬运设备（MHE）与机械布局紧密相关，并且在维修或制造系统的生产率中起着重要作用。由于每个MHE在冲突标准方面都具有不同的特征，并且设计专家可能会就定性标准陈述不同的主观判断，因此可以将物料搬运设备选择问题（MHESP）视为一个多标准组。决策（GMCDM）问题。在本文中，首先使用一种类型为2的模糊集（T2FS），称为高斯区间类型2的模糊集（GIT2FSs），作为权重标准和子标准的传统三角隶属函数（MF）的替代方法并评估有关子标准的替代方案。然后执行GIT2FS的综合价值方法，以将关于每个子标准的每个备选方案的评估表示为GIT2FS，并将标准（子标准）的权重分别转换为单个模糊等级和权重。然后，采用模糊加权平均（FWA）方法将每个备选方案相对于子标准的单个模糊评级以及子准则在每个标准下的单个模糊权重与聚合加权评级进行集成。在下一阶段，将ELECTRE III（消除和选择翻译现实-消除和选择翻译现实）与GIT2FS结合使用，以通过新的排名方法选择最佳的MHE。此外，一些算术运算和属性已扩展到GIT2FS。此外，为了展示其潜在的应用，该建议的方法在一个实际案例研究和一个示例性例子中得以实现，然后将排名结果与文献中其他排名结果进行比较。最后，进行敏感性分析以显示所得结果的鲁棒性和稳定性。