# Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence
## 2 Literature Review
### Aggregation Experts'Preferences  
Generally, FMEA is teamwork-based and should be regarded as a group decision process [13]. It is imperative to use a suitable aggregation operator to aggregate the experts' preferences to form a group decision preference before obtaining the risk priority of failure modes.  
In the literature, various aggregation operators have been employed to aggregate the experts' preferences to construct a collective assessment matrix. For example, many researchers often utilize the arithmetic averaging operator, which assumes that the importance of each FMEA team expert is equal, to fuse the experts' preferences [14; 15; 16]. In reality, FMEA team experts come from different departments and industries, possess different backgrounds and expertise, and thus have different importance. The arithmetic averaging operator is highly simple but it does not reflect the important difference of experts.  
To handle this problem, the weighted averaging (WA) operator and its extended form have been employed by many researchers to form a group decision preference in FMEA risk assessment [17; 18; 19; 20; 21]. In addition, [PERSON] et al. [22] presented a hybrid FMEA risk evaluation model for assessing the risk of failure modes under an interval-valued intuitionistic fuzzy environment, which utilizes an order weighted averaging (OWA) operator to aggregate the experts' preferences.  
The WA operator and the OWA operator have their own advantages and disadvantages, which consider the importance of the input arguments themselves and their location, respectively. To synthesize the advantages of the WA and OWA operators, [PERSON] and [PERSON] [23] proposed a hybrid weighted averaging (HWA) operator, which can reflect both the given importance and the ordered position of the input arguments. Subsequently, [PERSON] et al. [24] presented an interval 2-tuple hybrid weighted averaging operator based on the HWA operator, and applied it to construct a collective evaluation matrix in FMEA risk assessment. Nevertheless, the above aggregation methods do not cover the interdependent relationships between the experts' preferences; they are only suitable to situations in which the input arguments are independent.  
The GBM operator has been focused on by many researchers in recent years because of its ability to capture the interdependent relationships between the input arguments. For instance, [PERSON] et al. [25] developed two new trapezoidal interval type-2 fuzzy GBM operators by extending the GBM operator to a trapezoidal interval type-2 fuzzy environment. [PERSON] [26] proposed some picture 2-tuple linguistic GBM operators, and applied these to handle multiple attribute decision-making problems. [PERSON] [27] presented a triangular fuzzy weighted Einstein GBM operator, and employed it to evaluate the psycholinguistic teaching effect. [PERSON] and [PERSON] [28] proposed the normal neutrosophic GBM operator and the normal neutrosophic weighted GBM operator, and also investigate their properties and special cases. In addition, the GBM operator has also been introduced into other fuzzy environments to fuse various fuzzy information [29; 30; 31; 32], such as Pythagorean fuzzy sets, interval-valued intuitionistic fuzzy sets, Pythagorean 2-tuple linguistic sets, and linguistic neutrosophic sets.