## 1 Introduction  
Configuring safety measures for the process systems is a crucial means to preventing and reducing the failure risk. These safety measures are generally called safety barriers (SBs). There are a variety of SBs in process systems, like corrosion detection devices, relief valves, flammable gas detective and alarm systems, and fire extinguishing apparatus. Different SBs have different functions and effects, which raises the important question of how well these SBs protect the system from failure threats, and which SBs are more effective. If these questions can be answered well, then a more reasonable configuration strategy for SBs may be devised according to their effectiveness. Therefore, how to evaluate the effectiveness of SBs has become a significant issue for system safety management. There are several analysis approaches for SBs in process systems at present, such as the Swiss cheese model [1], safety barrier diagram (SBD) [2], barrier and operational risk analysis (BORA) [3], layer of protection analysis (LOPA) [4], fault tree analysis (FTA), event tree analysis (ETA) [5], Petri nets [6], Bayesian networks [7], and the bow-tie (BT) model [8]. Among these approaches, the BT model has attracted great attention due to its integration of FT and ET, which can intuitively and clearly describe system failure scenarios and the roles of SBs. According to its use, the BT model can be used for qualitative and quantitative analyses. The former is primarily used to identify which basic events or combinations will lead to the final accident, as well as to help engineers understand the nature and functions of SBs. However, the qualitative analysis cannot quantify the influence degree of SBs on system failure. Fortunately, the latter can reach such a goal as long as all the data associated with the occurrence probabilities of basic events with or without SBs can be obtained. The quantitative BT analysis cannot be separated from high-quality and sufficient data. But in practice, things often go contrary to our wishes. On the one hand, because of the insufficient knowledge of the system, the parameters used in the BT model (like failure probability data) may be inaccurate and incomplete; on the other hand, the complexity of the system and its behavior often result in the simplification of the assumptions in the analysis process [9]. All these uncertainties can negatively affect the availability and credibility of BT analysis. Therefore, in order to mitigate this issue, several approaches have been proposed to handle uncertainty data, such as fuzzy set theory (FST), evidence theory, and rough set theory [10; 11]. Among these, FST has been broadly applied in the BT model for risk assessment because of its complete theoretical basis and good usability. [PERSON] et al. [12] proposed a probability assessment method that combined FST, BT analysis, and Bayesian updating technology to assess accidents in natural gas distribution station systems. [PERSON] [13] applied the Z-number to the FT to investigate the server failure consequences of hydrocarbon storage tanks. [PERSON] et al. [14] applied a risk analysis framework of a fuzzy BT model for maritime transportation. [PERSON] [15] combined the BT model and type-2 fuzzy set for risk quantification. [PERSON] [16] carried out a static electricity risk failure analysis of oil tankers using the BT model with fuzzy logic and CREAM. To a certain extent, a fuzzy BT model can handle uncertainty effectively during analysis, but the traditional FST still has its limitations. The membership degree of the elements in a certain set is a value in the range of [0, 1] for FST. Therefore, the membership value simply indicates the degree to which the element belongs to the set, and it cannot take into account the non-membership degree originated from experts' lack of knowledge or hesitancy. To overcome this issue, [PERSON] [17] proposed the intuitionistic fuzzy set (IFS) theory.