## 1 Introduction  
With the increasing demand for infrastructure construction, more and more long tunnels are being planned. The TBM construction method has been widely used in the construction of long tunnels because of its advantages of high tunnelling efficiency and good construction safety. However, these advantages can only be realized on the basis of correct TBM selection. When the TBM selection is wrong, TBM often has low tunnelling efficiency, frequent downtime and even casualties. For example, during the construction of the S tunnel in Japan, the open TBM frequently encountered the problem of jamming because of wrong TBM selection [1]. [PERSON] (2016) summarized the problems of TBM in the construction of a Himalayan tunnel and found that wrong TBM selection was the direct reason for the low tunnelling efficiency [2]. [PERSON] (2016) evaluated the performance and tunnelling efficiency of TBM when tunnelling in a fault fracture zone or soft surrounding rock, and the results showed that the New Australian Tunnelling Method (NATM) should be used instead of the TBM method in this stratum [3]. [PERSON] et al. (2016) believed that TBM selection is an important countermeasure to solve TBM problems in complex strata, fault fracture zones, high in situ stress rock mass and limited excavation conditions. [4]. Therefore, it is very important to construct a TBM selection decision-making model so as to select the correct TBM for construction conditions in the project planning stage. TBM construction involves construction management, geological conditions, adverse geology, rock-machine contact and electromechanical control. The most important of these are adverse geology and geological conditions. Geological conditions and adverse geology are difficult to quantify [5; 6; 7; 8; 9; 10]. Many researchers have made many efforts to solve this problem. [PERSON] (2004), based on the fuzzy concept, constructed a risk assessment methodology for an underground construction project [11]. [PERSON] (2011) proposed a fuzzy comprehensive evaluation method based on Bayesian networks to assess the risk of deep foundation pits [12]. [PERSON] (2015) analyzed the construction risk of slagging, clamping and cutter damage during shield tunnel construction by combining fault tree analysis with AHP [13]. [PERSON] (2017) constructed a decision-making model for risk analysis of subway construction projects, which combines the fuzzy comprehensive evaluation method with the Bayesian network [14]. [PERSON] (2019) used trapezoidal fuzzy numbers to characterize the risk events and evaluate the risk during the construction of excavation [15]. [PERSON] (2021) combined Pythagoras with triangular fuzzy numbers to construct a mixed fuzzy set for quantitative analysis of risk events in excavation [16]. [PERSON] (2022) proposed an open TBM tunnelling adaptability evaluation method based on hydraulic engineering in Xinjiang and verified the reliability of this method through a case study [17]. It can be seen that there is a relatively mature application background to evaluate various problems of the tunnel and underground engineering by using fuzzy mathematics theory. Many scholars have studied the TBM selection method. [PERSON] (2007) constructed the TBM selection model by the decision tree method [18]. [PERSON] (2010) analyzed the characteristics of open TBM, single-shield TBM and double-shield TBM. Additionally, this research group constructed a TBM selection model based on risk assessment [19]. [PERSON] (2011) used TOPSIS and fuzzy AHP methods to assess the suitability of various tunnel construction methods for the Ghomroud tunnel [20]. [PERSON] (2012) believes that TBM selection is a multi-objective decision-making problem, and he adopted the triangular fuzzy number and the TOPSIS method to select TBM [21]. In view of the geological problems of Jinping II Hydropower Station, [PERSON] (2008) summarized the construction experience of TBM and put forward suggestions for TBM selection and construction measures [22].