## 3 Methodology
### Data Analysis
#### 3.3.1 A Fuzzy Set Algorithm  
First, the data obtained from the questionnaire survey has the characteristics of subjectivity. The fuzzy set theory is suitable for dealing with such type of data. In addition, the fuzzy set algorithm can effectively integrate the opinions of different subjects, which has been confirmed in previous similar studies [39]. Therefore, fuzzy set theory was adopted to integrate the opinions of designers and constructors in order to establish a comprehensive indicator system. The use of this method includes four steps. First, a fuzzy set was defined to determine the distribution of membership functions. Second, the memberships were calculated for the designer group and the constructor group, respectively. Third, the union operator serves to calculate the comprehensive membership per indicator. At last, the indicator set was determined by referring to the resulted comprehensive memberships. The symbol \(\overline{A}\) is employed to represent a set of sustainability indicators of steel structures. This set is defined as a fuzzy set \(\overline{A}_{D}\) and \(\overline{A}_{C}\), which represents the assessment indicator set of designers and constructors, respectively. \[\overline{A}=\mu_{\overline{A}}(\mathrm{x}_{0})/\mathrm{x}_{0}+\mu_{\overline{A }}(\mathrm{x}_{1})/\mathrm{x}_{1}+\ldots=\sum_{i=0}^{n}\mu_{\overline{A}}( \mathrm{x}_{i})/\mathrm{x}_{i} \tag{1}\]  
where \(\mathrm{x}_{i}\) is the ith indicator; \(n\) is the number of indicators; \(\mu_{\overline{A}}(\mathrm{x}_{i})\) is the membership of \(\mathrm{x}_{i}\) in the fuzzy set \(\overline{A}\). Particularly in Equation (1), \"+\" and \"/\" are the symbols of the fuzzy set. \(\mu_{\overline{A}}(\mathrm{x}_{i})/\mathrm{x}_{i}\) means that the membership of \(\mathrm{x}_{i}\) in \(\overline{A}\) is \(\mu_{\overline{A}}(\mathrm{x}_{i})\). The distribution of membership functions includes rectangular distribution, trapezoidal distribution, \(\mathrm{K}^{\mathrm{th}}\) order parabola, normal distribution, and Cauchy distribution [40]. There are two types of statistical tests, including a parametric statistical test and a nonparametric statistical test [41]. The parametric method has the specific requirement that the data to be analyzed must fall in a normal distribution. In contrast, the non-parametric approach does not need such a particular distribution [42]. In the study, the W test's non-parametric method was adopted to explore the survey results' distribution. The W test's null hypothesis is that the population is normally distributed if the \(p\)-value is higher than 0.05. According to the fuzzy set theory, the probability that a variable belongs to a set is equal to the degree of membership in a fuzzy set [43]. Hence, Equation (2) is used to calculate memberships in two groups--designers and constructors. \[\mu_{\overline{A}_{D(C)}}(\mathrm{x}_{i})=\int_{Q}^{\infty}f(S_{\mathrm{x}_{ i}})d\mathrm{x}=1-P_{f} \tag{2}\]where \(\mu_{\overline{A}_{D(C)}}(\mathrm{x_{i}})\) indicates that the membership of indicator \(\mathrm{x_{i}}\) in the fuzzy set \(\overline{A}_{D}\) or \(\overline{A}_{C}\); \(f(S_{\mathrm{x_{i}}})\) is a membership function, \(P_{f}\) indicates the probability that the variable does not belong to the set. The introduction of parameter \(Z\) aims to calculate the value of \(P_{f}\) when \(f(S_{\mathrm{x_{i}}})\) is normally distributed. Equation (3) is used to calculate the \(Z\) value. \[Z=(M-Q)/\mathrm{SD} \tag{3}\]  
where \(M\) and \(S.D.\) represent the average score and standard deviation of an indicator. \(Q\) is equal to 3 in line with the definition of the five-point Likert Scale. The comprehensive membership is defined by using Equation (4) [44] and calculated by using Equation (5). The larger the value, the more important the indicator.