## 3 Application  
To depict the application and effectiveness of the proposed methodology, a construction project from a previous study [2] has been selected. This project includes 18 activities. The project manager tends to crash the duration of activities so as to attain the determined project duration. Information on project activities is provided and presented in Table 2.  
Initially, using available data, the mathematical model of the CRQT problem under time constraints is constructed. Now, the main purpose is to find the optimal set of activities to be crashed with minimal additional cost, threatening risk, and reduced quality. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{\ \begin{tabular}{c} **Fuzzy** \\ **Duration** \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} **Fuzzy** \\ **Crashing Cost** \\ \end{tabular}  } & \multicolumn{6}{c}{**Reduced**} & \multicolumn{6}{c}{**Risk Value (\(Pr^{\star}\)D), \(u_{ji}\)=1,2, \(r\) = 1,..., 4**} & \multirow{3}{*}{\(MR_{j}\)} \\ \cline{3-11}  & & & \(u_{jt}\)=1,2 & & **1** & & & **2** & & **3** &  
The proposed multi-objective fuzzy model is separately solved with two approaches, namely, fuzzy credibility theory and the goal attainment method as well as the method of [PERSON] et al. [37] and the augmented \(\varepsilon\)-constraint method using GAMS software. Pareto-optimal solutions from the two presented approaches are presented in Tables 3 and 4. In Table 3, some Pareto-optimal solutions through the fuzzy credibility method and goal attainment method are presented. The \(Wo_{i}\) and \(B_{i}\) represent the weights and goals determined for each goal, respectively. \(OF_{i}\) indicate the value of the project's objective functions (cost, risk, and quality criteria) for each Pareto-optimal solution. \(G\) is the optimal value of the goal attainment method. The last column also depicts the optimal sets of activities and their crashing values. In fact, in this methodology, various weight and goal values for objective functions can generate Pareto-optimal solutions. For example, one of the optimal solutions is that the first, fourth, and fifth activities must be crashed by two days, and the seventh activity must be crashed by one day. In this solution, the additional cost, threatening risk value, and reduced quality values are 3496, 1.17, and 0.052, respectively. Table 4 presents some Pareto-optimal solutions for the given application through the method of [PERSON] et al. [37] and the augmented epsilon constraint method. This table also depicts the optimal set of activities, their crashing values, and the values obtained for each objective function. By examining the results of both methods and existing common Pareto-optimal solutions, the correctness and efficiency of the two methods in the TCT problem are proven. It should be noted that both methods have advantages and disadvantages; the application of these methods in other issues requires their adaptation to the assumed problems. The methodology of this research enables project managers to choose the optimal set of project activities for crashing so as to reduce the duration of their projects as long as they can. On the other hand, the results of this approach provide knowledge to project managers about changes in project status, such as additional costs imposed, threatening risk incurred, and reduced quality due to project time crashing. Access to this important information enables them to make indispensable provisions for project cost -risk and quality criteria at an appropriate time. In order to demonstrate the accuracy of the obtained results as well as the advantages of the proposed fuzzy approaches, the introduced project is solved using the fuzzy \(\alpha\)-cut method [43], which is regarded as another efficient fuzzy solution method, and the