## 3 Methodology
### Quantifying Strategies' Impact on CLP  
An FCM model of CLP is developed for simulating the relationships among the most value-adding CLP factors and quantifying the impact on CLP of the selected top-ranked improvement strategies. FCM is a soft computing technique for modeling and simulating dynamic systems such as a CLP environment by mimicking the process of developing a cognitive map in a human mind [19]. Generally, the manual process for developing an FCM is using expert knowledge to evaluate the strength of causal relationships in terms of weights using linguistic variables such as \"Low\", \"Medium\", and \"High\". During the simulation, the value of CLP factor \(C_{j}\) at time \(t\) is calculated using Equation (19), as proposed by [PERSON] [51]  
\[A_{j}^{(t)}=f\left(\sum_{ \begin{subarray}{c}i=1\\ j\
eq i\end{subarray} }^{M}w_{ij}\left(2A_{i}^{(t-1)}-1\right)+\left(2A_{j}^{(t- 1)}-1\right)\right) \tag{19}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Strategy** & **Closeness Coefficient** & **Rank** \\ \hline S11 & 0.8496 & 1 \\ S2 & 0.8341 & 2 \\ S13 & 0.8026 & 3 \\ S7 & 0.7899 & 4 \\ S6 & 0.7665 & 5 \\ S9 & 0.7201 & 6 \\ S16 & 0.7099 & 7 \\ S12 & 0.6991 & 8 \\ S8 & 0.6961 & 9 \\ S14 & 0.6900 & 10 \\ S1 & 0.6875 & 11 \\ S3 & 0.6644 & 12 \\ S15 & 0.6418 & 13 \\ S10 & 0.6215 & 14 \\ S5 & 0.6005 & 15 \\ S4 & 0.5704 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CLP improvement strategy ranking. where \(w_{ij}\) is the strength of the causal relation between two CLP factors \(C_{i}\) and \(C_{j}\), and denoted via a causal edge from \(C_{i}\) to \(C_{j}\); \(w_{ij}\) ranges from \(-1\) (absolute negative causality) to \(0\) (no causality) and \(1\) (absolute positive causality). In Equation (20), \(f(. )\) is an activation function that is formulated as sigmoid threshold function in this study  
\[f_{(x)}=\frac{1}{1+e^{-\lambda(x-h)}} \tag{20}\]  
where \(\lambda\) and \(h\) are real positive numbers that control slope and offset of the function, respectively. Higher values of \(\lambda\) make the function more sensitive to the fluctuations of \(x\)[20]. When no expert is available or the model contains a large number of relationships, an FCM cannot be developed through the manual process of using expert knowledge [52]. For such cases, learning processes can be applied to automatically determine near-optimal weights for the relationships. FCM learning algorithms can be grouped into three types based on their underlying learning paradigm: (1) Hebbian-based, (2) error-driven, or (3) hybrid. Hebbian-based learning algorithms, such as nonlinear Hebbian learning (NHL), are unsupervised methods and do not require historical data. Their main drawback is their dependency on expert knowledge, since they require initial weight of causal relationships [53]. Error-driven learning algorithms, such as the real-coded genetic algorithm (RCGA), generates weight matrices by attempting to fit the FCM model to a set of historical data. Several studies illustrated that these algorithms increase FCM robustness, functionality, and generalization abilities [54]. Hybrid learning algorithms employ a combination of the other two types to take advantage of the fast speed and effectiveness of Hebbian-based methods and the global search and generalization ability of error-driven methods [55]. In the proposed method, an initial FCM model is developed based on the importance of the most value-adding CLP factors, then the strength of a causal relation between two factors \(C_{i}\) and \(C_{j}\) is quantified by a numerical weight \(w_{ij}\in[-1,\ 1]\). Three types of causal relationships among the factors exist: (1) positive causality (\(w_{ij}>0\)), which means an increase or decrease in \(C_{i}\) causes the same result in \(C_{j}\); (2) negative causality (\(w_{ij}<0\)); (3) no causality (\(w_{ij}=0\)). After the strengths of all relationships are assessed, each improvement strategy is considered in the model, one at a time, in order to determine the quantitative effect of each strategy on construction productivity.