# A Fuzzy-Based Decision Support Model for Risk Maturity Evaluation of Construction Organizations
## 3 Research Methodology
### Data Analysis and Evaluation
#### 3.4.1 Analytic Network Process (ANP)  
ANP is an advanced multi-criteria decision-making method which considers the interdependencies between different factors throughout a relationship network [7]. It determines the relative weights, which reflect the relative importance, of all the defined factors based on the data captured from the participants [16]. In this study, the Super Decisions software was employed for the computational processes [17]. Figure 2 shows a simple ANP network within two clusters, a criteria cluster (\(C_{1}\)) and an alternative cluster (\(C_{2}\)). The (\(C_{1}\)) cluster includes the sub-decision factors and the (\(C_{2}\)) cluster consists of key decision factors. The interdependency between the elements of these two clusters are shown with two-way arrows between them as shown in Figure 2. In this study, the sub-decision factors were individuals' opinions and the key decision factors are the defined attributes APR, AIR, AAR, ARR, AIRR, and AMR.  
The goal was to prioritize the attributes based on their relative weights. This was done by comparing: (1) the attributes with respect to each individual's opinion, and (2) the individuals' opinions with respect to each attribute. The five-point scale method was utilized for scoring the relative importance (1 = very low, 2 = low, 3 = medium, 4 = high and 5 = very high). For instance, in comparing attribute one with respect to the first individual, if this individual was involved in the maturity evaluation of that particular attribute (as shown in Table 6), it got a very high weight (5), otherwise its weight is considered as a function of its level of authority including high (individuals at portfolio level), medium (individuals at program level), low (individuals at project level). Subsequently, a comparison between the individuals' opinions with respect to each of the attributes was performed on a pairwise basis. For instance, in the first part of the questionnaire, the individuals were asked to score how much importance does an attribute have compared to another attribute concerning the goal. The assigned weights were utilized to construct the pairwise comparison matrices corresponding to each cluster. For all the pairwise comparisons, the inconsistency ratios were less than 10% as recommended by [PERSON] [18]. Subsequently, these matrices were used as inputs to form the unweighted supermatrix. Then, the weighted supermatrix was attained by normalizing the unweighted supermatrix. In other words, each column in the unweighted supermatrix was normalized based on the summation of its cells. Finally, the limited supermatrix was generated by raising the weighted supermatrix to considerable powers until convergence. The first column in the limited matrix showed the global weights. By normalizing that column and summing up the weights, the attributes were prioritized based on their relative weights.  
Figure 3 shows the elements of the ANP supermatrix and sub-matrix [19]. Considering the clusters in the decision network, Figure 2, as (\(C_{p}\)), \(p\) = 1, 2,..., \(m\) and given each cluster (\(up\)) elements, shown by (\(s_{p1}\), \(s_{p2}\),..., \(s_{pmn}\)), then Figure 3a represents the decision network's supermatrix. (\(W_{ij}\)) of the network supermatrix is shown in Figure 3b where (\(W_{ij}\)) shows the dependency of the elements in the (\(i\)th) cluster on the elements in the (\(j\)th) cluster. In case there was no dependency between the two elements  
Figure 2: Analytic network process (ANP) model structure.  
of the (\(i\)th) and (\(j\)th) clusters, zero value was entered in the supermatrix. The result of the ANP will be used in the following section to calculate the overall expected value of the organization risk maturity.