Assessment of project characteristics affecting risk occurrences in construction projects using fuzz

2.1. Characteristics of Construction Projects

The previous studies identifying project characteristics are summarized in this section and presented in Table 1. Table 1. Summary of the literature review Reference

Brief description of the study The authors focused on the risks of Chinese projects performed via joint ventures, and they identified 25 risks related to the characteristics of the projects derived from both external and internal groups. The project value, location of the project, contract value and Bing and Tiong project duration are the project characteristics indicated in this study. However, the effect [17] of each characteristic on the risk occurrence was not determined. Furthermore, only a few numbers of project characteristics were proposed, which failed to represent the project holistically. They investigated the effects of construction project characteristics on the performance of Design-Build and Design-Bid-Build projects. The gross floor area of the project, payment Ling et al. [18] mode to the contractor, and type of the building are the project characteristics investigated in this study. They investigated the impact of 13 project characteristics on international joint ventures. Ozorhon et al. The results of structural equation modeling (SEM) provide evidence that project [19] characteristics have a great impact on the performance of international joint ventures. They tried to establish a link between project characteristics and project’s profitability. The study suggested that the climate and weather conditions, technical complexity of the Han et al. [20] project and clarity of the contract document are the project characteristics that can affect profitability. The authors investigated the effect of project characteristics on the performance of a Cho et al. [21] construction project. The authors classified project characteristics into two groups as the project environment and project participants. The analysis was performed using SEM. They aimed to identify risk paths in international construction projects by using the SEM Eybpoosh et al. method. The authors proposed the project type, region, project size, project delivery [22] system and contract type as the characteristics of construction projects. The authors identified new project characteristics through a case study (a residential construction project in Dubai). They considered the new project characteristics as the Fidan et al. [7] robustness in the project design, project construction, external project condition, project management and project contract conditions. Besides, 14 sub-characters were proposed for these characteristics. They quantified project complexity using 12 project characteristics. The effects of the Nguyen et al. [23] project characteristics on project complexity were ranked via descriptive analysis. They extracted six project characteristics through a literature review, and the effect levels Liu et al. [24] of project characteristics on the project delivery systems were determined by analyzing the data collected from a questionnaire survey. The effect of project complexity on the cost and schedule performance was investigated in this study. Project complexity was measured through a set of project characteristics. These Nguyen et al. [25] characteristics include the project size in terms of capital, the ambiguity of project scope, climate conditions, geological conditions, and the accessibility of the site. They developed a system based on project characteristics, named as the company size, Penaloza et al. project type and construction area to monitor the complexity and resilience of construction [26] projects. The authors linked the project complexity to project success via a hybrid SEM-FCM Luo et al. [27] method. The results indicated that information, goals, and environmental complexities are negatively correlated with project success.

2.2. Fuzzy set theory and fuzzy AHP

Many decision-making tasks cannot be quantified due to the existence of a high level of complexity in these tasks. However, the human brain can handle complex problems by using imprecise knowledge rather than precise knowledge. This mechanism of the human brain is the main inspiration of the Fuzzy set. The Fuzzy set theory proposed by Zadeh [28] works similarly to human reasoning, which is capable of generating decisions under the circumstances of approximate information and uncertainty. The specific purpose of the fuzzy set theory is to mathematically represent uncertainty and vagueness to provide a formalized tool for dealing with the imprecision. In other words, the fuzzy set theory can deal with the vagueness of human thought, whereas traditional computing systems necessitate precise and certain knowledge that is not available in many real-world problems. In addition, the fuzzy set theory also helps to simplify many engineering problems as knowledge can be expressed more naturally by using fuzzy sets. Especially, the use of linguistic variables is one of the critical aspects of the fuzzy logic application to express the problem in a more natural way, since linguistic variables such as “large” and “medium” are used rather than the numbers (E.g., Likert’s scale) [29]. Therefore, the respondents can explain their opinions clearer compared to giving numerical answers. The analytic hierarchy process (AHP) was developed by Saaty [30] and became one of the most popular multi-criteria decision-making methods [29], [31], [32]. The method decomposes a decision-making problem into a system of hierarchies of objectives, attributes (or criteria), and alternatives. The mechanism of AHP includes decompositions, pairwise comparisons, and priority vector generation and synthesis. The AHP is a reliable tool; however, it still cannot reflect the vagueness of the human thinking style. Whereas, the Fuzzy set theory can combine any “crisp” methodology or theory by fuzzifying these definitions to include the human thinking style. Therefore, the Fuzzy AHP was developed to solve hierarchical problems [33]. In essence, both AHP and Fuzzy AHP methods are used to capture experts’ opinions, and the Fuzzy AHP handles the impreciseness of the humans’ judgments in a more effective way [34].

3.1. Literature review and data collection

At the initial stage of this study, the characteristics of the construction projects were identified by conducting a literature survey via Google Scholar and Scopus. The literature review indicated that a limited number of studies that investigated the relationship between project characteristics and the risk occurrence have been conducted as stated above. Moreover, a limited number of characteristics were proposed in these studies. Therefore, the scope of the literature review was widened to extract as many project characteristics as possible. In addition, some studies proposed the same characteristics under different names. Therefore, to refine the list, these characteristics were identified and merged with each other. Finally, a list of 12 main project characteristics and 14 subproject characteristics was extracted from the studies of researchers such as Bing and Tiong [17], Ling et al. [18], Han et al. [20], Cho et al. [21], Eybpoosh et al. [22], Fidan et al. [7], Nguyen et al. [23], Liu et al. [24] and Penaloza et al. [26], and these characteristics were represented in Table 2. Table 2. Characteristics of construction projects. Main Characteristics Project type Country Project delivery system Project value Duration Total construction area Contract type Design-related characteristics

Construction-related characteristics External conditions-related characteristics

Sub-characteristics D1: Complexity of design D2: Completion level of design D3: Constructability level D4: Quality of design C1: Complexity of construction methods C2: Accessibility of the site E1: Comprehensiveness of geotechnical investigation E2: Climate & weather conditions P1: Strictness of quality management requirements P2: Strictness of environmental management requirements P3: Strictness of safety management requirements P4: Strictness of project management requirements CC1: Vagueness in contract clauses CC2: Clarity of contract documents

In the second stage of this study, a questionnaire survey was prepared. This questionnaire consisted of three parts. In the first part, the respondents provided information about themselves and their companies. The second part included the pairwise comparisons of the main criteria. In the third part, respondents completed the pairwise comparisons of sub-criteria. In addition, all pairwise comparisons were made based on linguistic variables. The use of linguistic variables allowed experts to reflect their opinions about the effect of project characteristics on risk occurrence more precisely, in turn, ambiguity is eliminated [38]. Another crucial point of this study is the determination of the sample size to reveal the reliability of the study. Saaty and Özdemir [39] stated that specific and strict rules do not exist for the required sample size for AHP surveys. However, experts should be chosen from different

constituencies to form political expediency. In addition, the AHP does not mandatorily necessitate a large sample size to give reliable results [40], since reliable results can be obtained even when one expert participated in the surveys [39]. By contrast, a large sample size may lead to unreliability due to the cold-called respondents [41]. In addition, a large sample size can even increase the degree of inconsistency [42]. Although a large sample size is not a prerequisite for reliable findings, the respondents who participated in AHP studies should be well-experienced to obtain reliable results. In other words, the quality of the data is more important than the quantity of the data. In this study, 15 experts were selected carefully using judgment sampling and their demographic information, which is shown in Table 3. Table 3 shows that the experts of this study have high experience in risk management in construction projects. In addition, they have major roles in their companies, and they also have high international experiences. Table 3. Demographics of the Respondents Sample Specifications Parent organization Size of the organization Experience of the organization in International CI Experience of the organization Experience of the respondent Experience of the respondent in risk management Education level

Another benefit of a small sample size is the fact that data can be gathered through face-toface interviews. This is crucial for collecting reliable data for the fuzzy AHP since most of the respondents can have problems in filling the questionnaires appropriately when they have limited information about the fuzzy AHP. Therefore, the consistency level can be a problematic issue in these studies. Individual meetings were set-up, and the questionnaire was explained to each of the respondents. Firstly, the respondents performed pairwise comparisons between the main criteria. In this matrix, the effects of the main criteria on the risk occurrence were compared based on six linguistic variables, namely, Just equal, Equally Important, Weakly Important, Moderately Important, Strongly More Important, Extremely Important. Secondly, pairwise comparison matrices were prepared for sub-criteria by using the same linguistic variables. In other words, five

matrices were prepared at the end of this stage. Then the results were analyzed by using the Fuzzy AHP.

3.2. Methodology followed throughout the analysis

This section includes the mathematical background of the Fuzzy AHP and the analysis results. The steps of Fuzzy AHP and the mathematical formulations are presented as follows. Step 1. Development of an AHP structure: As stated above, project characteristics were extracted from the literature, and these characteristics were used to propose a model that shows the relationship between the project characteristics and occurrence of risks. A typical AHP model structure includes main criteria and sub-criteria, which are the characteristics of the projects in this study. Namely, some characteristics were grouped with respect to their similarities, such as design-related characteristics and construction-related characteristics. Figure 2 shows the final structure of the AHP. Effects of the characteristics of a construction project on occurence of project risks Project type

Figure 2. AHP model structure Step 2. Re-arranging pairwise comparison matrices by using fuzzy numbers: This step can also be called fuzzification. Namely, pairwise comparison matrices were filled by the experts using linguistic variables, and these pairwise comparisons were re-arranged using fuzzy numbers given in Table 4. In other words, these matrices were fuzzified. Triangular fuzzy numbers were used for fuzzification in this study. Three parameters (l, m, u) are used to define the triangular fuzzy numbers. “l” denotes the smallest possible value, “m” indicates the most likely value, and “u” denotes the largest possible value that describe a fuzzy event.

Step 3. Application of Chang’s extent analysis method: At the previous stage, all matrices were fuzzified. Since there is no commercial software for the application of the fuzzy AHP, a MATLAB script was coded in-house to solve fuzzy AHP matrices by following Chang’s extent analysis method. This method was used to find the weights of each characteristic. Chang [33]’s extent analysis is a method of using crisp mathematical concepts to address fuzzy quantities. Let 𝑋 = (𝑥1 , 𝑥2 , 𝑥3 , … … … , 𝑥𝑛 ) be an object set and 𝑈 = (𝑢1 , 𝑢2 , 𝑢3 , … … … 𝑢𝑚) be a goal set. Chang’s extent analysis method dictates that extent analysis for each goal, 𝑔𝑖 is performed, respectively. Firstly, the value of the fuzzy synthetic extent should be calculated as follows: 𝑗 −1

𝑗 𝑗 To calculate [∑𝑛𝑗=1 ∑𝑚 𝑗=1 𝑀𝑔𝑖 ] , perform the fuzzy addition operation of 𝑀𝑔𝑖 (𝑗 = 1, 2, … … … , 𝑚) values such that: 𝑗

And then the inverse of the vector in Eqn (3) is calculated as follows: 𝑗 −1

Finally, the value of the fuzzy synthetic extent is calculated, and the degree of possibility was obtained using the value of the fuzzy synthetic extent. The following equations, Eqn (5), Eqn (6), Eqn (7) are used to calculate probability values. After obtaining the possibilities, the weight vectors were calculated, and eventually, the normalized weights vector was calculated to determine the weight of each project feature. The degree of possibility of 𝑀2 = (𝑙2 , 𝑚2 , 𝑢2 ) ≥ 𝑀1 = ((𝑙1 , 𝑚1 , 𝑢1 ) is defined as: 𝑉(𝑀1 ≥ 𝑀2 ) = 𝑠𝑢𝑝[min(𝜇𝑀1 (𝑥) , 𝜇𝑀2 (𝑦))]

When a pair (𝑥, 𝑦) exists such that 𝑥 ≥ 𝑦 and 𝜇𝑀1 (𝑥) = 𝜇𝑀2 (𝑦) = 1, then 𝑉(𝑀1 ≥ 𝑀2 ) = 1. Therefore, the degree of the possibility is as follows, since M 1 and M2 are convex fuzzy numbers: 𝑉(𝑀1 ≥ 𝑀2 ) = 1, if 𝑚1 ≥ 𝑚2 ; (6) Otherwise; 𝑉(𝑀1 ≥ 𝑀2 ) = ℎ𝑡𝑔 𝑀1 ∩ 𝑀2 =

Both M1 and M2 values are needed to make the comparison given above. The degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers Mi (i=1, 2, ……., k) can be defined by Eqn (8) 𝑉(𝑀 ≥ 𝑀1 , 𝑀2 , … … . 𝑀𝑘 )= 𝑉[(𝑀 ≥ 𝑀1 )] and (𝑀 ≥ 𝑀2 ) and……and [(𝑀 ≥ 𝑀𝑘 )] = 𝑚𝑖𝑛𝑉(𝑀 ≥ 𝑀𝑖 ); (8) 𝑖 = 1, 2, 3, … … … , 𝑘 Assuming that, 𝑑′ (𝐴𝑖 ) = min 𝑉(𝑆𝑖 ≥ 𝑆𝑘 ) for =1, 2, …..n; k≠I, the weigh vector (W) is calculated by using the following formula: 𝑊 ′ = (𝑑′ (𝐴1 ), (𝐴2 ), … … … 𝑑′ (𝐴𝑛 ))𝑇

Where: 𝐴𝑖 (𝑖 = 1, 2, 3, … … … , 𝑛) are n elements. The last step is the normalization which is calculated using the equation given below: 𝑊 = (𝑑(𝐴1 ), 𝑑(𝐴2 ), … … … … … … 𝑑(𝐴𝑛 )) 𝑇

Step 4. Calculating the fuzzy Eigen Value: After Chang’s extent analysis was applied to the pairwise comparison matrices, the Eigen value of each matrix was calculated to check the consistency of these matrices. A consistency check is another strength of the AHP method that no other multi-criteria decision-making method can achieve. The consistency of each matrix is checked by using the consistency index (C.I.) and consistency ratio (C.R) as proposed by Saaty [30]. The consistency of a matrix is evaluated by using Eqns (11) and (12): 𝐶. 𝐼. = 𝐶. 𝑅 =

Where:  𝑚𝑎𝑥 is the largest Eigen value of the comparison matrix, n is the dimension of the matrix, and R. I. is the random consistency index of the matrix chosen from Table 5. Table 5. RI of random matrices [43] 𝑛 RI 𝑛 RI

According to Saaty [30], the overall consistency ratio should be equal to or less than 10%. Otherwise, the answers of the experts are considered to be inconsistent [44]. In such a case, the decision makers must check their answers.

Table 6. The normalized weight of criteria and sub-criteria Main Criteria Project type Country Delivery system Project value Duration Total construction area type Contract

Normalized Weights of Criteria 0.0741 0.0873 0.0751 0.0929 0.0727 0.0632 0.0962

Since in-house codes were written for this study, to avoid any coding errors, the computational accuracy was tested using the data presented by Chang [33], Işık and Aladağ [45]. This verification showed that the analysis conducted with coded MATLAB script gave the same results as these studies; therefore, the codes were determined as reliable. In addition, the 1456

consistency check feature was also added to the system, and all matrices were found consistent. The consistency ratios of the matrices were 0.0077, 0.0076 and 0.0071 for the pairwise comparisons of the main criteria, design-related characteristics, and the project management characteristics, respectively. It should be noted that consistency can be checked only when the matrix size is greater or equal to 3 [30]. Thus, there are no consistency measures for constructionrelated characteristics, external-related characteristics, and project-management related characteristics. Finally, the weights of the project characteristics obtained as a result of fuzzy AHP analysis were given in Table 6.