DESIGN AND PILOT RUN OF FUZZY SYNTHETIC MODEL (FSM) FOR RISK EVALUATION IN CIVIL ENGINEERING

. Most of the current construction risk assessment tools deliver unsatisfactory results because the prerequisite for their effective applications rely on the availability of high quality data especially during the early stage of a project. Unfortunately, such data are limited, ambiguous or even not exist due to the great uncertainty inherent in construction projects. Based on Fuzzy Synthetic Analysis (FSA), a model development team was formed among construction engineers, IT professionals, and Mathematicians in developing a holistic risk assessment model to estimate the construction risks especially for the situations with incomplete data and vague environments. Through qualitative scales defined by triangular fuzzy numbers used in pairwise comparisons to capture the vagueness in the linguistic variables, a risk assessment model using Analytic Hierarchy Process (AHP) was developed. The Pilot Run revealed the developed Fuzzy Synthetic Model (FSM) could accelerate the decision-making process and provide optimal allocation of project resources to mitigate possible risks detrimental to the success of a project in terms of time, cost, and quality.


Introduction
In the past few years, several quantitative-based approaches have been introduced for construction risk management such as Fault Tree Analysis, Monte Carlo Analysis, and Sensitivity Analysis (Ahmed et al. 2007). These sophisticated methods could deal with massive numerical data to deliver reliable statistical risk result. However, the availability of high quality data especially during the early stage of projects is a prerequisite for their effective applications (Sii, Wang 2003). Unfortunately, such data are limited, ambiguous or even not exist due to the great uncertainty inherent in construction projects. Therefore, the quantitative approaches could not suitably and effectively handle the risks (Franceschini, Galleto 2001).
In the mid of 1960s, Professor Lofti Zadeh introduced fuzzy logic to mathematically represent the uncertainty and vagueness inherited in the real world (Zadeh 1965). Scholars have presented the use of fuzzy logic in construction projects such as duration management (Zieliń ski 2005;Chen, Hsueh 2007), cost estimation (Cheng et al. 2010;Idrus et al. 2011), risk management (Zhang, Zou 2007;Lee, Lin 2010), safety management (Dagdeviren, Yü ksel 2008), supply chain management (Chen, Huang 2006;Wei et al. 2007) and earned value management (Naeni et al. 2011). The extensive application of Fuzzy logic in the realm of construction demonstrated its easiness to be developed, understood and applied (Kasabov 1996). According to Dweiri and Kablan (2006), fuzzy logic is an excellent tool that could greatly improve the chances of achieving a better quality construction project. Eventually, it resulted in superior project performance and subsequent project success in the field of construction. Fuzzy logic is a tool to deal with decision-making environments characterized by vagueness, impression, and subjectivity (G., Bojadziev, M. Bojadziev 2007). The integration of Fuzzy logic in project risk management could give rise to satisfactory results by effectively addressing the uncertainties and subjectivities associated with construction activities. Moreover, fuzzy logic provides a more realistic way than traditional mathematical models to cope with problems that are vague in nature (Heshmaty, Kandel 1985). Based on Fuzzy Set Theory (FST), this study intends to develop a holistic risk assessment model using to estimate the construction risks especially for situations with incomplete data and vague environments. This paper introduces the principles and algorithm of its risk assessment framework. Further, a Pilot Run for the developed Fuzzy Synthetic Model (FSM) is presented.

Fuzzy logic and FST in construction risk management
Fuzzy Set Theory (FST), or, Fuzzy Logic, resembles human ability in inferring an approximate answer to a question based on a store of knowledge that is vague, inexact, incomplete, or not totally reliable (Zadeh 1978). In other words, Fuzzy logic simulates the way human brain works to solve real-world problems (Yager 2002) such as in forecasting, decision making, and management, which are characterized by uncertainty, impression, and subjectivity (G. Bojadziev, M. Bojadziev 2007;Negnevitsky 2004).
No construction project is risk free. Risk can be managed, minimized, shared, transferred or accepted. It cannot be ignored (Latham 1994). Over years, scholars have proposed a variety of risk management methodologies for real practise, yet most of them are similar in process, following a systematic three-step approach: identify, assess, and mitigate construction risks (Flanagan, Norman 1993;Berkeley et al. 1991;Lyons, Skitmore 2004). Out of the three steps, risk assessment process is the most controversial issue (Baloi, Price 2003). Meantime, there were a few research studies attempted to use FST to formalize subjectivity issues in the construction risk analysis. One of the earliest FST-based approaches was outlined by Nguyen (1985) to solve decision-making problems during the selection of bid contracts. Kangari and Riggs (1989) presented a composited fuzzy-knowledgebased system to analyze risk but revealed the limitations of probability-based approach in risk assessment process: difficult in the quantifying qualitative data, where precise data is unavailable in real situation. This issue activated the subsequent courses of exploration to investigate the fatal weakness of the probability approach in construction project risk evaluation.
Being pioneers in adopting Analytic Hierarchy Process (AHP) within construction decision problem analysis, Mustafa and Al-Bahar (1991) assessed risks through the appraising of probability and impact of risk occurrence. AHP was developed by Saaty (1980Saaty ( , 1990 to cope with complex decision-making problems. AHP was applied by Dey et al. (1994) and Riggs et al. (1994) to combine objective and subjective data as an attempt to analyze cost risk where risk was modelled as Probability-Impact (PÁI). Zhi (1995) proposed using AHP to evaluate risk in international projects. Chun and Ahn (1992) on the other hand, integrated FST into risk analysis model to quantify the imprecision inherent in the accident progression event trees. Using FST, Paek et al. (1993) established a risk algorithm for the assessment of bidding price of construction projects. Wirba et al. (1996) applied FST to capture human reasoning in the identification and evaluation of risks.
In the 2000s, since the outset of millennium, there have been rigorous investigations to efficaciously model and evaluate the construction project risk. Risk began to be dealt comprehensively using multi-criteria decision-making (MCDM) techniques to facilitate the complex decision-making process in risk assessment. Despite the availability of many others techniques, both AHP and FST turned out as the most favoured methodologies in handling ill-defined subjective problems. They were perceived as the best ever approaches in problem-solving that encompassing multiple criteria. For instance, Hastak and Shaked (2000) proposed an AHP model to assess the risk of overseas projects. Baccarini and Archer (2001) used both the probability and impact risk parameters to rank project risks. Likewise, Jannadi and Almishari (2003) attempted to analyze risks concerned with project activities. Risk is modelled by probability and ''exposure'' to all hazards of an activity. Ward and Chapman (2003), however, criticized on the PÁI risk model that it yielded unnecessary uncertainty by oversimplifying the estimation of risk impact and probability. Zhang (2007) expounded the deficiencies of the PÁI grid. Alternatively, ''project vulnerability'' is introduced to enhance the recognition of risk consequences. In the same year, Cagno et al. (2007) used the PÁI risk model to quantify the cost risk by determining the sources of risks, affected activities, and risk owners. Besides, a three-dimensional risk model called Significance-Probability-Impact was presented where ''significance'' is defined as the degree to which a practitioner assesses risk intuitively. Recently, Cioffi and Khamooshi (2009) generated a probabilitybased model to estimate the overall risk impact on contingency budget. Based on both AHP and decision tree, Dey (2001) sought to effectively manage construction cost risk as early as on the inception stage. In addition, Dikmen et al. (2007a) adopted AHP to appraise uncertainties and opportunities of the overseas construction projects. The overall project risk level was computed by multiplying the relative impact and the relative likelihood of each risk. All the individual risk impacts were summed up to obtain final score. In contrast, Zayed et al. (2008) applied AHP to allocate weighs to risks before calculating the risk level. Some researchers attempted to integrate FST into risk assessment process. They focus mainly on the improvement of the efficiency of the conventional risk assessment tools, though rather new tools have been proposed by Huang et al. (2001) and Cho et al. (2002). Using the risk hierarchical breakdown structure, Tah and Carr (2000) proposed a fuzzy qualitative risk assessment model, where experts' subjective judgments were captured within the model to assess the risk impact. Noticing the drawback of FST in such an application, Tah and Carr (2001) proposed a new combination rule in the aggregation process of a predominant risk factor. Choi et al. (2004) developed a FST model to analyze risks using objective probabilities, subjective judgments, and linguistic variables. Similarly, Shang et al. (2005) designed a Fuzzy-based mechanism for risk assessment for the conceptual design stages of a construction project. Zheng and Ng (2005) applied FST to assess the cost and budget in construction projects.
In addition, Thomas et al. (2006) generated a fuzzy fault tree to enhance risk assessments by considering the opinions of different experts. A fuzzy decision-making model was designed by Wang and Elhag (2007) for a bridge construction project. The model evaluates risks based on the likelihood and consequences of occurrence. In consideration of overseas projects, Dikmen et al. (2007b) adopted an influence diagrams to create a fuzzy risk assessment approach to prioritize risk based on cost excess of budget. Meanwhile, Zeng et al. (2007) used FST to cope with uncertainty whereas AHP was applied to decompose and to prioritize multiple risk sources. Risks were first described in linguistic values and later transformed into fuzzy numbers. In the most recent, Lee and Lin (2010) suggested the use of AHP in fuzzy risk assessment in construction projects. Linguistic terms and Fuzzy numbers were directly adopted, rather than the use of quantitative data in risk assessment process. Likewise, Nieto-Morote and Ruz-Vila (2011) presented a risk assessment framework based on the FST, which could effectively capture the subjective judgements decompose large number of risks. The most notable distinction was the adoption of a risk discrimination algorithm to solve the inconsistencies in the computation process. Table 1 overviews the developed risk assessment techniques from 1980s till the year of 2011.

Fuzzy Analytic Hierarchy Process (Fuzzy-AHP)
Fuzzy-AHP has been extensively adopted to solve qualitative MCDM problems in the context of construction risk assessment. Together with hierarchical structure analysis, FST could excellently handle the ambiguity inherited in the conventional data evaluation process, which encompasses identification, evaluation, and prioritization of the MCDM problems (Chen 2001). One of the significant aspects of Fuzzy-AHP is its ability in solving ill-defined and vague problems in construction projects and reaching a reliable final decision (Zeng et al. 2007;Zhang et al. 2002;An et al. 2005). Being proven to be more advanced and efficacious in tackling complex MCDM problems, Fuzzy-AHP generally follows a process, structured in a three-step approach, namely: a) generation of risk hierarchy tree; b) pairwise comparison to establish fuzzy comparison matrix; c) fuzzy prioritization of criteria.

Generation of risk hierarchy tree
Taxonomy of a typical hierarchy tree associated with construction project risks is shown in Figure 1. The complex decision problems can be formulated in the form of simple hierarchy tree. The overall goal is placed at the highest level. The criteria affecting the goal are located in the middle levels. The lowest level presents the decision options. Before the hierarchy tree is structured, different risk factors have to be exhaustively recognized. Usually, the construction practitioners have intuitive methods of recognizing a risk source. This is in accordance with the statement of Wang et al. (2004) that experts prefer to intuitively identify risks using experience and knowledge gained from previous contracts. There are, anyhow, some formal risk identification tools such as Checklist, Influence Diagrams, Cause and Effect Diagram, Failure Mode and Effect Analysis, and Fault Trees Analysis (Zavadskas et al. 2010;Tah, Carr 2000).
Nevertheless, large construction projects tend to adopt formalized risk identification tools, and vice versa. All the sources of uncertainties identified are classified within the hierarchy tree structure so that they can be thoroughly evaluated. Various risk classification methods are shown in Table 2. The methods adopted to classify construction risks depend largely on the nature of a project as well as the management skills of experts. Once the decomposition of risk problems into a hierarchy tree is completed, risk assessment process is carried out to determine the relative importance, dominance or preference of the decision criteria with regards to the goal of the problems.

Pairwise comparison to establish Fuzzy comparison matrix
The importance weighs of criteria is determined in the pairwise comparison manner. Anyhow, the difference between pairwise comparison process in Fuzzy-AHP and normal AHP is in the use of Fuzzy comparison scale, where Fuzzy numbers are integrated into the original comparison scale to substitute the nine exact numbers in Fuzzy-AHP. Experts could intuitively express their preferences as the Fuzzy numbers could accurately describe the expert's verbal judgments in the process Zadeh (1965). The Fuzzy comparison scale works excellent in capturing the subjective experience and knowledge of experts through the application of the Fuzzy numbers (Chang, Yeh 2002;Kahraman et al. 2004) within Fuzzy-AHP. Using the advanced comparison scale, experts could express their judgments using natural languages such as ''equally important'' and ''absolutely more important'' which are directly corresponding to Fuzzy scale of (1, 1, 1) and (17/2, 9, 19/2), respectively. Reciprocal scale is adopted whenever the later criterion j is more dominant than the former criterion i. As such, the expert no longer face difficulty in giving fixed judgments, which is in the form of exact numbers, but rather interval judgments, which is in the form of Fuzzy numbers. There are various types of Fuzzy numbers proposed in Fuzzy comparison scale, yet the triangular and trapezoidal shapes are the most frequently used membership functions in construction risk analysis practice due to their simplicity in application . They have been proven to be able to efficaciously formulate problems where the data available is of subjective and vague (Kahraman et al. 2004;Chang et al. 2007). In comparison, the triangular shape membership functions are the most often used in representing the Fuzzy numbers (Karsak, Tolga 2001) (1987) Probability theory Cost Kangari and Riggs (1989) FST â The 1990s Yeo ( Pedrycz (1994) expressed that a triangular Fuzzy number (TFN) is the easiest and simplest way to approach the convex functions. Moreover, if the pairwise comparison process involves group-decision-making, the experts' preferences on particular criterion have to be aggregated. This is because experts with different background and experience would have different preference on a particular criterion. Hence, it needs to aggregate the individual preferences into the group preference to average out the relative importance weightings of the criteria. The aggregation process is carried out for every criterion, until all criterions have their own group preferences. The groups preferences, which are remain in Fuzzy numbers, are arranged in a systematic manner to yield a Fuzzy comparison matrix. Pairwise comparison is used to calculate the relative importance weighing of each risk criterion with the incorporation of Fuzzy numbers to capture the sub-jective expert's judgments in the process. The output is a Fuzzy comparison matrix (Ding, Liang 2005;Xu, Chen 2007).

Fuzzy prioritization of criteria
Since Saaty (1980) had proposed the AHP, many researchers enrolled in the extension of the eigenvector priority method to overcome its inconsistency in producing results. As an attempt to produce reliable final priority weighs, researchers adopted different types of Fuzzy prioritization approaches, for instance, the earliest attempt in prioritizing fuzzy weighs was accomplished by van Laarhoven and Pedrycz (1983) in which triangular fuzzy numbers were compared according to their membership functions. Likewise, Buckley (1985) used trapezoidal fuzzy numbers to integrate the fuzzy priorities of comparison ratios. A new approach called Fuzzy Synthetic Analysis (FSA) for computation of a sequence of weigh vectors (Chang 1996) suggested the application of extent analysis method for the synthetic extent values of the Fuzzy pairwise comparisons. The term ''synthetic'' expresses the process of evaluation whereby several individual criterions of an evaluation are synthesized and aggregated to a final form. Despite the diversity of Fuzzy prioritization approaches, FSA is the most abundant used method in the literatures indicating its popularity in prioritizing decision variables. It has been perceived as the best prioritizing method due to its simple and easy in application (Chan, Kumar 2007).

Methods and procedures in developing FSM
To appropriately conduct the qualitative technique in the development of FSM, a developing team was established consisting of construction engineers, IT professionals, risk managers, and mathematicians.
Owing to the nature of the developers where their experiences, perceptions, and opinions are necessities to the enhancement of the model, the qualitative approach was adopted in this study. The qualitative technique enables on-the-spot directness to the information in which rapid, immediate response could be obtained from the elites, where it is not possible when the quantitative technique such as questionnaire surveys are conducted. The developing team consists of a range of experts of different specialties, whose detailed information regarding their contribution towards the birth of FSM is summarised in Table 3. The use of probability theory to deal with the construction project of one-time characteristic complicates the risk analysis process. Conventional approaches are impractical in those real situations where high quality data are absent yet they could not effectively deal with the subjective human assessments, for instance, the fixed scale of 1Á9 used in the pairwise comparison process is incapable to   describe the interval judgment of experts. The authors adopted the Fuzzy-AHP technique as the decisionmaking framework for construction risk analysis in the developed model since the Fuzzy-AHP allows a more accurate description of the subjective data, where the fuzzy pairwise comparisons are more rational in reflecting experts' uncertain judgments than crisp one. Such a model could facilitate the decision-making process, where the complex uncertainty inherited in subjectivity is able to be captured and mitigated optimally. The project performance is significantly affected by construction risks in concerns of cost, time, and quality. The developed FSM is to holistically solve multi-criteria complex problems in the real practice of construction. The algorithm of the proposed model consists of six phases, which are discussed as follows.

Establishment of risk assessment team
Owing to the large burdens during the project risk analysis, the decision-making process was conducted by a group of risk assessment experts. Due to their different background, experience, and knowledge, each expert in the risk assessment team has different impacts on the final decision. The experts with higher degree of knowledge and more related experience on the targeted project have more substantial impact in the risk assessment process so that their contribution factors are given more weigh in the model. This is due to the reason that the final result is more consistent as the risk analysis process is undertaken comprehensively by different experts with various competencies. The contributions factors are used to determine the weighing for different evaluators. Basically, the relative weighing of the experts is determined by their competence on the basis of their experience, knowledge, and expertise related to the targeted project. The formulas for contribution factors are presented in Section 5. The risk assessment team is responsible to classify and to structure all potential risks within a hierarchy tree in the next step.

Structure a hierarchy tree
Structuring of a hierarchy tree aims to decompose the goal into adequate details in which all the criteria could be thoroughly assessed. Generally, the top level of the hierarchy tree is the overall goal of the decision problem. In the context of construction risk analysis, the goal is defined as risk evaluation. The subsequent levels present the general risk sources, then their specific risk factors, which are evaluated. The lowest level is the alternative of decision options, with regards to the goal, which are determined based on the kind of results desired in the end of analysis. To determine the decision criteria, it entails the understanding of the underlying factors impacting the goal. Hence it is essential to investigate all potential sources of uncertainty likely to affect a project. The recognized risks are classified in a way that the risks with similar characteristics are grouped together in the hierarchy. The construction uncertainty is commonly modelled based on the integration of two risk parameters: a) the probability of occurrence and b) severity of risk impact. The hierarchy tree was constructed as shown in Figure 2. The complex decision problems were structured within a simple hierarchical structure, where the decision criteria were placed comprehensively into five levels. The top level is defined as ''Construction Project Risks'' to reflect the overall goal. It is followed by two risk parameters that serve as the evaluation basis for risks. The third level is where all major risk sources are located, with their respective risk factors in the subsequent level. The lowest level presents the project objectives including time, cost, and quality. As illustrated in Figure 2, the general risks and their specific sub-factors are located respectively in the third and the fourth level. Eventually, the project objectives such as time, cost, and quality are placed in the bottom level. It could mitigate the uncertainty depending on the relative risk impact towards the project objective. Compromises such as targeted budget, good scheduled time, and high project quality

Construction Risk Modelling
Step 2: Project Objectives Developer H measured risk impacts with regards to project objectives such as time, cost, and quality during the risk analysis process.
Step 3: AHP's Comparison Method Developer H applied Pairwise Comparison process within the developed model, where the risks were compared to determine which one was more dominance than the others in a project.

I 51 Female Kuala Lumpur Mathematician
Step 4  are guaranteed when all the project objectives are accomplished.

Pairwise comparison using Fuzzy comparison scale
The risk assessment process is carried out once the hierarchy tree is established. Most frequently there are multiple contradicting risk sources existing in a project. This complicates the decision-making process as the experts need to consider various criteria simultaneously. Hence, it is a necessity to prioritize risks for further attention. To do so, the experts need to firstly determine the relative weigh of each criterion in the same hierarchy, via pairwise comparison process, so that their relative priority weighs could be calculated. The greatest advantage of pairwise comparison is that the experts are allowed to focus on the comparison of just two objects, which makes the observation as free as possible from extraneous influences. To systematically capture the valuable subjective judgments of experts in the risk analysis, Fuzzy comparison scale is proven to be accurate and intuitive in reflecting the qualitative judgments where decision makers could specify preferences in the form of natural language regarding the importance of each criterion. The most common used Fuzzy numbers are both the triangular and trapezoidal Fuzzy number (TFN). In this study, the simplest form of TFN was applied for representing the linguistic judgments, as TFN was sufficient to produce a reliable result. The fuzzy scale of TFN is intuitively easy to use and to calculate so that it was adopted to improve the pairwise comparison process.

Aggregation of individual TFNs into group TFN
Every individual in the risk assessment team has a TFN preference for criterion in the hierarchy tree. The individual TFNs of particular criterion should be aggregated into the group TFN preference. The rationale of this step is to integrate all the individual TFN preferences for particular criterion so that the Fuzzy comparison matrices remain consistent. The aggregation process is completed once the individual TFNs of every criterion in the hierarchy tree are converted into group TFN. All group TFNs are arranged in a matrix structure, which is called ''Fuzzy comparison matrices''. Consequently, the relative priority weigh of each criterion was calculated using the Fuzzy prioritization method in the next step.

Calculation of priority weighs at different hierarchy level
It is usually not possible to address all risks with a same degree of attention, as resources available for risk management are limited. Concentration on risks with higher priority is essential for efficient risk management. This step aims to calculate the relative priority weighs of decision criteria in the same level, with respect to their upper criterions. Since the conventional eigenvector prioritization method is being doubt of its consistency, the Fuzzy prioritization method was used in this step to calculate the final priority weighs in the proposed model.

Systemization of results
The relative priority weigh of each criterion attained through previous steps was synthesized to obtain the final priority weigh. This process was computed by synthesizing all relative priority weighs of particular decision criteria from the bottom level to the top level. The outcome is a normalized vector of the overall weighs of the alternatives, which are then ranked in order. In response to the final ranking of each criterion, the users can take risk mitigation actions. Risk mitigation is a plan that reduces risk impact on the project performance. Options available for mitigation include ''control'', ''avoidance'', and ''transfer''. A mitigation plan could be carried out to reduce or to eliminate the risks with the selected higher priority weighs, with respect to the time, cost and quality of a project.

Mechanism and appearance of the developed FSM
Eventually, a Fuzzy Synthetic Model, abbreviated as FSM, was developed as shown in Figure 3. There are six steps within the model, which are delineated in the following sections.
Step 1: Establishment of Risk Assessment Team. In this step, the weighs were calculated to allocate difference contribution factors to the experts. If there Step 2: Structuring Risk Hierarchy Tree. The risk identification process was conducted based on the nature of a project. This is to anticipate potential risks on the stage of project development. The intuitive method was applied. The risks identified were structured into a simple hierarchy tree. The risks are grouped on the basis of their characteristics and the level of decomposition is non-limited. It depends on the variables to be measured in a project.
Step 3: Pairwise Comparison Using Fuzzy Comparison Scale. Pairwise comparison was carried out to determine the relative importance weighs of criteria. Every expert in the risk assessment team is required to  (2) where Ã represents a fuzzified reciprocal n-n judgment matrix containing all pairwise comparison ã ij between elements i and j for all i, j 0 {1, 2, . . ., n}; û and all ã ij are triangular fuzzy numbers ã ij 0 (l ij , m ij , u ij ) with l ij the lower and u ij the upper limit and m ij is the point where the membership function m(x) 0 1.
Step 4: Aggregation of Individual TFNs into Group TFN. The pairwise judgments of individual TFNs were aggregated into a group Fuzzy number using the operational laws base on Zadeh (1965), which are defined as: Á Fuzzy addition: Á Fuzzy multiplication: Á The inverse of triangular fuzzy number M =l 1 ,m 1 ,u 1 ): Á The scalar multiplication of a triangular fuzzy number: Step 5: Fuzzy Synthetic Analysis. Fuzzy synthetic analysis was carried out to calculate the relative priority weighs of criteria. According to Chang (1996), there are three procedures involved as described below: Procedure 1: Calculate the Fuzzy Synthetic Extent Values: Procedure 2: Calculate the Degree of Possibility: Procedure 3: Calculate the Normalized Weigh Vectors: Assuming that: for k 0 1, 2, . . ., n; k " i. Then the weigh vector is given by Eq. (14): where: A 1 (i 0 1, 2, . . ., n) are n elements. Via normalization of W?, the normalized weigh vectors are as Eq. (15): where W is a non-fuzzy number.
Step 6: Synthesizing Final Weighs. Finally, the relative priority weighs of the criteria were synthesized across the hierarchy tree to produce final weighs with respect to project objectives. Consequently, risk controlling process could take place to mitigate and monitor the highest risky uncertainty.

Pilot Run and validation of FSM
The Pilot Run project for the developed FSM was conducted with a G7 contractor who managed to assess the potential risks in a ten-floor high-rise building project at Kepong, Kuala Lumpur. The goal is to take into account all the possible impact of risks towards the project objectives. The Pilot Run project is presented here to validate the implementation of the developed FSM.

Pilot Run: established risk assessment team
Four experts in the G7 contractor were selected to form a risk assessment team. The profiles of these 4 experts are presented in Table 4. Prior to the risk analysis process, the contribution factor for the first expert c 1 was calculated based on his working experience related to the risk assessment on this type of construction, so that his weighing was determined by Eq. (16). Similarly, the contribution factors for other experts were calculated as shown in Table 4:

Pilot Run: pairwise comparison using fuzzy scale
In this step, pairwise comparison for every criterion was conducted at all these 5 levels in the hierarchy structure. Triangular fuzzy numbers (TFNs) in the pairwise comparison scale were used to determine the priorities of different criteria. Table 5 demonstrates the pairwise comparison results on determining the relative importance weighs for criteria with respect to ''Weather'' at level 4.

Pilot Run: aggregation of individual TFNs into group TFN
In this step, the contribution factor of each expert was multiplied with the corresponding individual TFNs.
All the individual TFNs were aggregated into the group TFN. The aggregation score of each criterion was calculated using Eqs (3), (4), and (6). For instance, the aggregation score of ''Cost and Time '' under ''Weather'' was calculated as (3.18,3.68,4.18) as shown in Eq. (17). The aggregated scores for other criteria were obtained in the same way. Once the aggregation process was completed, the fuzzy comparison matrix of the criteria was produced as shown in    Using these vectors, Eqs (9) to (12) were used to obtain the degree of possibility. The results are: V S Cost ! S Quality ¼ 1; V S Quality ! S Time ¼ 1; V S Quality ! S Cost ¼ 1: Similarly, using Eq. (13), the results were calculated as: Given by Eqs (14) and (15), the weigh vector is W w ? 0 (0, 1, 1) T . Finally, via normalization of W w ?, the normalized weigh vector from Table 6 was calculated by using Eq. (16) as W w 0 (0, 0.5, 0.5) T , where W w are non-fuzzy numbers. This step was repeated for each criterion at each level in the hierarchy tree to derive their normalized weigh vectors. The matrices of pairwise comparisons and their respective normalized weigh vector at level 4, level 3, level 2, and level 1 are presented in Tables 7, 8, 9, and 10, respectively.

Pilot Run: synthesized final results
Finally, the combination of priority weighs for each criterion at all levels were computed to determine overall priority weighs for the risks with respect to time, cost, and quality. The synthesized results are given in Table 11. The graphic results as shown in Figs 5 and 6 indicate that the project has higher risk in cost than in time and quality. Mitigation plan could then be executed to monitor and to control those risks with a high ranking to ensure their accordance with project objectives.  V S Quality ! S Time ; S Cost ¼ V S Quality ! S Cost and S Quality ! S Cost ¼ 1:

Validation of FSM
A validation process of the developed FSM was carried out to determine whether this model was of application value for risk evaluation in construction practices, which was conducted online by randomly selected 9 practitioners in the construction sector worldwide. Each parameter was given a 10-scale evaluation. The validation results as shown in Table 12 indicate that the developed FSM could systematically help practitioners to evaluate construction risks. The values of flexibility, accessibility, completeness, reliability, user friendly level, assistance in decision-making, and adaptability for complexity are acceptable.

Benefits and limitations
The advantage of a Fuzzy-AHP model is that it could efficiently quantify the valuable subjective data to cope with multiple contradicting risk problems. Taking project objectives such as time, cost, and quality into consideration are very important in the risk assessment process. As to guarantee project success, it entails effective risk management of a project. Compared with those existing methods, the FSM developed in this study has the following benefits: a) it accelerates the decision-making process. Construction practitioners could conduct a complicated risk assessment process effectively using the developed model which is simple and systematic in evaluation and computation; b) it gives more convincing result with the consideration of project objectives within the framework, hence it aids in an optimal allocation of project resources to mitigate possible risks detrimental to the success of a project in terms of time, cost, and quality; c) it is able to capture the vagueness of human thinking style and to ensure the consistency in multi-criteria decisionmaking process; and d) it could be used in measuring risks across different stages of a project life cycle, from the inception till the completion of a project. Nevertheless, the developed FSM has a shortcoming that the computational fuzzy calculations in this model are rather time-consuming, which needs to be optimized in future study.

Conclusions and recommendations
Aiming to remove complex and unreliable process arising in subjective judgments during construction risk assessments, the developed FSM provides an appropriate approach to tackle the fuzziness involved in the decision-making process. The pilot run revealed that the FSM could accelerate the decision-making process and could provide optimal allocation of project resources to mitigate possible risks detrimental to the success of a project in terms of time, cost, and quality. Further efforts are recommended in developing a decision support tool to conduct the tedious fuzzy calculations to facilitate the overall risk assessment process. Besides, since the computational fuzzy calculations in the developed model is rather timeconsuming, the simplification and the optimization of the fuzzy calculation process should be paid attention to in future research works.