A Novel Safety Risk Assessment Based on Fuzzy Set Theory and Decision Methods in High-Rise Buildings

Abstract

The high-rise construction industry has particular features, such as prolonged construction periods and constant change in the workplace. These features may have turned it into the most dangerous industry, given its significant mortality rate. This research aims to identify effective criteria for high-rise buildings’ safety issues and rank the most critical risks to level up the safety of these projects. This research is divided into two phases: In Phase I, the effective criteria in the literature on the occurrence of accidents are divided into three main classes, and their weights are determined using the best–worst method. In Phase II, the existing risks are ranked using the fuzzy Vlse Kriterijumska Optimizacija Kompromisno Resenje (FUZZY VIKOR) method. The results indicate that safety training and monitoring, which account for approximately 35% of the total weight, are the most influential criteria for risk occurrence. The risk of falling from heights has been ranked first as the most critical safety risk according to the eight criteria, including safety training and monitoring. The total weight of criteria in which falling from height attains the first rank equals 0.688. Damages caused by working with manual tools and equipment have the highest priority in four criteria, and the total weight of 0.1591 attains the second rank. The results of this research comply with the current situation of the construction industry and pave the way for future research on high-rise construction projects.

1. Introduction

There is no international definition for high-rise buildings. According to the National Fire Protection Association (NFPA), in the US, buildings higher than 23 m or seven floors are considered high-rise buildings [1]. Article III of the National Building Regulations of Iran defines high-rise buildings as buildings higher than 23 m. Regardless of these definitions, the growing trend of constructing high-rise buildings is significant, especially in metropolises [2]. Many developed countries have taken various measures to tackle the accidents and damages of working on construction projects. However, developing countries are more subject to accidents caused by construction due to a lack of safety regulations and adequate knowledge of this field [3]. According to the Tehran Fire Department’s report, construction projects in Iran account for a significant 30% of mortality [4]. The persisting growth in high-rise buildings highlights the importance of safety risk analysis to make an accurate evaluation of the risks threatening these buildings. Risks threaten the success of a project. Thus, risk management is an arranged process of identifying, assessing, and responding to risks during the life cycle of a project in order to reduce and control risks [5]. Thus far, no exhaustive research has assessed the influential critical factors on high-rise buildings in Tehran. The results of this work can assist safety experts in reducing accidents in high-rise projects. Due to population growth and in response to economic development in Metropolises such as Tehran, the construction industry is moving toward high-rise buildings, such as hotels, commercial-office complexes, and residential buildings [6]. Since safety function in high-rise buildings is a safety challenge, proper prioritization of safety risks in planning, financing, and risk management processes is paramount [7]. In constructing high-rise buildings, safety regarding injuries, accidents, and mortality has remained a global concern. Accordingly, examining safety factors, such as personal protection equipment, falling from heights, and scaffold problems, is critical in constructing high-rise buildings [3].

In previous studies, risk assessment was carried out according to severity, occurrence probability, and occurrence frequency of these risks without considering criteria weight. The fuzzy multiple-criteria decision-making (MCDM) method is an integrated set that makes a suitable decision in risk assessment. Weight parameters of specialists usually include different mentalities. Based on the analyses conducted, this study proposes a novel idea for assessing safety risks in high-rise buildings using a variety of safety management criteria. Accordingly, by integrating linguistic expressions and fuzzy numbers in the collaborative decision, an attempt is made to tackle problems in traditional methods and help decision makers identify the most important safety risks concerning influential criteria. Research objectives are as follows:

Proposing a combinatorial decision-making model to determine the weights of the effective criteria in the occurrence of safety accidents in high-rise buildings.

Determining and ranking the most critical safety risks in high-rise buildings to prevent these accidents.

Therefore, the necessity of safety risk assessment and ranking in the construction of high-rise buildings is evident. Here, we used the relatively new best–worst method (BWM) and the fuzzy VIKOR method to identify and prioritize the most significant safety risks in high-rise buildings of Tehran to improve safety performance in construction sites. There are methods based on paired comparisons, such as the analytic hierarchical process (AHP), to extract the weights of effective criteria in the decision-making process. The number of paired comparisons is one of the problems of this method. We used the BWM method, which has fewer paired comparisons, to circumvent this problem, resulting in more compliance. The fuzzy VIKOR method is a powerful method to solve multi-criteria decision-making problems with contradicting criteria in a discrete space with uncertainties.

The main advantages of the study are safety risk evaluation in a high-rise building, a combination of multi-criteria decision-making techniques, the investigation of various factors influencing the occurrence of various safety risks, falling from a height being the most important risk in high-rise buildings and safety supervision and training being the most important factors involved in preventing accidents. In this research, Section 2 presents an overview of the research literature on safety risks in the construction industry, Section 3 elaborates on the research method, Section 4 presents the application of the proposed method for 30 high-rise projects in Tehran as a case study, and Section 5 presents and discusses the results of implementing the model. Eventually, Section 6 includes the conclusion of the study and research limitations.

2. Literature Review

Risk assessment involves a joint effort to identify potential capacities that may be actualized contingent on environmental conditions and people. Recently, safety risk assessment has become a critical issue in managing construction projects [8]. Considering that the systematic assessment of safety risks is classification and response to risk, prioritizing risks and finding strategies to reduce risk can be considered an instance of multi-criteria decision-making. The proper implementation of safety risk assessment in high-rise buildings requires systematically prioritizing and weighing the criteria based on environmental conditions and expert judgment [8]. The assessment of occupational risk is a key criterion for reaching an acceptable level of safety. In the assessment process, many factors can complicate the assessment due to insufficient and incorrect information. Thus, traditional approaches for identifying and assessing risk often fail, hence the significance of implementing a fuzzy deduction system to overcome these deficiencies. The fuzzy set theory can explore the uncertainties related to risk factors that are usually based on experts’ responses to assessment questionnaires. These responses are analyzed based on paired comparisons. In many cases, however, paired comparisons do not produce a compatible matrix [5]. Identifying probable risks requires a comprehensive list of risks per occupation at the project site. Checklists are one of the most frequently used risk assessment tools in the construction industry [9]. Extensive studies are performed to introduce a deep insight into the construction industry’s types and causes of intrinsic accidents. Some studies focus on tracing the underlying factors for accidents that are specific to the construction industry, while some only specify the main types of building-related incidents [9]. The evidence suggests there might be interactions between the involved factors. For example, temporal risks can affect expenditure risks. Multi-criteria decision-making methods are the most common tools for solving construction project problems. In these methods, some options are assessed against the criteria. Construction projects in complex and irregular environments need various risk criteria for assessment. In this regard, multi-criteria decision-making methods are particularly efficient [10]. Amiri et al. used fuzzy logic for assessing job risks. They studied six main factors in the occurrence of incidents, including human, organizational, managerial, and equipment and resources [11].

2.1. Managerial Factors

Management as an indirect factor can increase or decrease risks and ensuing incidents [12]. In recent years, risk management has been studied extensively in construction projects because of its scientific importance. Today, a deep knowledge of the environment and the ability to make impeccable decisions are needed because of the speed of changes and imminent dangers. The factors in risk management include safety training of workers, motivation and the reward and punishment system, organizing the committee of safety and occupational health, suitable supervision, workplace safety, and control of contractors. A portion of these incidents can be prevented by timely management [13,14]. Management commitment is an essential organizational factor in implementing safety plans, with a critical role in accidents. Management commitment is regarded as a value in a project [15]. Safety culture originates from individual and communal values, including beliefs, understanding and insight, and behavioral patterns, setting the style and skill of safety management in a project. The continuous growth of high-rises has increased the need for safety and health management. Hence, it is necessary to manage the factors of incidents and approaches to prevent them in high-rise construction sites [15,16]. Based on safety management and occupational health requirements, there should be at least one safety manager in each construction project who should supervise the implementation of safety measures [17]. Workers systematically engage in unsafe activities for various reasons, including pressure from production, lack of safety culture, lack of sufficient training, and insufficient allocation of resources. Therefore, employers must adopt more comprehensive approaches to produce safety behaviors, which increase workplace safety and form attitudes, beliefs, and behaviors in workers. Despite the vast research on safety training and creating positive attitudes, it has been suggested that training is largely ineffective in changing workers’ attitudes [18].

2.2. Individual Factors

Age, education, gender, and many other factors influence the formation of safety attitudes. Attitude is vital in determining people’s behavior. Attitudes determine how workers behave and require them to accept workplace instructions. All these steps need training to form the attitude of the workers [19]. Accidents are generally caused by unsafe conditions and unsafe behavior. During the past decades, steps have been taken to eliminate unsafe conditions by using protective equipment, developing management systems, rules and regulations, and providing training. In order to reduce unsafe behaviors, factors that cause such behaviors must be identified [20,21]. The height of high-rise buildings is associated with a wide range of management problems, including the impact of temperature stress on the floors and various physiological and psychological effects on the workers on the upper floors [13]. Many sources describe the absence of personal protective equipment as the main cause of accidents. Proper use of protective equipment can also prevent accidents. Motivated workers are more committed to working and abiding by safety principles [15]. The analysis shows that tolerance of safety risks among workers is influenced by the mental perception of people, their knowledge and work experiences, and work-related characteristics. To develop a good safety culture, the attitude of the workers must be changed by adopting the best work practices [22,23]. Current occupational safety laws and regulations are designed to protect workers’ lives. These rules affect construction efficiency and increase construction costs, preventing the workers from properly following the rules. Wang et al. presented a model to discover the relationship between unsafe behaviors and violations of regulations to investigate unsafe behavior patterns for preventing accidents in construction sites in Taiwan. They determined 13 priority rules to create a safe space in the workplace. They showed that 80% of unsafe behaviors in Taiwan were caused by violations of regulations related to equipment and occupational health and safety measures. Behaviors related to fall prevention and scaffolding have the highest percentage of frequency in the workplace. In particular, rebar and formwork workers are the most common violators of the rules [24]. In construction sites, most casualties are caused by falls due to misuse of personal protective equipment (PPE) [25,26]. Tom Wang et al. presented a research model based on structural equation modeling and mediation analysis with the aim of technology acceptance, safety management practices, and safety awareness to explain the acceptance of PPE by workers. In the United States, 70% of construction workers’ fatal falls are due to failure to use personal protective equipment. By examining the importance of using personal protective equipment in preventing accidents, it was found that by developing effective safety measures, including encouraging workers to use PPEs, we will see a reduction in casualties and injuries [25]. Several factors influence the use or lack of use of personal protective equipment among workers. However, the effectiveness of these devices in any work situation has not been confirmed. There have been extensive studies on the factors responsible for using these gears. Proper use of PPE can normally protect the head, eyes, ears, hands, feet, and whole body. They are also known as the last resort to deal with hazards before they occur. These accessories cannot be used in some jobs, and sometimes workers refuse to wear them due to discomfort. Various factors influence these safety measures, such as job status, safety training, knowledge, and previous experiences [27].

2.3. Environmental Factors

The construction site is a high-risk environment for workers. Hazardous tools, machines, and materials in the project environment are among such risks. In addition to these risks, the interaction of different work teams creates complex potential scenarios. Coordinating these factors is a significant safety challenge because each group has specific and sometimes different goals. However, the workplace is a shared environment. Thus, the involved factors affect and are affected by each other. On the same basis, health and occupational safety is a necessary field for the construction industry to prevent workplace accidents and ensure workers’ welfare. In addition, several economic, psychological, organizational, environmental, and technical factors are associated with safety risks. For example, four types of accidents relating to working at heights, including scaffolds, falling from height, impacting with objects, and falling objects (tools), can have various reasons [13]. The construction industry contributes to economic growth and infrastructure development, and heavy machinery for different activities and displacements is one of its vital assets. Accidents in the machinery section often severely affect the project’s time and expenditure. Machinery and tools have always been among the causes of accidents in the building industry. Tower cranes are known as the main symbol of high-rise buildings, and because of their key roles, they are one of the eminent equipment in construction projects [6]. Machinery- and tools-related accidents always constitute a major part of incidents. However, severe effects such as death and permanent disability occur in high-rise sites. Machinery accidents, including tower cranes, frequently occur in high-rise projects. Increased use of tower cranes in building workplaces increases accidents and fatalities due to various factors, such as assembling, lifting objects, and disconnecting devices. J. Y. Kim et al. studied the cause of tower crane accidents using the AHP method. They revealed the most important factors of accidents: the weak sight of the operator for remote control and weak management while lifting objects and controlling the surrounding environment [28]. Bedi et al. studied the cause of accidents during the on-site operation of machinery. They divided the factors into the work process, people, and project environment. They reported that factors such as insufficient maintenance of the machinery, operator negligence, insufficient training, human factors, and the situation of the project site could affect the occurrence of accidents. They suggested uplifting the know-how and the skills of the workers and machine operators to reduce the occurrence of these accidents [29]. The safety of the worker should be guaranteed in the workplace. Scaffolds are very useful in construction projects for the façade, plastering, lighting, and painting tasks. Studying the quality of scaffold accidents is necessary to prevent similar accidents and take control measures. Factors such as knowledge of the Health, Safety, Environment (HSE) rules and regulations, inspection and control of scaffolding contractor companies, and the operator’s education level can affect workplace incidents [30]. Accidents in high-rise buildings usually occur in temporary structures since they are easily damaged due to dismantling and repeated use [6]. Blazik et al. assessed scaffolds and the probability of their failure in construction sites. They investigated the failure mechanism in 120 existing scaffolds at different locations in Poland. The factors studied in that paper were scaffold models, technical conditions and geometric defects, load capacity, the anchor formed in the scaffold, and the ground on which the scaffold rests. They reported that reliability is higher in scaffolds used in a maximum of 12 weeks. However, the results could differ in scaffolds with more complex frames and geometry and in modular scaffolds [31]. The summary of the literature review is shown in

Table 1. A summary of the research background.

Reference	The Investigated Criteria			Ranking	Weight	The Method Used	Sub-Criteria	Research Field
	Individual Factors	Management Factors	Environmental Factors
Present study	✓	✓	✓	✓	✓	BWM, and Fuzzy VIKOR	Safety attitude and perception, experience and skill, training, surveillance, ….	Weighting influential factors in safety risk occurrences and prioritizing these risks in high-rise construction buildings
[1]		✓	✓			semi-structured interviews and a questionnaire	Management measures, Management measures, safety environment worker safety quality	Critical Success Factors for Safety Management of High-Rise Building Construction Projects in China
[2]					✓	AHP, FCE	Safety signs, personal protection equipment, falling from a height, scaffold break down, working conditions, and personal factors	Identifying influential factors to safety accidents in high-rise projects
[4]				✓		Interview, fuzzy numbers	Accident severity, effect, and probability of occurrence	Safety risk assessment and risk prioritization in high-rise building projects
[5]				✓	✓	FAHP, TOPSIS	Time, cost, quality, safety	assess the overall risks of construction projects
[6]			✓				working environment, exposure to hazardous condition, work at high elevation, inadequate safety protection and temporary structures	Preliminary study on the identification of safety risks factors in the high-rise building construction
[7]						Interview, NVivo 11 software, and zoom software		Integration of drone, RFID, GPS, and BIM for assessing safety accidents in high-rise building projects
[13]	✓	✓				Questionnaire	Safety education and training of workers, safety incentive or reward system, suitable supervision, safety environment	Analysis of Critical Management Factors for High Rise Building Construction Projects
[15]	✓	✓	✓			DEMATEL		Determining the most important factors in falling from a height
[17]		✓					Safety monitoring	safety planning and monitoring processes of a high-rise building construction project in Chile
[18]	✓	✓	✓	✓		FTOPSIS, FDMATEL, FANP	Safety culture, safety attitude, monitoring, training	Assessment of safety culture among job positions in high-rise construction
[21]	✓					Questionnaire	Safety motivations and prohibitions, safety attitudes and beliefs, client safety climate, contractor competency, safety supervision and management, safety behaviors, contract management, social climate, psychological unsafety	Factors affecting unsafe behavior in construction projects
[22]						Fuzzy logic, ANN	HSE	identifying the causes for accidents and implementing solutions
[26]						Questionnaire	Safety helmet, eye protectors, ear protectors, mark and respirator, protective gloves, safety belts, safety footwear, protective clothing	Using personal protective equipment in construction projects, Malaysia
[28]	✓					Questionnaire	Psychological distress	the relationship between safety measures and human error with the objective of identifying the impact of psychological distress among workers working at heights within the construction industry
[32]				✓		FAHP, PRAT	Accident risks physical risks environmental risks	Risk analysis and assessment in the Greek construction sector
[33]	✓	✓	✓			Fuzzy Pythagoras, AHP, Fine Kinney	Risk occurrence probability, number of repetitions, risk severity	Health and occupational safety risk assessment in excavation process at a construction site
[34]						Checklist, Fuzzy AHP	Sanitation, safety, environmental risks	HSE risks in high-rise buildings in Tehran
[35]						Interview	Direct management, indirect management	Qualitative study, safety leading methods in construction projects
[36]						Excel software		Effect of training workers working at height by virtual reality
[37]				✓		Fuzzy FMEA, Fuzzy VIKOR	Risk occurrence, severity, and detection probability	Crane evaluation
[38]				✓	✓	FAHP, TOPSIS	Probability, severity, exposure, detectability, worsening factor	Rating of safety risks in green high-rise construction
[39]	✓			✓			Fault of person, accidents, injury, ancestry and social environment	Investigating reasons behind accidents
[40]	✓	✓				Pareto-Lorenz	Technical causes, organizational causes, and human causes	Investigating the reasons be-hind falling from a height
[41]						GPS, BIM, RFID, BLE	Monitoring approaches	Preventing individuals from falling from a height, using a monitoring system
[42]	✓					Questionnaire	Demographic Cognitive Psychological	Causes of workers’ unsafe behaviors
[43]			✓	✓		AHP	Risk analyses of lifting equipment	Elevator risks
[44]				✓	✓	FBWM, IVFTOPSIS	Severity and probability	Worker’s safety risks assessment
[45]						Questionnaire, AHP, IoT	Safety monitoring	Safety monitoring
[46]	✓	✓	✓			Questionnaire, Microsoft Excel	Economic impact, social impact	Identifying reasons behind construction accidents in Egypt

.

2.4. Multi-Criteria Decision-Making Methods

Multi-criteria decision-making methods (MCDM) have evolved to be compatible with different types of plans. In the past decades, multi-criteria decision-making has been widely used to develop new methods and improve the efficiency of existing methods. Identifying different MCDM methods and presenting the advantages and disadvantages of each method is an essential step in developing a research foundation [47]. Multi-criteria decision making includes several steps: substitutions, criteria creation, evaluation options, criteria weighting determination, and the ranking method [48]. Decision making refers to the selection of a collection of options that are satisfactory. The essence of MCDM is to rank the available options based on the criteria and information provided by the decision makers with a particular approach. It also covers a significant part of modern decision making in systems engineering and management sciences, which, in turn, is a diverse branch of fields, such as engineering and economics [47]. Kaya et al. applied a combination of two TOPSIS and AHP methods as a multi-criteria decision-making model to investigate real conditions in smart buildings [49]. Moreover, Yeganeh et al. used the fuzzy FMEA method for risk management in LSF buildings during the design, construction, and operation phases, entailing risk identification, risk assessment, and risk response. The effects of these risks on project time and cost were evaluated, and according to the results, the risks involved in the construction and operation phases are higher than those involved in the design phase [50]. Since modular construction differs from conventional construction, risk management in conventional construction cannot be applied to the modular type. Li et al. used the AHP method to rank the risks in these buildings. They investigated the influencing risk factors of cost and time in such projects [51]. Kamranfar et al. combined ANP and DMATEL decision-making techniques to identify the obstacles to green building development in district 22 of Tehran. Considering the economic, environmental, and sociocultural criteria, their results revealed that economic factors ranked first among the obstacles to developing such buildings [52]. Urban waste management is among the most recent issues in metropolises, the mismanagement of which would lead to catastrophic results in the future. Shahsavar et al. integrated the three decision-making techniques of AHP, ELECTERE, and TOPSIS to develop integrated urban waste management in Mashhad through multi-criteria decision making. Their results suggested that urban waste recycling would increase citizen satisfaction from 49 to 64% [53]. AHP and TOSIS are two common MCDM tools. In reality, however, they fail to reflect the expert assessments accurately. Therefore, the present research attempts to apply other techniques, such as the fuzzy VIKOR and best–worst methods, as approaches that are more compatible with the results.

2.4.1. Best–Worst Method

BWM is an MCDM method that determines the relative importance of criteria in paired comparisons of decision makers by solving a linear or nonlinear problem [54]. The BWM method is one of the multi-criteria decision-making techniques that deals with effective factors and criteria in decision making for weighing. This method, consisting of quantitative and qualitative criteria, helps decision makers make logical decisions. Inconsistency in the paired comparison matrix is the major problem in the AHP method, leading to confusing results. In addition to this disadvantage, the number of paired comparisons increases as the number of criteria rises. In order to fill this gap, Rezaei proposed a method to minimize the number of paired comparisons by structured paired comparisons. Instead of $n\left(n-1\right)/2$, the number of comparisons, the BWM method requires a $2n-3$ number of comparisons. The steps of this method are listed as follows:

First step: selecting and determining decision-making criteria sets hierarchically.

Second step: determining the best (the most important and desired) criteria and the worst (the least important and undesired) criteria.

Third step: determining the importance of the best criteria concerning other criteria with a number between 1 and 9, where $a_{Bj}$ indicates the importance of the best criterion over the criterion j.

Fourth step: determining the importance of other criteria relative to the worst criterion with a number between 1 and 9, where $a_{jw}$ indicates the importance of criterion j over the worst criterion.

Fifth step: finding the optimal weights of criteria and $\mathsf{\xi }+$ (optimum) using the following mathematical equations.

${\mathsf{\xi }}^{+}$is considered the paired comparison index; the closer it is to zero, the higher the compatibility level [30].

$\min \mathsf{\xi }$

$\mathrm{s}.\mathrm{t}.$

$$\left|{\mathrm{W}}_{\mathrm{b}}-{\mathrm{a}}_{\mathrm{Bj}}{\mathrm{W}}_{\mathrm{j}}\right|\le {\mathsf{\xi }}^{\mathrm{L}},\mathrm{for}\mathrm{all}\mathrm{j}$$

$$\left|{\mathrm{W}}_{\mathrm{j}}-{\mathrm{a}}_{\mathrm{jw}}{\mathrm{W}}_{\mathrm{w}}\right|\le {\mathsf{\xi }}^{\mathrm{L}},\mathrm{for}\mathrm{all}\mathrm{j}$$

$${{\displaystyle \sum }}_{\mathrm{j}}{\mathrm{W}}_{\mathrm{j}}=1,{\mathrm{W}}_{\mathrm{j}}\ge 0,\mathrm{for}\mathrm{all}\mathrm{j}$$

(1)

Since ranking options require determining the weight of each criterion, and the VIKOR method does not determine the weight, we took advantage of linear BWM to weigh the criteria. Selecting an appropriate method in risk assessment affects the results. Thus, it must be not only scientific, but also applicable and objective.

• Compatibility of data in BWM

In order to tackle the compatibility problems of previous methods, this method determines data compatibility by specifying the decision maker’s preferences so that the case is reviewed if the range is not acceptable. According to the following equation, the compatibility ratio is determined based on the input data:

$${\mathrm{CR}}^{\mathrm{I}}=\underset{\mathrm{J}}{\max }{\mathrm{CR}}^{\mathrm{I}}$$

(2)

$${\mathrm{CR}}_{\mathrm{j}}^{\mathrm{I}}=\left\{\begin{array}{cc}\frac{\left|{\mathrm{a}}_{\mathrm{Bj}}\times {\mathrm{a}}_{\mathrm{jW}}-{\mathrm{a}}_{\mathrm{BW}}\right|}{{\mathrm{a}}_{\mathrm{BW}}\times {\mathrm{a}}_{\mathrm{BW}}-{\mathrm{a}}_{\mathrm{BW}}},& {\mathrm{a}}_{\mathrm{BW}}>1\\ 0,& {\mathrm{a}}_{\mathrm{BW}}=1\end{array}\right.$$

(3)

Table 2. Allowable thresholds for input-based consistency ratio.

Criteria Number
9	8	7	6	5	4	3	Scale
0.1667	0.1667	0.1667	0.1667	0.1667	0.1667	0.1667	3
0.2683	0.2577	0.2527	0.2206	0.1898	0.1529	0.1112	4
0.2960	0.2844	0.2716	0.2546	0.2306	0.1994	0.1354	5
0.3262	0.3221	0.3144	0.3044	0.2643	0.1990	0.1330	6
0.3403	0.3251	0.3144	0.3029	0.2819	0.2457	0.1294	7
0.3657	0.3620	0.3408	0.3154	0.2958	0.2521	0.1309	8
0.3662	0.3620	0.3517	0.3333	0.3062	0.2681	0.1359	9

shows the inconsistency of the input data in terms of the number of criteria in the problem, as well as the scales used in pairwise comparisons [54].

2.4.2. Fuzzy VIKOR Method

The fuzzy VIKOR method was invented to solve multi-criteria decision-making problems where the criteria have different and heterogeneous units and were developed under uncertainty based on fuzzy VIKOR. In this method, the triangular fuzzy number can be used to define quantities, where the criteria and their weights can be fuzzy numbers. The fuzzy triangular numbers could be used for defining inaccurate quantities. If the estimation of A_i is demonstrated concerning the criterion $C_j$ with the fuzzy number ${\tilde{\mathrm{x}}}_{\mathrm{ij}}=\left({\mathrm{l}}_{\mathrm{ij}},{\mathrm{m}}_{\mathrm{ij}},{\mathrm{u}}_{\mathrm{ij}}\right)$, the steps will be as follows [48].

• Determining the positive and negative ideal for each criterion in the form of (j = 1, 2, 3, …, n);

$${\tilde{f}}_j^{+}=\left(l_j^{+},m_j^{+},u_j^{+}\right),{\tilde{f}}_j^{-}=\left(l_j^{-},m_j^{-},u_j^{-}\right)$$

(4)

If the criterion is of the profit and positive type, then:

$${\tilde{f}}_j^{+}=\underset{i}{\mathit{max}}{\tilde{x}}_{ij},{\tilde{f}}_j^{-}=\underset{i}{\mathit{min}}{\tilde{x}}_{ij}$$

(5)

If the criterion is of the cost and negative type:

$${\tilde{f}}_j^{-}=\underset{i}{\mathit{max}}{\tilde{x}}_{ij},{\tilde{f}}_j^{+}=\underset{i}{\mathit{min}}{\tilde{x}}_{ij}$$

(6)

2.

If $j=1,\dots .,n,$ and $i=1,\dots .,m$, the normal fuzzy subtractions are obtained via the following equations:

For the positive or profit criteria:

$${\tilde{d}}_{ij}=\left({\tilde{f}}_j^{+}\ominus {\tilde{x}}_{ij}\right)/\left(u_j^{+}-l_j^{-}\right)$$

(7)

For the negative or cost criteria:

$${\tilde{d}}_{ij}=\left({\tilde{x}}_{ij}\ominus {\tilde{f}}_j^{+}\right)/\left(u_j^{-}-l_j^{+}\right)$$

(8)

3.

Calculating the weighted fuzzy summation ${\tilde{\mathrm{s}}}_{\mathrm{i}}=\left({\mathrm{s}}_{\mathrm{i}}^{\mathrm{l}},{\mathrm{s}}_{\mathrm{i}}^{\mathrm{m}},{\mathrm{s}}_{\mathrm{i}}^{\mathrm{u}}\right)$ and the maximum fuzzy performance ${\tilde{\mathrm{R}}}_{\mathrm{i}}=\left({\mathrm{R}}_{\mathrm{i}}^{\mathrm{l}},{\mathrm{R}}_{\mathrm{i}}^{\mathrm{m}},{\mathrm{R}}_{\mathrm{i}}^{\mathrm{u}}\right)$ is obtained using the equations below:

$${\tilde{s}}_i={\displaystyle \sum }_{j=1}^n\oplus ({\tilde{w}}_j\otimes {\tilde{d}}_{ij})$$

(9)

$${\tilde{R}}_i=\underset{j}{\mathit{max}}({\tilde{w}}_j\otimes {\tilde{d}}_{ij})$$

(10)

In the equations above, ${\tilde{\mathrm{w}}}_{\mathrm{j}}$ is the fuzzy weight of the criteria.

4.

The values ${\tilde{\mathrm{Q}}}_{\mathrm{i}}=\left({\mathrm{Q}}_{\mathrm{i}}^{\mathrm{l}},{\mathrm{Q}}_{\mathrm{i}}^{\mathrm{m}},{\mathrm{Q}}_{\mathrm{i}}^{\mathrm{u}}\right)$ are calculated using the equations below:

$${\tilde{\mathrm{Q}}}_{\mathrm{i}}=\frac{\mathrm{v}\left({\tilde{\mathrm{s}}}_{\mathrm{i}}\ominus {\tilde{\mathrm{s}}}^{\ast }\right)}{{\mathrm{s}}^{\mathrm{ou}}-{\mathrm{s}}^{\ast \mathrm{l}}}\oplus \frac{\left(1-\mathrm{v}\right)\left({\tilde{\mathrm{R}}}_{\mathrm{i}}\ominus {\tilde{\mathrm{R}}}^{\ast }\right)}{{\mathrm{R}}^{\mathrm{ou}}-{\mathrm{R}}^{\ast \mathrm{l}}}$$

(11)

That in the above relationships

$${\tilde{\mathrm{s}}}^{\ast }=\underset{\mathrm{i}}{\min }{\tilde{\mathrm{s}}}_{\mathrm{i}},{\mathrm{s}}^{\mathrm{ou}}=\underset{\mathrm{i}}{\max }{\mathrm{s}}_{\mathrm{i}}^{\mathrm{u}}$$

(12)

$${\tilde{\mathrm{R}}}^{\ast }=\underset{\mathrm{i}}{\min }{\tilde{\mathrm{R}}}_{\mathrm{i}},{\mathrm{R}}^{\mathrm{ou}}=\underset{\mathrm{i}}{\max }{\mathrm{R}}_{\mathrm{i}}^{\mathrm{u}}$$

(13)

where the maximum group compromise is established, and $\mathrm{v}=0.5$ is defined as the group profitability maximum $\mathrm{v}$.

5.

Defuzzification of the quantities above using the median to the second weight and their conversion to the absolute values;

6.

Arranging the absolute values $S,Q,andR$ in descending order and ranking the options;

7.

Determining the compromise solution in terms of the optimal quantity $Q,$ if the two conditions below are established.

First condition: the acceptable merit if the first and second ranks are A’ and A”, respectively, based on the quantity $Q$.

If the inequality below is established

$$Adv\ge DQ$$

(14)

$$Adv=\left[Q\left(A^{″}\right)-Q\left(A^{\prime }\right)\right]/Q\left(A^{\left(m\right)}-Q\left(A^{\prime }\right)\right]$$

(15)

where $\mathrm{DQ}=1/\left(\mathrm{m}-1\right)$ and $\mathrm{Q}\left({\mathrm{A}}^{\left(\mathrm{m}\right)}\right)$ are the ultimate M option in the content list $Q$.

Second condition: the acceptable stability in decision making if option A’ has the first place in terms of parameters S and R.

If each of the aforementioned conditions is not established, then a set of compromise solutions is discussed.

• Alternative ${\mathrm{A}}^{\prime }$ and ${\mathrm{A}}^{″}$ if only Condition 2 is not satisfied.
• Alternatives ${\mathrm{A}}^{\prime }$, ${\mathrm{A}}^{″}$,…., A^(H), if Condition 1 is not satisfied, A^(H) is the last alternative with which Condition 1 is not satisfied i.e.,$\mathrm{Q}\left({\mathrm{A}}^{\left(H\right)}\right)-\mathrm{Q}\left({\mathrm{A}}^{\prime }\right)<\mathrm{DQ}$for maximum H [48].

2.4.3. Fuzzy Sets

Most daily fields deal with uncertain data that classic mathematics might not be successfully modeled. The fuzzy method was introduced to tackle uncertainties. In this method, decision makers can express their preferences by linguistic variables. The construction industry is more subject to various risks than other industries. Given that risk is influenced by various factors, such as human error and insufficient information due to its nature, risk analysis in this industry is complicated, especially in the initial stages [55]. Trapezoidal and triangular fuzzy numbers (TFN) are special fuzzy numbers that are usually employed in different decision-making problems. In the present study, fuzzy triangular numbers express ambiguities in decision-makers’ responses.

Definition 1.

Number$\tilde{a}$is defined as a TFN, and its membership function is indicated below:

$${\mathrm{u}}_{\tilde{\mathrm{a}}}\left(\mathrm{x}\right)=\left\{\begin{array}{c}0,\mathrm{X}<\mathrm{l}\hfill \\ \frac{\mathrm{x}-\mathrm{l}}{\mathrm{m}-\mathrm{l}},\mathrm{l}\le \mathrm{x}<\mathrm{m}\hfill \\ \frac{\mathrm{u}-\mathrm{x}}{\mathrm{u}-\mathrm{m}},\mathrm{m}\le \mathrm{x}\le \mathrm{u}\hfill \\ 0,\mathrm{x}>\mathrm{u}\hfill \end{array}\right.$$

(16)

A TFN can be indicated as (l, m, u), in which u, m, and l are the lowest, medium, and highest values in the introduced set $\tilde{\mathrm{a}}$. Figure 1 demonstrates a TFN [56].

Definition 2.

If two TFN numbers are$\tilde{a}=\left(a_l,a_m,a_u\right)$and$\tilde{b}=\left(b_l,b_m,b_u\right)$, algebraic operations, including addition, subtraction, multiplication, division, and multiplication of a scalar number by fuzzy number, are expressed as follows [57]:

$$\tilde{\mathrm{a}}\oplus \tilde{\mathrm{b}}=\left({\mathrm{a}}_{\mathrm{l}}+{\mathrm{b}}_{\mathrm{l}},{\mathrm{a}}_{\mathrm{m}}+{\mathrm{b}}_{\mathrm{m}},{\mathrm{a}}_{\mathrm{u}}+{\mathrm{b}}_{\mathrm{u}}\right)$$

(17)

$$\tilde{\mathrm{a}}\ominus \tilde{\mathrm{b}}=\left({\mathrm{a}}_{\mathrm{l}}-{\mathrm{b}}_{\mathrm{u}},{\mathrm{a}}_{\mathrm{m}}-{\mathrm{b}}_{\mathrm{m}},{\mathrm{a}}_{\mathrm{u}}-{\mathrm{b}}_{\mathrm{l}}\right)$$

(18)

$$\tilde{\mathrm{a}}\otimes \tilde{\mathrm{b}}=({\mathrm{a}}_{\mathrm{l}}{\mathrm{b}}_{\mathrm{l}},{\mathrm{a}}_{\mathrm{m}}{\mathrm{b}}_{\mathrm{m}},{\mathrm{a}}_{\mathrm{u}}{\mathrm{b}}_{\mathrm{u}})$$

(19)

$$\tilde{\mathrm{a}}\oslash \tilde{\mathrm{b}}=({\mathrm{a}}_{\mathrm{l}}/{\mathrm{b}}_{\mathrm{u}},{\mathrm{a}}_{\mathrm{m}}/{\mathrm{b}}_{\mathrm{m}},{\mathrm{a}}_{\mathrm{u}}/{\mathrm{b}}_{\mathrm{l}})$$

(20)

$$\mathsf{\lambda }\tilde{\mathrm{a}}=\left({\mathsf{\lambda }\mathrm{a}}_{\mathrm{l}},{\mathsf{\lambda }\mathrm{a}}_{\mathrm{m}},{\mathsf{\lambda }\mathrm{a}}_{\mathrm{u}}\right)$$

(21)

$${\tilde{\mathrm{a}}}^{-1}=\left(\frac{1}{{\mathrm{a}}_{\mathrm{u}}},\frac{1}{{\mathrm{a}}_{\mathrm{m}}},\frac{1}{{\mathrm{a}}_{\mathrm{l}}}\right)$$

(22)

In order to obtain clear results in MCDM defuzzification, converting Fuzzy numbers to a defined and certain value is required. There are various methods for defuzzification. If $\tilde{\mathrm{a}}=\left({\mathrm{a}}_{\mathrm{l}},{\mathrm{a}}_{\mathrm{m}},{\mathrm{a}}_{\mathrm{u}}\right)$ is a TFN, its absolute value can be obtained using the following equation and median over second weight [55]:

$$\mathrm{crisp}\left(\tilde{\mathrm{a}}\right)=\frac{{\mathrm{a}}_{\mathrm{l}}+2{\mathrm{a}}_{\mathrm{m}}+{\mathrm{a}}_{\mathrm{u}}}{4}$$

(23)

3. Materials and Methods

Not obeying safety factors in high-rise building construction lays the foundation for grave dangers and damage to workers and costs imposed on the employee. In order to reduce such accidents, increase efficiency, and improve safety levels in construction sites, identifying and assessing safety risks are vital for managing, controlling, and reducing the implications of these risks. Many criteria are influential to safety risks. Accordingly, selecting safety risks in the presence of various criteria is a multi-criteria decision-making problem that studies risks concerning different criteria and ranks them. The present study consists of three main steps. First, safety risks in high-rise buildings and influential factors to these risks are identified. In this step, the decision-making group members were determined, including ten experts in Tehran’s high-rise building construction field. All participants in the present study were construction industry experts in Tehran with a minimum of five years of relevant working experience. Participants were also asked to mention their academic degree, organizational position, and working history, and clarify which project stakeholder they were operating with at the time of research. As

Table 3. Information about the experts that participated.

Participants Evaluation Criterion	Sub-Criterion	Participation Percentage
Education level	BSc	20%
	MSc	50%
	PhD	30%
Work experience	5 to 10 years	20%
	10 to 20 years	30%
	20 years and over	50%
Organizational position	Senior manager	20%
	Intermediate manager	20%
	Operational manager	60%
Which of the project stakeholder you are?	Customer	10%
	Contractor	50%
	Consultant	20%
	Project manager	20%
Major	Civil engineering	40%
	Architectural engineering	30%
	Electrical equipment engineering	10%
	Mechanical equipment engineering	0%
	Industrial engineering	0%
	Project management	20%

demonstrates, most respondents had a master’s degree in civil engineering and a working history of over 20 years in contract. Information about the experts that participated in the research is shown in Table 3. In order to determine the weight of decision makers, three criteria are employed, including organizational position, educational degree, and work experience. Afterward, the global and local weight of each main criterion and sub-criterion is determined using the BWM method. In the final step, first, the linguistic scales are introduced, and then the performance is determined concerning criteria using a criterion–option matrix. Ultimately, the final rank of risks is determined. Figure 2 demonstrates the procedure of this study.

4. Case Study

In this section, to evaluate the safety risks in high-rise buildings in Tehran, the proposed model shows the application of the method mentioned earlier in real-world conditions. The case study was performed on 30 buildings with a minimum occupation area of 350 m² and a height of 8–10 stories in Parand city situated 30 km southwest of Tehran in Tehran province. In this step, the identified risks are categorized into six major groups. The existing risks were identified by studying the existing literature. Considering the high number of risks and ten experts to answer the questions, the research procedure is time-consuming, and the possibility of errors increases. Thus, all the risks with the more severe occurrence and higher probability are divided into six main groups so that the research has a logical procedure. the results were as shown in

Table 4. The identified risks.

Abbreviations	The Main Identified Risks
A1	The severe damages caused by working with the manual tools
A2	Excavations, buildings adjacent to excavations, and issues related to deep excavation
A3	Fire
A4	Electrocution
A5	Falls from height (fall)
A6	Damages caused by working with machinery and equipment

. All the participant experts agreed with the presented classification.

4.1. The Investigated Criteria

After identifying the evaluated criteria from the literature review, the most important criteria were determined. Each of them was categorized into three groups, management, individual, and environmental factors, according to Figure 3. By reviewing the existing literature in this area, effective criteria for the occurrence of dangers were identified. The most critical criteria effective on risk occurrence were identified based on the views of the experts. Furthermore, Ardeshiri et al. divided all criteria into three general classes: individual, managerial, and group factors [20].

4.2. The Weight of the Investigated Criteria

The weights of the criteria were determined based on the viewpoints of the experts via a questionnaire. The questionnaire was prepared based on the best–worst method.

Each expert presented their preference once for the main criteria and then for the sub-criteria.

Table 5. Best-to-others and others-to-worst vectors for main criteria.

Preference of the Best Criterion over Others
MC3	MC2	MC1	Best Criterion	Decision Maker
7	1	2	MC2	DM1
1	8	5	MC3	DM2
1	6	3	MC3	DM3
8	1	8	MC2	DM4
9	1	2	MC2	DM5
9	1	3	MC2	DM6
7	1	7	MC2	DM7
5	8	1	MC1	DM8
9	1	3	MC2	DM9
9	1	2	MC2	DM10
Preference of Other Criteria over the Worst Criterion
8	MC2	MC1	Worst Criterion	Decision-Maker
1	9	2	MC3	DM1
5	2	1	MC1	DM2
8	1	2	MC2	DM3
1	5	2	MC3	DM4
1	9	2	MC3	DM5
1	9	3	MC3	DM6
3	5	1	MC1	DM7
3	1	3	MC2	DM8
1	7	2	MC3	DM9
1	9	2	MC3	DM10
MC3	MC2	MC1	threshold	Decision-Maker
0.0000	0.0476	0.0714	0.1359	DM1
0.0000	0.55	0.0000		DM2
0.0333	0.0000	0.0000		DM3
0.0000	0.0535	0.1428		DM4
0.0000	0.0000	0.0694		DM5
0.0000	0.0000	0.0000		DM6
0.3333	0.0476	0.0000		DM7
0.125	0.0000	0.0892		DM8
0.0000	0.0277	0.0555		DM9
0.0000	0.0000	0.0694		DM10

,

Table 6. Best-to-others and others-to-worst vectors for sub-criteria sc1-sc5.

Preference of the Best Criterion over Others
SC5	SC4	SC3	SC2	SC1	Best Criterion	Decision Maker
1	2	8	9	8	SC5	DM1
1	8	6	4	7	SC5	DM2
1	2	4	2	8	SC5	DM3
6	5	4	7	1	SC1	DM4
5	1	4	9	6	SC4	DM5
6	9	1	5	4	SC3	DM6
4	7	3	3	1	CS1	DM7
4	3	6	9	1	SC1	DM8
6	8	3	5	1	CS1	DM9
1	2	8	9	6	CS5	DM10
Preference of Other Criteria over the Worst Criterion
SC5	SC4	SC3	SC2	SC1	Worst Criterion	Decision Maker
9	2	5	1	3	CS2	DM1
8	1	4	3	4	SC4	DM2
5	3	4	3	1	SC1	DM3
2	2	3	1	7	SC2	DM4
5	7	5	1	4	SC2	DM5
6	1	9	7	5	SC4	DM6
3	1	3	2	1	SC4	DM7
6	4	6	1	9	SC2	DM8
5	1	5	2	8	SC4	DM9
9	2	33	1	4	SC2	DM10
SC5	SC4	SC3	SC2	SC1	threshold	Decision Maker
0.000	0.0892	0.4305	0.000	0.2083	0.3062	DM1
0.000	0.000	0.2857	0.0714	0.3571		DM2
0.0535	0.0535	0.1428	0.0357	0.0000		DM3
0.119	0.0714	0.1190	0.000	0.000		DM4
0.222	0.0277	0.1527	0.0000	0.2083		DM5
0.375	0.000	0.0000	0.3611	0.1527		DM6
0.119	0.000	0.0476	0.142	0.142		DM7
0.2083	0.0416	0.375	0.0000	0.000		DM8
0.3928	0.000	0.125	0.0357	0.000		DM9
0.000	0.0694	0.2083	0.0000	0.2083		DM10

,

Table 7. Best-to-others and others-to-worst vectors for sub-criteria sc6-sc10.

Preference of the Best Criterion over Others
SC10	SC9	SC8	SC7	SC6	Best Criterion	Decision Maker
3	7	4	1	9	SC7	DM1
8	2	9	1	5	SC7	DM2
2	7	2	6	1	SC6	DM3
3	2	7	1	5	SC7	DM4
2	2	9	2	1	SC6	DM5
4	4	9	1	7	SC7	DM6
2	7	2	4	1	CS6	DM7
5	1	3	8	7	SC9	DM8
4	7	2	1	2	CS7	DM9
3	2	4	1	9	CS7	DM10
Preference of Other Criteria over the Worst Criterion
SC10	SC9	SC8	SC7	SC6	Worst Criterion	Decision Maker
3	5	8	9	1	CS6	DM1
4	4	1	6	6	SC8	DM2
3	1	2	4	4	SC9	DM3
2	3	1	6	5	SC8	DM4
2	2	1	4	9	SC8	DM5
3	2	1	9	6	SC8	DM6
2	1	2	8	9	SC9	DM7
6	9	9	1	2	SC7	DM8
1	1	2	7	4	SC9	DM9
3	4	3	9	1	SC6	DM10
SC10	SC9	SC8	SC7	SC6	threshold	Decision Maker
0.000	0.361	0.319	0.000	0.000	0.3062	DM1
0.319	0.138	0.000	0.041	0.291		DM2
0.0238	0.000	0.0714	0.404	0.071		DM3
0.0238	0.0238	0.000	0.023	0.428		DM4
0.0694	0.0694	0.000	0.013	0.000		DM5
0.0416	0.138	0.0000	0.000	0.458		DM6
0.0714	0.000	0.0714	0.595	0.047		DM7
0.392	0.0178	0.339	0.0000	0.107		DM8
0.0714	0.000	0.0714	0.000	0.023		DM9
0.000	0.0138	0.0416	0.0000	0.000		DM10

and

Table 8. Best-to-others and others-to-worst vectors for sub-criteria sc11-sc18.

Preference of the Best Criterion over Others
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	Best Criterion	Decision Maker
5	6	9	6	3	6	5	1	SC11	DM1
5	6	4	5	7	5	6	1	SC11	DM2
4	5	2	7	5	2	7	1	SC13	DM3
9	5	4	6	5	1	5	6	SC13	DM4
8	6	5	3	4	6	1	6	SC12	DM5
6	1	7	5	9	6	6	8	SC17	DM6
4	5	2	3	9	8	4	1	CS11	DM7
6	7	5	8	7	6	7	1	SC11	DM8
3	6	7	3	5	1	5	6	CS13	DM9
4	5	9	5	4	5	6	1	CS11	DM10
Preference of Other Criteria over the Worst Criterion
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	Worst Criterion	Decision Maker
3	3	1	6	6	6	8	9	CS16	DM1
7	3	2	5	1	4	3	7	SC14	DM2
3	4	3	1	4	3	4	5	SC15	DM3
1	6	2	4	6	6	7	5	SC18	DM4
1	4	2	6	7	4	9	4	SC18	DM5
8	9	6	4	1	4	5	4	SC14	DM6
4	5	2	3	1	6	4	6	SC14	DM7
5	4	3	1	4	8	4	9	SC15	DM8
1	3	1	4	4	7	4	3	SC16	DM9
2	5	1	4	6	5	4	9	SC16	DM10
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	threshold	Decision Maker
0.0833	0.125	0.000	0.375	0.125	0.375	0.4305	0.000	0.3620	DM1
0.6666	0.2619	0.0238	0.4285	0.000	0.3093	0.2619	0.000		DM2
0.119	0.3095	0.0238	0.000	0.3095	0.0238	0.5	0.0476		DM3
0.000	0.2916	0.0138	0.2083	0.2916	0.0416	0.3611	0.2916		DM4
0.000	0.2857	0.0357	0.1785	0.3571	0.2857	0.0178	0.2857		DM5
0.541	0.000	0.4583	0.1527	0.000	0.2083	0.2916	0.3194		DM6
0.0972	0.2222	0.0694	0.000	0.000	0.5416	0.0972	0.0416		DM7
0.3928	0.3571	0.125	0.000	0.3571	0.7142	0.3571	0.0178		DM8
0.0952	0.2619	0.000	0.119	0.3095	0.000	0.3095	0.2619		DM9
0.0138	0.2222	0.000	0.1527	0.2083	0.2222	0.2083	0.000		DM10

specify the vector of the importance of the best criterion to other criteria and the significance of other criteria to the worst criterion. Considering that the linear best–worst method is used for determining the weights of the criteria for investigating discordance in paired comparisons, Formula (3) in Section 2.4.1 was used. The numbers specified in Table 5, Table 6, Table 7 and Table 8 indicate contradictory data. These data should be corrected before introduction to the BWM model. Thus, the decision makers were consulted again, and the contradictory data were posed and corrected. The results are shown in

Table 9. The improved significance level of the best criteria to the other and the other to the worst for the major criteria.

Preference of the Best Criterion over Others
MC3	MC2	MC1	Best Criterion	Decision Maker
7	1	2	MC2	DM1
1	3	5	MC3	DM2
1	6	3	MC3	DM3
8	1	4	MC2	DM4
9	1	2	MC2	DM5
9	1	3	MC2	DM6
2	1	7	MC2	DM7
5	8	1	MC1	DM8
9	1	3	MC2	DM9
9	1	2	MC2	DM10
Preference of Other Criteria over the Worst Criterion
MC3	MC2	MC1	Worst Criterion	Decision Maker
1	9	2	MC3	DM1
5	2	1	MC1	DM2
8	1	2	MC2	DM3
1	5	2	MC3	DM4
1	9	2	MC3	DM5
1	9	3	MC3	DM6
3	5	1	MC1	DM7
3	1	3	MC2	DM8
1	7	2	MC3	DM9
1	9	2	MC3	DM10
MC3	MC2	MC1	threshold	Decision Maker
0.0000	0.0476	0.0714	0.1359	DM1
0.0000	0.05	0.0000		DM2
0.0333	0.0000	0.0000		DM3
0.0000	0.0535	0.0357		DM4
0.0000	0.0000	0.0694		DM5
0.0000	0.0000	0.0000		DM6
0.0238	0.0476	0.0000		DM7
0.125	0.0000	0.0892		DM8
0.0000	0.0277	0.0555		DM9
0.0000	0.0000	0.0694		DM10

,

Table 10. Revised best-to-others and others-to-worst vectors for sub-criteria sc1-sc5.

Preference of the Best Criterion over Others
SC5	SC4	SC3	SC2	SC1	Best Criterion	Decision Maker
1	2	4	9	8	SC5	DM1
1	8	6	4	7	SC5	DM2
1	2	4	2	8	SC5	DM3
6	5	4	7	1	SC1	DM4
5	1	4	9	6	SC4	DM5
4	9	1	5	4	SC3	DM6
4	7	3	3	1	CS1	DM7
4	3	4	9	1	SC1	DM8
6	8	3	5	1	CS1	DM9
1	2	8	9	6	CS5	DM10
Preference of Other Criteria over the Worst Criterion
SC5	SC4	SC3	SC2	SC1	Worst Criterion	Decision Maker
9	2	5	1	3	CS2	DM1
8	1	4	3	2	SC4	DM2
5	3	4	3	1	SC1	DM3
2	2	3	1	7	SC2	DM4
5	7	5	1	4	SC2	DM5
6	1	9	2	5	SC4	DM6
3	1	3	2	1	SC4	DM7
6	4	6	1	9	SC2	DM8
3	1	5	2	8	SC4	DM9
9	2	33	1	4	SC2	DM10
SC5	SC4	SC3	SC2	SC1	threshold	Decision Maker
0.000	0.0892	0.1527	0.000	0.2083	0.3062	DM1
0.000	0.000	0.2857	0.0714	0.1071		DM2
0.0535	0.0535	0.1428	0.0357	0.0000		DM3
0.119	0.0714	0.1190	0.000	0.000		DM4
0.222	0.0277	0.1527	0.0000	0.2083		DM5
0.2083	0.000	0.0000	0.0138	0.1527		DM6
0.119	0.000	0.0476	0.142	0.142		DM7
0.2083	0.0416	0.208	0.0000	0.000		DM8
0.1785	0.000	0.125	0.0357	0.000		DM9
0.000	0.0694	0.2083	0.0000	0.2083		DM10

,

Table 11. Revised best-to-others and others-to-worst vectors for sub-criteria sc6-sc10.

Preference of the Best Criterion over Others
SC10	SC9	SC8	SC7	SC6	Best Criterion	Decision Maker
3	3	4	1	9	SC7	DM1
2	2	9	1	5	SC7	DM2
2	7	2	3	1	SC6	DM3
3	2	7	1	3	SC7	DM4
2	2	9	2	1	SC6	DM5
4	4	9	1	7	SC7	DM6
2	7	2	2	1	CS6	DM7
5	1	3	8	7	SC9	DM8
4	7	2	1	2	CS7	DM9
3	2	4	1	9	CS7	DM10
Preference of Other Criteria over the Worst Criterion
SC10	SC9	SC8	SC7	SC6	Worst Criterion	Decision Maker
3	5	3	9	1	CS6	DM1
4	4	1	6	6	SC8	DM2
3	1	2	4	4	SC9	DM3
2	3	1	6	5	SC8	DM4
2	2	1	4	9	SC8	DM5
3	2	1	9	4	SC8	DM6
2	1	2	8	9	SC9	DM7
3	9	3	1	2	SC7	DM8
1	1	2	7	4	SC9	DM9
3	4	3	9	1	SC6	DM10
SC10	SC9	SC8	SC7	SC6	threshold	Decision Maker
0.000	0.0833	0.0416	0.000	0.000	0.3062	DM1
0.0138	0.138	0.000	0.041	0.291		DM2
0.0238	0.000	0.0714	0.119	0.071		DM3
0.0238	0.0238	0.000	0.023	0.190		DM4
0.0694	0.0694	0.000	0.013	0.000		DM5
0.0416	0.138	0.0000	0.000	0.263		DM6
0.0714	0.000	0.0714	0.214	0.047		DM7
0.125	0.0178	0.0178	0.0000	0.107		DM8
0.0714	0.000	0.0714	0.000	0.023		DM9
0.000	0.0138	0.0416	0.0000	0.000		DM10

and

Table 12. Revised best-to-others and others-to-worst vectors for sub-criteria sc11-sc18.

Preference of the Best Criterion over Others
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	Best Criterion	Decision Maker
5	6	9	5	3	6	5	1	SC11	DM1
5	6	4	5	7	5	6	1	SC11	DM2
4	5	2	7	5	2	4	1	SC13	DM3
9	5	4	6	5	1	5	6	SC13	DM4
8	6	5	3	4	6	1	6	SC12	DM5
6	1	7	5	9	6	6	8	SC17	DM6
4	5	2	3	9	8	4	1	CS11	DM7
6	7	5	8	7	6	7	1	SC11	DM8
3	6	7	3	5	1	5	6	CS13	DM9
4	5	9	5	4	5	6	1	CS11	DM10
Preference of Other Criteria over the Worst Criterion
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	Worst Criterion	Decision Maker
3	3	1	6	6	3	4	9	CS16	DM1
2	3	2	3	1	4	3	7	SC14	DM2
3	4	3	1	4	3	4	5	SC15	DM3
1	6	2	4	6	6	7	5	SC18	DM4
1	4	2	6	7	4	9	4	SC18	DM5
3	9	3	4	1	4	5	4	SC14	DM6
4	5	2	3	1	4	4	6	SC14	DM7
3	4	3	1	4	4	4	9	SC15	DM8
1	3	1	4	4	7	4	3	SC16	DM9
2	5	1	4	6	5	4	9	SC16	DM10
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11	threshold	Decision Maker
0.0833	0.125	0.000	0.2916	0.125	0.125	0.1527	0.000	0.3620	DM1
0.0714	0.2619	0.0238	0.1904	0.000	0.3093	0.2619	0.000		DM2
0.119	0.3095	0.0238	0.000	0.3095	0.0238	0.2142	0.0476		DM3
0.000	0.2916	0.0138	0.2083	0.2916	0.0416	0.3611	0.2916		DM4
0.000	0.2857	0.0357	0.1785	0.3571	0.2857	0.0178	0.2857		DM5
0.125	0.000	0.1666	0.1527	0.000	0.2083	0.2916	0.3194		DM6
0.0972	0.2222	0.0694	0.000	0.000	0.3194	0.0972	0.0416		DM7
0.1785	0.3571	0.125	0.000	0.3571	0.2857	0.3571	0.0178		DM8
0.0952	0.2619	0.000	0.119	0.3095	0.000	0.3095	0.2619		DM9
0.0138	0.2222	0.000	0.1527	0.2083	0.2222	0.2083	0.000		DM10

.

The numbers specified in the table that are greater than the limit of 0.1359 are inconsistent data that should be corrected using the best–worst method before entering.

The experts should correct their viewpoints to correct the inconsistent data over the determined limit.

As the above tables show, nine data are greater than the expected limit and should be corrected by revision of the experts’ viewpoints and changing the importance of criteria concerning each other.

The values specified in the above tables show that some of the experts’ answers have unacceptable inconsistency and should be corrected before entering the model.Thus, the experts should be referred to again, and the relative importance values of the related criteria should be revised. The corrected values and corresponding consistency rates are shown in Table 9, Table 10, Table 11 and Table 12. Corrected values in these tables are used as the model input in the linear best–worst method.

As indicated, all values are in the acceptable range by correcting the criterion importance.

According to Table 2, all the corrected values are less than the limit and can be accepted.

With the corrections in the experts’ viewpoints, the numbers in the above table are also acceptable and considered the best–worst method input.

We used the solver feature of Excel to determine the weight of best criteria in the best–worst method.

Considering each decision-maker’s weight, the average weights were specified for the entire criteria. Each decision-maker’s weight or value was defined concerning the three criteria: education level, occupational background, and organizational position.

Table 13. Group average of criteria using the best–worst method and decision makers.

Main Criteria
MC3			MC2		MC1
0.2822			0.4384		0.2794			Group average
Sub-criteria CS1 to CS5
SC5		SC4	SC3		SC2	SC1
0.2899		0.1017	0.2170		0.0878	0.3036		Group average
Sub-criteria CS6 to CS10
SC10		SC9	SC8		SC7	SC6
0.0646		0.049	0.0670		0.4005	0.4189		Group average
Sub-criteria CS11 to CS18
SC18	SC17	SC16	SC15	SC14	SC13	SC12	SC11
0.0870	0.1144	0.0807	0.1002	0.1139	0.1372	0.1423	0.2243	Group average

specifies the weight of each decision maker and the grand mean of each primary and secondary criterion.

Each secondary criterion’s global or total weight was obtained by multiplying the local weight of the secondary criteria by the pertinent primary criteria.

Table 14. Local and global weights and ranking of the sub-criteria.

Rank	Global Weights	Local Weights	Sub-Criteria	Main Criteria Weights	Main Criteria
3	0.0848	0.3036	SC1	0.2794	MC1
16	0.0245	0.0878	SC2
6	0.0606	0.2170	SC3
12	0.0284	0.1017	SC4
4	0.0810	0.2899	SC5
1	0.1836	0.4189	SC6	0.4384	MC2
2	0.1755	0.4005	SC7
11	0.0293	0.0670	SC8
18	0.0214	.0490	SC9
13	0.0283	0.0646	SC10
5	0.0633	0.2243	SC11	0.2822	MC3
7	0.0401	0.1423	SC12
8	0.0387	0.1372	SC13
10	0.0321	0.1139	SC14
14	0.0282	0.1002	SC15
17	0.0228	0.0807	SC16
9	0.0323	0.1144	SC17
15	0.0245	0.0870	SC18

presents the values of the total weight of the criteria and the secondary criteria’s ranking. As indicated in Table 14, in the context of safety, training, supervision, attitude, and safety understanding ranked first to third among the studied criteria.

4.3. The Decision Matrix Formation

The investigated criteria with a quantitative or occasionally fuzzy nature were evaluated by surveying the group members using verbal scales indicated in

Table 15. The variables used in this research.

TFN	Abbreviation	Linguistic Variable
(0.9, 1, 1)	VG	Very Good
(0.7, 0.9, 1)	G	Good
(0.5, 0.7, 0.9)	MG	Medium Good
(0.3, 0.5, 0.7)	F	Fair
(0.1, 0.3, 0.5)	MP	Medium Poor
(0, 0.1, 0.3)	P	Poor
(0, 0, 0.1)	VP	Very Poor

. Afterward, the corresponding fuzzy numbers were considered concerning the experts’ view on the performance of each risk concerning that criterion. The overall decision matrix was formed by adding the weight of each criterion according to

Table 16. The decision matrix; an illustrative example.

SC18(-)	SC16(-)	SC15(-)	SC14(-)	SC13(-)	SC12(-)	SC11(+)	SC10(-)	SC9(+)	SC8(-)	SC7(+)	SC6(+)	SC5(+)	SC4(+)	SC3(+)	SC2(-)	SC1(+)	Criteria
0.02455	0.0228	0.02827	0.0321	0.0387	0.0401	0.0633	0.02832	0.0214	0.0293	0.1755	0.1836	0.081	0.0284	0.0606	0.02453	0.0848	Weights Alternatives
(0.433, 0.633, 0.5)	(0, 0.066, 0.233)	(0.433, 0.633, 0.833)	(0.9, 1, 1)	(0.3, 0.5, 0.7)	(0.9, 1, 1)	(0.3, 0.5, 0.7)	(0.433, 0.633, 0.5)	(0.033, 0.166, 0.366)	(0.233, 0.433, 0.633)	(0.633, 0.5, 0.9)	(0.1, 0.2, 0.366)	(0.7, 0.866, 0.966)	(0, 0.1, 0.3)	(0.633, 0.8, 0.9)	(0.13, 0.3, 0.5)	(0.333, 0.5, 0.666)	A1
(0.566, 0.766, 0.933)	(0, 0, 0.1)	(0.3, 0.5, 0.7)	(0.1, 0.3, 0.5)	(0.9, 1, 1)	(0.066, 0.233, 0.433)	(0.3, 0.5, 0.7)	(0.1, 0.3, 0.5)	(0, 0.1, 0.3)	(0.1, 0.3, 0.5)	(0.7, 0.9, 1)	(0.7, 0.9, 1)	(0, 0, 0.1)	(0.1, 0.3, 0.5)	(0.566, 0.766, 0.933)	(0, 0.1, 0.3)	(0.633, 0.833, 0.966)	A2
(0.1, 0.3, 0.5)	(0.1, 0.3, 0.5)	(0.433, 0.633, 0.833)	(0, 0, 0.1)	(0.1, 0.3, 0.5)	(0, 0, 0.1)	(0.1, 0.3, 0.5)	(0.233, 0.433, 0.633)	(0.1, 0.3, 0.5)	(0.033, 0.166, 0.366)	(0.233, 0.433, 0.633)	(0.133, 0.266, 0.433)	(0.13, 0.3, 0.5)	(0, 0.1, 0.3)	(0.366, 0.566, 0.766)	(0.13, 0.3, 0.5)	(0.266, 0.433, 0.366)	A3
(0.033, 0.133, 0.3)	(0, 0, 0.1)	(0.3, 0.5, 0.7)	(0, 0, 0.1)	(0, 0.033, 0.166)	(0.366, 0.566, 0.766)	(0.1, 0.3, 0.5)	(0.233, 0.433, 0.633)	(0, 0, 0.1)	(0.1, 0.3, 0.5)	(0.166, 0.366, 0.566)	(0.366, 0.566, 0.766)	(0.7, 0.9, 1)	(0, 0.1, 0.3)	(0.3, 0.5, 0.7)	(0.033, 0.166, 0.366)	(0.7, 0.9, 1)	A4
(0, 0, 0.1)	(0, 0.033, 0.166)	(0.166, 0.366, 0.566)	(0.166, 0.366, 0.566)	(0.566, 0.733, 0.866)	(0.7, 0.9, 1)	(0.5, 0.7, 0.9)	(0.766, 0.933, 1)	(0.1, 0.3, 0.5)	(0.3, 0.5, 0.7)	(0.766, 0.933, 1)	(0.766, 0.933, 1)	(0.766, 0.933, 1)	(0, 0.1, 0.3)	(0.766, 0.933, 1)	(0.3, 0.5, 0.7)	(0.766, 0.933, 1)	A5
(0.1, 0.3, 0.5)	(0, 0.1, 0.3)	(0.1, 0.3, 0.5)	(0.1, 0.3, 0.5)	(0.9, 1, 1)	(0.233, 0.433, 0.633)	(0.5, 0.7, 0.9)	(0.5, 0.7, 0.866)	(0, 0.1, 0.3)	(0.5, 0.7, 0.866)	(0.633, 0.833, 0.966)	(0.633, 0.833, 0.966)	(0.1, 0.3, 0.5)	(0.5, 0.7, 0.9)	(0.7, 0.866, 0.966)	(0.1, 0.3, 0.5)	(0.1, 0.3, 0.5)	A6

In the table above, the + sign indicates profit, and the - sign indicates the cost.

.

4.4. Ranking the Options

In order to rank the most critical safety risks in high-rise buildings, the fuzzy VIKOR algorithm was used (

Table 17. The decision matrix of the group members.

Decision Matrix for Illustrative Example
SC18(-)	SC17(-)	SC16(-)	SC15(-)	SC14(-)	SC13(-)	SC12(-)	SC11(+)	SC10(-)	SC9(+)	SC8(-)	SC7(+)	SC6(+)	SC5(+)	SC4(+)	SC3(+)	SC2(-)	SC1(+)	Criteria
0.02455	0.0323	0.0228	0.02827	0.0321	0.0387	0.0401	0.0633	0.02832	0.0214	0.0293	0.1755	0.1836	0.081	0.0284	0.0606	0.02453	0.0848	Weights Criteria
(0, 0, 0.1)	(0, 0.1, 0.3)	(0, 0, 0.1)	(0.1, 0.3, 0.5)	(0, 0, 0.1)	(0, 0.033, 0.166)	(0, 0, 0.1)	(0.5, 0.7, 0.9)	(0.1, 0.3, 0.5)	(0.1, 0.3, 0.5)	(0.033, 0.166, 0.366)	(0.766, 0.933, 1)	(0.766, 0.933, 1)	(0.766, 0.933, 1)	(0.5, 0.7, 0.9)	(0.766, 0.933, 1)	(0, 0.1, 0.3)	(0.766, 0.933, 1)	F+
(0.566, 0.766, 0.933)	(0.9, 1, 1)	(0.1, 0.3, 0.5)	(0.433, 0.633, 0.833)	(0.9, 1, 1)	(0.9, 1, 1)	(0.9, 1, 1)	(0.1, 0.3, 0.5)	(0.766, 0.933, 1)	(0, 0, 0.1)	(0.5, 0.7, 0.866)	(0.166, 0.366, 0.566)	(0.1, 0.2, 0.366)	(0, 0, 0.1)	(0, 0.1, 0.3)	(0.3, 0.5, 0.7)	(0.3, 0.5, 0.7)	(0.1, 0.3, 0.5)	F-
(0.356, 0.678, 0.535)	(0, 0.4, 0.7)	(−0.2, 0.132, 0.466)	(−0.091, 0.454, 1)	(0.8, 1, 1)	(0.134, 0.467, 0.7)	(0.8, 1, 1)	(−0.25, 0.25, 0.75)	(−0.074, 0.37, 0.44)	(−0.532, 0.268, 0.934)	(−0.159, 0.320, 0.720)	(−0.16, 0.519, 0.44)	(0.444, 0.814, 1)	(−0.2, 0.067, 0.3)	(0.222, 0.666, 1)	(−0.191, 0.19, 0.524)	(−0.242, 0.285, 0.714)	(0.111, 0.481, 0.741)	A1	${\tilde{d}}_{ij}=\left({\tilde{f}}_j^{+}\ominus {\tilde{x}}_{ij}\right)/\left(u_j^{+}-l_j^{-}\right)$
(0.499, 0.821, 1)	(0.6, 0.9, 1)	(−0.2, 0, 0.2)	(−0.272, 0.272, 0.818)	(0, 0.3, 0.5)	(0.734, 0.967, 1)	(−0.034, 0.233, 0.433)	(−0.25, 0.25, 0.75)	(−0.444, 0, 0.444)	(−0.4, 0.4, 1)	(−0.319, 0.16, 0.56)	(−0.28, 0.039, 0.359)	(−0.26, 0.036, 0.333)	(0.666, 0.933, 1)	(0, 0.444, 0.888)	(−0.238, 0.238, 0.62)	(−0.428, 0, 0.428)	(−0.222, 0.111, 0.407)	A2
(0, 0.321, 0.535)	(0.2, 0.6, 0.866)	(0, 0.6, 1)	(−0.091, 0.454, 1)	(−0.1, 0, 0.1)	(−0.066, 0.267, 0.5)	(−0.1, 0, 0.1)	(0, 0.5, 1)	(−0.296, 0.147, 0.592)	(−0.8, 0, 0.8)	(−0.399, 0, 0.399)	(0.159, 0.599, 0.919)	(0.37, 0.741, 0.963)	(0.266, 0.633, 0.87)	(0.222, 0.666, 1)	(0, 0.524, 0.905)	(−0.242, 0.285, 0.714)	(0.444, 0.555, 0.815)	A3
(−0.071, 0.142, 0.321)	(−0.267, 0.033, 0.3)	(−0.2, 0, 0.2)	(−0.272, 0.272, 0.818)	(−0.1, 0, 0.1)	(−0.166, 0, 0.166)	(0.266, 0.566, 0.766)	(0, 0.5, 1)	(−0.296, 0.147, 0.592)	(0, 0.6, 1)	(−0.319, 0.16, 0.56)	(0.239, 0.679, 1)	(0, 0.407, 0.704)	(−0.234, 0.033, 0.3)	(0.222, 0.666, 1)	(0.094, 0.618, 0.1)	(−0.381, 0.094, 0.522)	(−0.26, 0.036, 0.333)	A4
(−0.107, 0, 0.107)	(−0.3, 0, 0.3)	(−0.2, 0.066, 0.332)	(−0.455, 0.09, 0.635)	(0.066, 0.366, 0.566)	(0.4, 0.7, 0.866)	(0.6, 0.9, 0.1)	(−0.5, 0, 0.5)	(0.295, 0.703, 1)	(−0.8, 0, 0.8)	(−0.079, 0.4, 0.8)	(−0.28, 0, 0.28)	(−0.26, 0, 0.26)	(−0.234, 0, 0.234)	(0.222, 0.666, 1)	(−0.334, 0, 0.334)	(0, 0.571, 0.1)	(−0.26, 0, 0.26)	A5
(0, 0.321, 0.535)	(0.4, 0.8, 0.1)	(−0.2, 0.2, 0.6)	(−0.545, 0, 0.545)	(0, 0.3, 0.5)	(0.734, 0.967, 1)	(0.133, 0.433, 0.633)	(−0.5, 0, 0.5)	(0, 0.444, 0.851)	(−0.4, 0.4, 1)	(0.16, 0.641, 1)	(−0.239, 0.119, 0.44)	(−0.222, 0.111, 0.407)	(0.266, 0.633, 0.9)	(−0.444,0,0.444)	(−0.285, 0.095, 0.428)	(−0.285, 0.285, 0.714)	(0.295, 0.703, 1)	A6
(0.008, 0.016, 0.013)	(0, 0.012, 0.022)	(−0.004, 0.003, 0.01)	(−0.002, 0.012, 0.028)	(0.025, 0.032, 0.032)	(0.005, 0.018, 0.027)	(0.032, 0.04, 0.04)	(−0.015, 0.015, 0.047)	(−0.002, 0.01, 0.012)	(−0.011, 0.005, 0.019)	(−0.004, 0.009, 0.021)	(−0.028, 0.091, 0.077)	(0.081, 0.149, 0.183)	(−0.016, 0.005, 0.024)	(0.006, 0.018, 0.028)	(−0.011, 0.011, 0.031)	(−0.005, 0.006, 0.017)	(0.009, 0.04, 0.06)	A1	$W_j\ast {\tilde{d}}_{ij}$
(0.012, 0.02, 0.024)	(0.019, 0.029, 0.032)	(−0.004, 0, 0.004)	(−0.007, 0.007, 0.023)	(0, 0.009, 0.016)	(0.028, 0.037, 0.038)	(−0.001, 0.009, 0.017)	(−0.015, 0.015, 0.047)	(−0.012, 0, 0.012)	(−0.008, 0.008, 0.021)	(−0.009, 0.004, 0.016)	(−0.042, 0.021, 0.077)	(−0.047, 0.006, 0.061)	(0.053, 0.075, 0.081)	(0, 0.012, 0.025)	(−0.014, 0.014, 0.037)	(−0.01, 0, 0.01)	(−0.018, 0.009, 0.034)	A2
(0, 0.007, 0.013)	(0.006, 0.019, 0.027)	(0, 0.013, 0.022)	(−0.002, 0.012, 0.028)	(−0.003, 0, 0.003)	(−0.002, 0.01, 0.019)	(−0.004, 0, 0.004)	(0, 0.031, 0.063)	(−0.008, 0.004, 0.016)	(−0.017, 0, 0.017)	(−0.011, 0, 0.011)	(0.027, 0.104, 0.161)	(0.067, 0.136, 0.176)	(0.021, 0.051, 0.07)	(0.006, 0.018, 0.028)	(0, 0.031, 0.054)	(−0.005, 0.006, 0.017)	(0.037, 0.047, 0.069)	A3
(−0.001, 0.003, 0.007)	(−0.008, 0.001, 0.009)	(−0.004, 0, 0.004)	(−0.007, 0.007, 0.023)	(−0.003, 0, 0.003)	(−0.006, 0, 0.006)	(0.01, 0.022, 0.03)	(0, 0.031, 0.063)	(−0.008, 0.004, 0.016)	(0, 0.012, 0.021)	(−0.009, 0.004, 0.016)	(0.041, 0.119, 0.175)	(0, 0.074, 0.129)	(−0.018, 0.002, 0.024)	(0.006, 0.018, 0.028)	(0.005, 0.037, 0.06)	(−0.009, 0.002, 0.012)	(−0.022, 0.003, 0.028)	A4
(−0.002, 0, 0.002)	(−0.009, 0, 0.009)	(−0.004, 0.001, 0.007)	(−0.012, 0.002, 0.017)	(0.002, 0.011, 0.018)	(0.015, 0.027, 0.033)	(0.024, 0.036, 0.04)	(−0.031, 0, 0.031)	(0.008, 0.019, 0.028)	(−0.017, 0, 0.017)	(−0.002, 0.011, 0.023)	(−0.049, 0.006, 0.063)	(−0.047, 0, 0.047)	(−0.018, 0, 0.018)	(0.006, 0.018, 0.028)	(−0.02, 0, 0.02)	(0, 0.014, 0.024)	(−0.022, 0, 0.022)	A5
(0, 0.007, 0.013)	(0.012, 0.025, 0.032)	(−0.004, 0.004, 0.013)	(−0.015, 0, 0.015)	(0, 0.009, 0.016)	(0.028, 0.037, 0.038)	(0.005, 0.017, 0.025)	(−0.031, 0, 0.031)	(0, 0.012, 0.024)	(−0.008, 0.008, 0.021)	(0.004, 0.081, 0.029)	(−0.049, 0, 0.049)	(−0.04, 0.02, 0.074)	(0.021, 0.051, 0.072)	(−0.012, 0, 0.012)	(−0.017, 0.005, 0.025)	(−0.006, 0.006, 0.017)	(0.025, 0.059, 0.084)	A6

). In this table, the criteria weights have a specific value, but the performance of each option is concerned with the criteria and fuzzy triangular numbers based on the experts’ viewpoints.

The values $R˜,S˜,Q˜$ were calculated based on Equations (9)–(11) and the results were as shown in

Table 18. The fuzzy values of the R˜, S˜, Q˜ parameters.

	${\tilde{\mathbf{S}}}_{\mathbf{i}}$	${\tilde{\mathbf{R}}}_{\mathbf{i}}$	${\tilde{\mathbf{Q}}}_{\mathbf{i}}$
A1	(0.068, 0.492, 0.691)	(0.081, 0.149, 0.183)	(−0.209, 0.243, 0.571)
A2	(−0.082, 0.254, 0.563)	(0.666, 0.933, 1)	(0.551, 0.51, 0.917)
A3	(0.112, 0.489, 0.798)	(0.067, 0.136, 0.176)	(−0.191, 0.235, 0628)
A4	(−0.033, 0.339, 0.654)	(0.041, 0.119, 0.175)	(−0.279, 0.141, 546)
A5	(−0.171, 0.165, 0.474)	(0.024, 0.036, 0.04)	(−0.374, 0, 0.374)
A6	(−0.087, 0.342, 0.591)	(0.025, 0.059, 0.084)	(−0.223, 0.112, 0.463)
${\tilde{\mathrm{S}}}^{\ast }$	(−0.087, 0.342, 0.591)
${\tilde{\mathrm{R}}}^{\ast }$		(0.024, 0.036, 0.04)
${\mathrm{S}}^{\ast \mathrm{l}}$	−0.087	${\mathrm{R}}^{\ast \mathrm{l}}$	0.024
${\mathrm{S}}^{\mathrm{ou}}$	0.798	${\mathrm{R}}^{\mathrm{ou}}$	0.183

. For fuzzification and conversion of this table’s numbers to specific values, the weighted mean method was used based on Equation (8).

Table 19. The options ranking concerning the certain values Q, R, and S.

Rankings (with Respect to)			Parameters			Alternatives
${\mathbf{Q}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{S}}_{\mathbf{i}}$	${\mathbf{Q}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{S}}_{\mathbf{i}}$
6	6	5	0.4127	0.1405	0.4357	A1
3	3	2	0.088	0.071	0.2472	A2
5	5	6	0.395	0.1287	0.472	A3
4	4	4	0.266	0.1135	0.3247	A4
1	1	1	−0.028	0.034	0.1582	A5
2	2	3	0.084	0.0567	0.297	A6

shows the specific values and the risk rankings.

This step should investigate the two conditions below for the first rank selection.

First condition: The acceptable merit:

$$Adv\ge DQ$$

$$DQ=1/\left(m-1\right)=1/\left(6-1\right)=0.2$$

$$Adv=\left[Q\left(A^\left(,,\right)\right)-Q\left(A^,\right)\right]/Q\left(A^\left(\left(m\right)\right)-Q\left(A^,\right)\right]=0.2541\ge 0.2\left(OK\right)$$

Second condition: The acceptable stability in decision-making.

Given that the first option in ranking $Q$ ranked first in terms of the S and R parameters, Option A5 (falling from height) ranked first and was identified as the most critical danger.

5. The Sensitivity Analysis of the Results

To analyze the research results and the sensitivity of the outputs of the ranking of safety risks obtained through the fuzzy VIKOR method according to different values of $v$, this section introduces the maximum group utility with its value ranging from 0 to 1 with 0.1 steps. The sensitivity analysis reveals the impact of the proposed decisions on the ranking of safety risks in terms of maximum group consensus, individual utility, and collective utility. Different risk rankings were determined by varying the value of v. According to

Table 20. Ranking changes with changes in maximum group agreement.

Changes V	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
A1	4	5	4	3	3	3	3	3	4	4
A2	5	6	6	6	6	6	6	6	3	5
A3	3	4	5	4	4	4	4	4	5	2
A4	6	2	2	2	2	2	2	2	2	3
A5	1	1	1	1	1	1	1	1	1	1
A6	2	3	3	5	5	5	5	5	6	6

, changes in the values of $v$ affected the final ranking results in two modes: greater than 0.8 and lower than 0.4. It is noteworthy that Option A5 (falling off a height) ranks first in all various modes of group consensus, indicating the substantial significance of this option. Furthermore, Option A4 (issues related to excavations and buildings’ adjacent to excavations) ranked second in most cases, except for $v=0.1$ and $v=1$. The results indicated that the two risks—falling off a height and issues related to excavation—are most significant in high-rise buildings. The sensitivity analysis proved that the research accomplished its objectives. It also indicated that with replication of the used procedure through other group agreements, the result would not change.

Analysis and Discussion

The current study aims to evaluate the safety risks in high-rises in Tehran and ultimately prioritize the most critical risks. In addition to risk evaluation, effective criteria were addressed. Weight allocation to the criteria can greatly help select the most critical safety risks. The investigated criteria weights were obtained using the viewpoints of ten senior managers in the construction industry via the questionnaire. Table 6 shows that the management factors had the highest significance level of impact in the occurrence of incidences. Concerning the viewpoint of the decision makers and the global weight of each criterion, training (SC6), surveillance (SC7), attitude and safety perception (SC1), using personal protection equipment (SC5), and safety space (SC11), were identified as the first to the fifth criteria, respectively, comprising the 60% of the overall weight of the criteria. SC6 (training) and SC7 (surveillance) comprised about 35% of the overall weight, indicating the higher significance level of the two mentioned factors. Using personal protection tools was found to be an important factor in the incidents, but it merely comprised 0.08% of the overall weight. These results indicate the necessity of utilizing safety training and surveillance and using personal protection equipment in construction workshops. After investigating and analyzing the contributing criteria in evaluating the safety risks and concerning the importance of the workforce in the construction industry, it is necessary to identify the critical safety risks and control them. Accordingly, we found that Option A5 (fall from height) is the most important factor threatening the workers by investigating six groups of the most critical safety dangers in high-rise buildings and comparing the options concerning the criteria (Table 19). Falling from a height ranked first in 8 out of 18 criteria, including SC1 (safety attitude and perception), SC2 (mental and physical issues), SC3 (experience and skill), SC5 (using personal protection tools), CS6(training), SC7 (surveillance), SC9 (rewarding and punishment), and SC10 (work-related pressure). The summation of the mentioned criteria weight was 0.688 concerning the global weight of each criterion. Additionally, the risk of working with manual tools and equipment in SC4 (education), SC8 (work shift), SC11 (safety space), and SC13 (equipment and machinery) ranked first, where the overall summation of these criteria was 0.1591. To mitigate the safety dangers creating irreparable damage, in addition to safety management, an HSE expert should be employed as an essential factor in preventing the dangers.

6. Conclusions

The present study examines the safety risks associated with high-rise buildings in Tehran. Below are the findings of this study. Studies conducted previously evaluated safety risks based on occurrence intensity, event probability, and recurrence numbers. This study attempted to place all available research according to its reoccurrence probability, intensity, and number in the main classifications. Additionally, three other important criteria were examined, such as individual, management, and environmental factors. According to the first section, the best–worst method was used to weigh the criteria, determine which factor is most effective, and determine where the investments should be made in order to avoid dangers. According to Table 14, the management factor with 0.4384 weight is the most effective in preventing dangerous occurrences. Education on safety and monitoring is one of the most important subsections in this section, which safety managers should consider. In the second section of the research, the fuzzy VIKOR method was used for ranking safety risks based on the experts’ opinions. In Table 19, the risk of falling down is listed first among the six critical categories of high-rise buildings hazards based on its probability of occurrence and likelihood of causing harm. This research used sensitivity analysis according to Table 20, in Section 5, which verifies the results regarding changing effective parameters and constant outputs.

It is crucial to identify factors that contribute to effective safety management in high-rise buildings in order to reduce incidents and increase employee efficiency. Researchers and project managers can benefit from the research findings.

In this research, 30 high-rise building projects were studied. Future research can focus on the number of studied buildings and a specific type of high-rise building with different uses. Additionally, the climate of the area in which the high-rise buildings are located can be focused on to examine the effect of these parameters in the outputs.