Evaluation of Road Safety Hazard Factors in Egypt Using Fuzzy Analytical Hierarchy Order of Preference by Similarity to Ideal Solution Process

Abstract

To address road accident losses, there is a need to prioritize safety factors, especially in high-risk locations on the road network, toward assuring a sustainable transport system. This paper proposes an approach for quantitative risk assessments of safety factors in hazardous road locations and involves the integration of the Fuzzy logic model, the Analytic Hierarchy Process (FAHP) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). This new innovative method offers a way to prioritize and select safety factors associated with hazardous locations using a hierarchical structure. To demonstrate the applicability of this method, a case study was conducted in Egypt. The assessment process involved active participation by professionals through multiple expert meetings. This collaborative approach ensures that the assessment incorporates valuable real-world knowledge and experiences. It analyzed road safety hazardous conditions across various sections, including intersections, non-intersection sections, narrow bridge sections, and curve sections. The application of FAHP-TOPSIS enables the determination of weights for safety factors within each section, facilitating the evaluation of safety indices between them and ranking the safety hazard sections. The achieved analysis revealed that the hazard safety factor index is comparatively higher in curved sections compared to other types of sections. Light utility poles and road barriers significantly affected the hazard index. By utilizing this approach, governments may make informed decisions regarding the allocation of resources and the implementation of safety measures at hazardous road locations.

1. Introduction

A hazard location is a distinct point or area within a road network that exhibits a heightened risk of accidents when compared to other locations. These hazard locations can encompass a range of road sections, including intersections, curves, non-intersection sections, as well as specific features such as narrow bridges or high-speed zones. The examination of hazard locations has multiple objectives. It aids in comprehending the particular conditions or factors that contribute to higher accident susceptibility in these areas, such as limited visibility, inadequate signage, insufficient lighting, or complex road geometries. This understanding is vital for the implementation of focused interventions and safety measures aimed at mitigating the risks associated with these locations. Furthermore, the examination of hazard locations facilitates the formulation of preventive strategies aimed at reducing both the frequency and severity of accidents. These strategies may involve the implementation of engineering interventions to enhance road infrastructure, the modification of traffic control measures, the promotion of driver education and awareness programs, or the enforcement of measures to ensure compliance with traffic regulations. In addition, studies on hazard locations play a vital role in enhancing road safety by providing valuable insights for transportation planning, policymaking, and resource allocation decisions. Through the identification of high-risk areas, governments and transportation authorities can prioritize their investments and allocate resources effectively to address safety concerns to assure a sustainable road network and improve the quality of life. This action ensures that interventions and initiatives are targeted where they are most needed, leading to improved road safety outcomes.

Different methods of multi-criteria decision making can be used as tools for enhancing decision-making modeling, each method offering unique approaches and advantages. The SIMUS (Sequential Interactive Model for Urban Systems) serves as a powerful tool that combines linear programming with matrix operations, making it particularly effective for complex urban planning and infrastructure decisions where multiple objectives must be balanced simultaneously [1]. SESP-SPOTIS (Stochastic Expected Solution Point-Stable Preference Ordering Towards Ideal Solution) strengthens decision modeling by integrating both subjective expert opinions and objective data through a systematic stepped approach, ensuring more balanced and reliable outcomes [2]. The ESP-COMET (Enhanced Similarity Procedure with Characteristic Objects Method) enhances decision modeling through its incorporation of the fuzzy set theory and similarity measures, making it especially valuable when dealing with uncertain or incomplete information while maintaining the ability to handle both qualitative and quantitative criteria effectively [3]. The RANCOM (RANking COMparison) method enriches the decision-making process by utilizing Monte Carlo simulation techniques to generate probabilistic insights into how different criteria weightings affect outcomes, providing decision-makers with a deeper understanding of the stability and reliability of their choices across various scenarios [4].

Further, it is generally not possible to implement all road safety elements identified due to the limited budget available for road safety improvement. Hence, it is needed to rank the safety factors for each section and hence determine hazardous locations so that, depending on the available budget, the priority of safety factors and the hazardous locations can be identified. In other words, this prioritization process enables the identification and ranking of safety factors, as well as the determination of hazardous locations based on their hazard safety index. However, the literature review indicated that most of the methodologies require accident data for this purpose. Comprehensive road accident data are rarely available. Therefore, the assessment process involved active participation from professionals, who provided their insights and expertise through multiple expert meetings. This collaborative approach ensures that the assessment incorporates valuable real-world knowledge and experiences.

The Analytic Hierarchy Process (AHP) is a popular tool in occupational safety research because it is straightforward and practical. For instance, Aminbakhsh et al. [5] developed an AHP-based framework to prioritize safety risks and pinpoint hazards in construction projects. Dağdeviren and Yüksel [6] sought to improve decision-making reliability and allow the quantification of evaluation criteria by integrating the fuzzy set theory into the traditional analytic hierarchy process, creating the Fuzzy Analytical Hierarchy Process (FAHP). The purpose of developing the FAHP was to boost decision-making dependability and enable the quantification of assessment indicators [7,8,9]. The Order of Preference by Similarity to Ideal Solution (TOPSIS) method operates on the principle that the optimal alternative is characterized by having the minimum distance from the ideal solution while simultaneously having the maximum distance from the negative ideal solution. The ideal solution represents an alternative that possesses the most favorable values across all relevant criteria, while the negative ideal solution represents a hypothetical alternative with the poorest criteria values [10,11]. This study utilized the combination between the FAHP and TOPSIS to determine the priority of safety factors associated with different road section types and hence rank the safety hazard locations.

There has been limited research conducted on ranking safety factors specifically related to different road cross-section types. Only a few studies have focused on risk analysis within this particular sector of roads. As a result, there is an urgent need to identify the most critical safety factors and determine the safety index levels for different road sections. This research study compiled a comprehensive list of nine safety factors for each cross-section type. To evaluate their ranking of safety factors within each road safety condition type, a questionnaire-based assessment is recommended. FAHP-TOPSIS can effectively apply to road hazard domains in Egypt. Its primary goal is to evaluate the weights of identified safety factors associated with cross-section roads, enabling the rational prioritization of the various involved safety factors as well as the determination of hazardous locations based on their hazard safety index.

In general, this study examines how safety factors in hazardous road locations can be prioritized and assessed quantitatively while considering budget constraints. This study aims to achieve three main objectives: developing a quantitative approach for assessing risk levels of safety factors at dangerous road locations, establishing a method to prioritize safety factors based on available resources, and integrating multiple decision-making tools (including Fuzzy logic, AHP, and TOPSIS) to create a more comprehensive assessment framework. This approach provides a structured methodology for addressing road safety concerns while optimizing limited resources.

2. Literature Review

Studying hazard locations on roads is critically important for several reasons, including accident prevention, improving road safety, guiding resource allocation, informing policy and planning decisions, raising public awareness, and enabling ongoing monitoring and evaluation. Understanding where hazards exist helps identify high-risk areas where accidents are more likely to occur. By analyzing these locations, potential risks and contributing factors can be uncovered, allowing for preventive measures like infrastructure improvements, enhanced visibility, and traffic control. Hazardous locations pose safety threats to all road users. Studying them provides insights into the specific issues that can inform targeted interventions to reduce accidents. It also enables effective resource allocation by prioritizing high-risk areas for safety investments, ensuring maximum impact. Furthermore, hazard location data guide the development of policies, regulations, and transportation planning like road network and crossing designs. Highlighting specific risky locations and associated hazards raises public awareness and promotes safer behavior. Finally, the regular monitoring and evaluation of interventions in hazardous areas allows for continuous enhancements to further improve road safety over time.

On the other hand, road accidents can have a substantial economic impact in several ways. First, they impose healthcare costs such as emergency services, hospitalization, rehabilitation, and long-term care for injuries and fatalities. Second, disabilities from accidents reduce productivity through lost work time and earning capacity. Moreover, time spent on medical treatment and legal proceedings decreases productivity. Third, property damage to vehicles, infrastructure, and public and private assets adds costs for repairs and replacement. Fourth, legal and administrative costs arise from investigations, insurance claims, lawsuits, and court cases related to accidents. Fifth, traffic congestion caused by accidents leads to wasted time, fuel consumption, and transportation inefficiencies that hurt businesses, logistics, and overall productivity. Sixth, frequent accidents prompt insurance companies to raise premiums to cover higher risks, burdening individuals and businesses. Finally, negative publicity and safety concerns from tourist-involved accidents can discourage visitors and reduce tourism revenue and activity. In summary, road accidents impose healthcare, productivity, property, legal, congestion, insurance, and tourism costs that collectively cause significant economic losses.

Zegeer [12] outlined recommendations to the Kentucky Bureau of Highways for identifying hazardous urban road locations. Their study found that the criteria for hazardous sites in cities should differ from rural areas. They described the number of accidents method, which ranks hazardous locations by the total accidents occurring in a given timeframe. Locations can also be compared using accident rates, which account for both accident history and traffic exposure. In summary, he recommended some urban-specific hazardous location criteria to the Kentucky Bureau of Highways by using accident numbers and rates to identify hazardous urban sites based on accident occurrence and exposure [12].

Identifying black spots, also known as hazardous road locations (HRLs), high risk sites, hotspots, or accident-prone areas, is the first step in road safety management [13]. Though research offers many definitions, there is no consensus on what constitutes a hazardous location [14]. A hazardous or accident-prone spot can be defined as any site experiencing more accidents compared to similar locations due to localized risk factors [15]. In summary, identifying hazardous road sites is crucial for safety management but lacks a standard definition. These locations generally experience more accidents than expected due to specific risks. They are known by various terms like black spots, hotspots, and accident-prone areas.

A number of statistical techniques have been employed historically to model accident rates at particular sites over defined time intervals, often relying on multiple linear regression. A core assumption in these models is that accident occurrence follows a normal distribution. However, such models tend to lack suitable statistical distributions to accurately characterize the inherent randomness and discreteness of vehicle accident events on roadways. As a result, they cannot appropriately represent accident probability or make valid probabilistic predictions about accident likelihood. In essence, conventional statistical methods like regression used for accident modeling incorrectly presume normality, when accidents are in fact random, discrete happenings. This inability to capture the underlying distribution means that these models are unsuitable for probabilistic accident forecasting [16].

A number of researchers explored modeling approaches for accident injury severity, including [17,18]. Other studies focused specifically on models of severe injury involvement, such as the work conducted by Jovanis and Blower [19,20].

Studying hazard locations involves analyzing past accident records, on-site observations, road characteristics, traffic patterns, and other relevant risk factors. This process provides transportation officials, researchers, and policymakers insights into the underlying causes and conditions contributing to increased accidents in these spots. However, most current studies rely on the statistical modeling of accident or conflict data to evaluate safety. While these methods have advanced understanding, they depend on substantial accident data that are difficult and costly to assemble, particularly for entire road networks, leading to data shortages. This problem is especially true in developing nations. An alternate approach is safety audits, which identify deficiencies without quantifiable metrics. In summary, prevailing methods like statistical modeling require scarce accident data but cannot quantify safety levels. Limited accident data, principally in developing regions, constrain conventional analytical road safety assessment techniques.

On the other hand, the Bayesian methodology offers significant advantages in analyzing road traffic accident data by effectively combining both dynamic and static model components. Its strength lies in its ability to process observed data likelihood through efficient forward filtering, making it particularly valuable for complex traffic safety analyses [21,22].

In addition, Więckowski et al. [23] has made significant contributions to the field of Multi-Criteria Decision Analyses (MCDAs). His work provides dual value through both methodological insights and practical applications, presenting a systematic approach to complex decision-making challenges. Through his comprehensive analysis, they developed actionable frameworks that bridge theoretical foundations with practical implementations, offering decision-makers concrete tools for real-world applications. His research extensively examines recent developments in MCDA methodologies, particularly highlighting their integration with Decision Support Systems (DSSs). The study’s significance lies in its thorough exploration of contemporary MCDA applications and their practical implications across various domains. Their findings have enhanced our understanding of how these analytical tools can be effectively deployed in modern decision-making contexts, providing valuable insights for both researchers and practitioners in the field. Their work has been particularly noteworthy in demonstrating how theoretical advancements in MCDAs can be translated into practical, implementable solutions for complex decision-making scenarios.

Road safety researchers in Egypt have conducted various studies to understand accident causation and develop preventive strategies. In one notable study focused on rural roads in Upper Egypt, ref. [24] developed accident prediction models that examined different road configurations, including straight sections, curved segments, and areas adjacent to agricultural, residential, and desert zones. Their analysis of accident data revealed a striking distribution of contributing factors; human error emerged as the predominant cause, accounting for 81% of accidents on the roadways studied. Vehicle-related issues were responsible for 15% of incidents, while road conditions and environmental factors played relatively minor roles at 2.2% and 1.8%, respectively. Among the notable advances in Egyptian road safety analytics, Wahaballa et al. [25] developed an innovative approach using fuzzy logic systems to predict highway accident patterns. Their predictive model demonstrated remarkable accuracy, achieving statistical reliability with a determination coefficient exceeding 87%. Based on these findings, they proposed a two-tiered approach to accident reduction: an immediate intervention strategy projected to decrease accidents by 15.2%, and a comprehensive long-range plan estimated to achieve a more substantial 42.3% reduction in accident occurrence. Further research in Egyptian traffic safety analysis was conducted by [26], who evaluated the effectiveness of simplified accident modeling approaches using limited variables designed for practical implementation. Their comparative analysis spanned a five-year period, examining both consolidated and detailed traffic accident data from Egyptian roadways. The research demonstrated that disaggregated datasets yielded superior modeling results compared to aggregated information. They clustered hazard factors into main categories without focusing on the dominant factors affecting accident occurrence and without providing any decision-making criteria. In a related study focusing on road maintenance strategies, ref. [27] introduced an advanced decision-making framework that integrated three key components; road condition assessments, safety parameters, and maintenance expenditures. Their probabilistic model revealed a critical insight; insufficient maintenance funding leads to compromised safety conditions and deteriorating pavement quality in certain road segments, primarily due to delayed maintenance interventions. These studies lacked the determination of hazard indices in Egypt.

On the other hand, multi-criteria decision making (MCDM) is the most commonly used methodology for analyzing various attributes simultaneously. Developed by Saaty [28], it provides a practical and robust tool for managing qualitative and quantitative factors that impact decision-making activities. The AHP is the most popular method within MCDM and has become an essential tool in a wide range of decision-making situations [29]. This method allows us to simulate decision making by considering differences in criteria perception. The AHP model is based on a hierarchical structure, encompassing multiple choices and enabling the use of sensitivity analysis for criteria. It highlights the appropriateness and misalignment of decisions resulting from multi-criteria decision making, simplifying decision making and estimations through paired comparisons [30].

In the conventional AHP formulation, human judgments are typically represented as precise integers, or crisp values in fuzzy logic terminology. However, in numerous real-world scenarios, the human preference model exhibits ambiguity, and decision-makers may feel hesitant or unwilling to assign precise numerical values to comparison judgments. This issue is particularly evident when evaluating safety factors for mitigating hazards on roads, as decision-makers often lack sufficient or accurate information. Consequently, this can result in suboptimal decisions that enhance the risk of harm. In addition, the AHP employs a mathematical approach to validate the reliability of pairwise comparisons. This validation is performed through a consistency measurement system developed by [28], which utilizes the principal Eigenvalue method, where the decision-maker’s judgments are considered logically sound when the consistent ratio falls below the threshold of 10%. This threshold serves as a mathematical benchmark for acceptable levels of inconsistency in human judgment during the pairwise comparison process. Furthermore, two frequently employed techniques in MCDM are the AHP and the TOPSIS [31].

On the other hand, this study addresses a significant gap in Egyptian safety studies, as comprehensive research on accident prevention factors in Egypt is a challenge. This study aims to identify and analyze the crucial safety factors that could contribute to reducing accident rates across the country. By examining these key safety elements and their potential impact, this research seeks to provide valuable insights that could help to develop more effective accident prevention strategies specifically tailored to the Egyptian context. This pioneering study will contribute to the existing body of knowledge on safety management and accident prevention within Egypt’s unique environmental, social, and infrastructural conditions.

In addition, a road safety analysis combines crucial public safety and economic considerations. By identifying hazardous conditions across different road scenarios, this study can both protect lives and optimize resource allocation. The innovative approach of combining multiple decision-support methods with comprehensive expert insights offers both theoretical value and practical applications. This methodology enables decision-makers to make evidence-based decisions about where and how to invest in road safety improvements, ultimately reducing accident-related costs while maximizing the impact of limited safety enhancement budgets.

Therefore, the primary objective of this paper is to propose a fresh approach within the AHP framework to address uncertain and imprecise safety factor evaluations during the questioning stages. In this approach, the decision-maker’s comparison judgments are expressed as fuzzy triangular numbers. This article introduces a novel fuzzy prioritization technique that generates crisp priorities, including criteria weights and alternative scores, by leveraging both inconsistent and consistent fuzzy comparison matrices. This paper presents an analysis of the combination between FAHP and TOPSIS methodologies in the context of decision making. It aims to prioritize the safety hazard factors in each hazard location and determine the ranking of these locations. To illustrate the application of FAHP-TOPSIS, a specific case study is presented, showcasing its use in evaluating the safety index. In general, this study compiled a comprehensive list of nine safety factors for four condition types. Administering a questionnaire-based assessment is recommended to rank the relative importance of these safety factors within each condition’s category. A quantitative risk assessment approach using FAHP-TOPSIS is presented in this paper for evaluating hazard factors on hazard roadways conditions, with potential applications in Egypt. The primary objective is assessing weights for the identified cross-section safety factors, enabling the systematic prioritization of the diverse range of factors and determining the ranking of hazard safety locations.

3. Data and Methodology

3.1. Data Collection

In order to determine the major safety factors contributing to hazards on roads in Egypt, a survey was conducted among road safety specialists. The survey focused on different road safety conditions, including intersections, non-intersection conditions, narrow bridge conditions, and curve conditions. Prior to the field survey, the questionnaires underwent a pilot test to ensure their effectiveness. During the pilot test, a small group of experts in road safety reviewed the questionnaires to assess their clarity and ease of understanding. The feedback received from the pilot test was then incorporated to enhance the questionnaires before they were administered in the field survey. The questionnaires utilized in the survey were designed as multiple-choice, allowing road safety specialists to select from a predefined list of possible answers. By employing this approach, valuable insights were gathered from experts in the field to collect data on road safety. The survey results were subjected to statistical analysis to identify the most prominent safety factors associated with hazards on roads in Egypt.

McConnell [32] recommended assembling a group of experts with diverse backgrounds, consisting of 5 to 14 individuals, and [33] recommended consulting ten experts to gather the respondents. And they considered that this number of experts is effective for obtaining the accurate results for the AHP [33]. Furthermore, several studies provided guidance on the optimal number of specialists needed for analytical studies. In the context of the AHP, different researchers proposed similar sample sizes. For instance, Ishizaka and Labib [34] advocated for engaging 10 to 15 participants to ensure robust AHP results. This range aligns with Whitaker’s [30] findings, which establish 10 participants as a suitable minimum threshold for conducting AHP studies.

Therefore, 10 experts specializing in safety engineering were consulted in this paper, and their opinions were incorporated in both phases mentioned previously. The age range of these experts varies from 27 to 66 years, while their combined experience spans from 8 to 28 years. Details of the used data that supporting the reported results can be found in the attached Supplementary Materials.

3.2. Safety Hazardous Factors in the Road

The evaluation of road safety hazard factors in Egypt using the Fuzzy AHP-TOPSIS methodology demonstrates a strong alignment between the research conclusions and the evidence presented. The chosen methodological approach effectively combines quantitative data from road safety statistics with qualitative expert judgments through fuzzy evaluations, providing a comprehensive framework for analyzing complex road safety challenges. This dual approach significantly strengthens the validity of the conclusions by integrating objective metrics with expert knowledge in a systematic manner.

The research methodology proves particularly suitable for this study’s objectives, as it effectively handled the inherent uncertainty in road safety assessments while enabling the prioritization of multiple hazard factors in a hierarchical manner. The two-step process, utilizing the Fuzzy AHP for establishing factor weights and the TOPSIS for a ranking based on ideal solutions, provided a robust analytical framework that ensures the conclusions are well grounded in both data and expert opinions. The practical application of this method demonstrates its realistic value, as it successfully addressed actual road safety challenges within the Egyptian context while considering local conditions and multiple stakeholder perspectives.

This research paper’s contribution to the field of road safety assessments could be enhanced by explicitly highlighting several novel indicators and methodological approaches. The integration of plastic pedestrian tubes (HF6) as a distinct safety factor represents an innovative consideration in road safety assessments, particularly in the Egyptian context where pedestrian safety infrastructure is crucial but often overlooked in previous studies. The comprehensive evaluation of Temporary Traffic Control Devices (HF7) as a separate category also demonstrates novelty, as many existing studies tend to focus primarily on permanent infrastructure elements. This paper’s approach lies in its combined analysis of both static safety features (like road barriers and illuminated signs) and dynamic elements (such as surface conditions and geometric configurations) within a single hierarchical framework using the Fuzzy AHP-TOPSIS methodology.

Another novel aspect is the specific consideration of light utility poles (HF3) as a distinct safety factor, which is particularly relevant in the Egyptian context where roadside infrastructure can significantly impact accident rates. This study also innovatively considered the interrelationships between these factors, rather than treating them as isolated elements, which is less common in the existing literature. The methodology’s adaptation to local conditions while maintaining international safety standards represents a novel approach to contextualizing road safety assessment.

This discussion aims to rank the road safety hazard location and assess the corresponding safety factors for each location. This assessment will help determine effective strategies to reduce accidents at road sections identified as black spots. A hierarchical risk assessment structure (HRS) was created with three levels to organize this analysis. The first level outlined the objective of ranking the hazard cross-section type and also the safety factors for each cross-section. Then, the second level contained the actual safety factors, including illuminated road signs (HF1), guideposts (HF2), light utility poles (HF3), raised road markings (HF4), road barriers (HF5), plastic pedestrian tubes (HF6), Temporary Traffic Control Devices (HF7), surface conditions (HF8), and Geometrics Conditions (HF9) of the roadway as shown in Figure 1. Finally, the road safety hazard locations were then decomposed at the third level into conditions such as those found at narrow bridges (C1), curves (C2), non-intersections (C3), and intersections (C4) as shown in

Table 1. Hazard location for the roads.

Serial	Hazard Location Code	Description of Hazard Location
1	C1	Narrow bridges
2	C2	Curve section
3	C3	Non-interesection
4	C4	interesection

. By utilizing a hierarchical structure in road safety analysis, it is generally possible to identify the importance index for each safety factor and hence determine the ranking of safety hazard locations. Furthermore,

Table 2. Safety factors for the roads.

Ser	Safey Factor Code	Safety Factor	Photo	Remark
1	HF1	Illuminated Road Signs [Light Ramp Signs, Road Signs]		Light Ramp Signs
				Road Signs
2	HF2	Guideposts
3	HF3	Light Utility Poles
4	HF4	Raised Road Marks
5	HF5	Road Barriers [Guardrail, Concrete Barriers]		Guardrail
				Concrete barriers
6	HF6	Plastic Pedestrian
7	HF7	Temporary Traffic Control Devices [“Delineator Tubes” and “Traffic Cones”]		Delineator Tubes
				Traffic Cones
8	HF8	Surface Conditions
9	HF9	Geometric Conditions

displays the photos for safety factors that can be used in each condition. In general, the primary objective of this study is to establish a ranking system for classifying various types of hazardous safety road cross-sections. Furthermore, the intention is to identify and analyze the safety factors associated with each specific cross-section.

3.3. FAHP-TOPSIS

While previous studies have explored similar topics, this research breaks new ground by specifically addressing uncertainty in expert assessments. By incorporating fuzzy variables into the AHP, this study provides a more nuanced and reliable approach to risk assessment. The methodology’s strength lies in its extensive collaboration with industry professionals, whose practical experience and insights were gathered through multiple consultation sessions. The effectiveness of this approach was validated through a successful application to a real-world case study, demonstrating its practical value beyond theoretical frameworks. The integration of FAHP and TOPSIS methodologies presents a robust and comprehensive decision-making framework that overcomes the limitations of using either method independently. This hybrid approach capitalized on the FAHP’s strength in structuring complex problems hierarchically and handling the uncertainty in expert judgments through fuzzy numbers, while leveraging the TOPSIS’s capability to provide clear ranking orders based on the concept of relative closeness to ideal solutions. The synergistic combination offers several key advantages: firstly, the FAHP effectively determined the weights of criteria by incorporating expert knowledge and handling the inherent vagueness in human judgments, ensuring more reliable priority vectors. Secondly, the TOPSIS complemented this step by efficiently processing these weighted criteria to rank alternatives based on their geometric distances from both positive and negative ideal solutions, providing a more rational and mathematically sound decision basis. Additionally, this hybrid methodology enhanced the reliability of the decision-making process by compensating for the subjective limitations of the AHP with the objective mathematical rigor of the TOPSIS while simultaneously addressing the uncertainty in real-world data through the fuzzy set theory. The integration also offers practical benefits in terms of computational efficiency and the ability to handle both qualitative and quantitative criteria, making it particularly suitable for complex transportation safety assessments where multiple factors and alternatives need to be evaluated systematically.

The analysis process begins with the first stage, which focused on identifying the hierarchical structure. This structure consists of three levels. The second level incorporates hazard factors in the road cross-sections, which were determined through a combination of expert judgment and a literature review. In the subsequent stage, the focus shifted to the identification of the relative weights of hazard factors. This step involved following several steps. The first step involved determining the fuzzy scale. Moving on to the second step, questionnaires were administered to gather opinions from 10 experts who were part of the investigation. Finally, in the third step, a pairwise comparison matrix was created using the fuzzy scale to evaluate the relative importance weights of safety factors. In the fourth step, weight calculation was performed using the fuzzy geometric mean method, encompassing the determination of fuzzy geometric mean value (r_i), fuzzy weights (W_i), the center of area (COA) of weights (W_i), and normalized weights. The third stage comprised identifying the relative weight of each safety factor at hazard cross-sections [C1, C2, C3, C4]. For the third stage: the utilization of the FAHP was employed to establish a relative weight importance for each hazard factor [HF1, HF2, HF3, HF4, HF5, HF6, HF7, HF8, HF9] in the road cross-sections. Ultimately, for the fourth stage, the TOPSIS method was employed to obtain rankings for both the safety hazard cross-sections and the safety factors associated with each cross-section. These steps culminated in determining the ranking of hazard conditions for different cross-sections [C1, C2, C3, C4]. Hazard index values were also identified to generate a map highlighting the most critical section vulnerable to hazards for each cross-section, thereby emphasizing the significance of safety factors. At the concluding stage, the FAHP-TOPSIS method’s flow chart, illustrated in Figure 2, offers a graphical depiction of the procedure used to rank the safety factors for each cross-section and the rankings of the individual cross-sections themselves. The foundational definitions of the fuzzy technique were first presented by Zadeh and Zimmermann [35,36]. Triangular fuzzy numbers can be used to tackle decision-making issues in uncertain situations.

A triangular fuzzy number is used in this method to indicate fuzzy comparative judgment. The least value, the most likely value, and the highest value are the three triangle fuzzy numbers, which are more appropriate for expert judgment for representing the uncertainty compared to using a single precise number. This study defined triangular fuzzy numbers as follows in light of earlier studies on the topic [37]. In an AHP decision problem, each level of the hierarchy contains a limited number of decision items. The top level of the hierarchy represents the ultimate goal, the bottom level represents all feasible alternatives, and the intermediate levels represent decision criteria and sub-criteria. The AHP model’s hierarchical structure can help decision-makers visualize a problem by breaking it down into its various criteria and sub-criteria. However, the pair-wise comparisons that are used in the AHP can be subjective and may not reflect the true uncertainty that decision-makers feel about the relative importance of the criteria. This is where the FAHP comes in. The FAHP is a fuzzy extension of the AHP that allows decision-makers to express their uncertainty about the relative importance of the criteria using fuzzy numbers. This action can help to improve the accuracy of the decision-making process and to reduce the ambiguity of alternative selections. On the other hand, reference [38] introduced the TOPSIS technique as a practical approach to address real-life MCDM problems. The objective of this paper is to conduct an analysis of the combination of FAHP and TOPSIS methodologies within the framework of decision-making. The focus is on prioritizing safety hazard factors in individual hazard locations and establishing the ranking of these locations. This method proves valuable for decision-makers and engineers as it facilitates the comparison and ranking of a set of alternative decisions.

4. Results and Discussion

The assessment of potential safety factors comprises two main stages: (1) The identification of safety factors and (2) the evaluation of the weight of safety factors. Each stage encompasses several specific steps. The following sections elucidate these phases and their corresponding stages, offering a comprehensive explanation.

In Phase one, the main aim is to identify safety factors, which are subsequently weighted using the FAHP methodology. Phase one consists of two stages, which are as follows:

Phase one—Stage I: The AHS hierarchical tree is recommended to organize safety factors at the second level and hence the road condition type as the third level as shown in Figure 1. Experts are interviewed to build the AHS, which outlines the factors in a visual structure as shown in Figure 1. This hierarchical approach effectively frames the safety index for each road condition.

Phase one—Stage II: The process of identifying safety factors necessitates active expert participation in collaborative meetings. These meetings ensure that a comprehensive list of factors with agreed-upon definitions are developed. A documentation review is utilized as a tool to extract relevant safety factors during this process. In essence, expert meetings with cooperative engagement are crucial to identify safety factors comprehensively using consistent definitions. A document review helps elicit important factors to include during the meetings.

Phase Two: The hierarchy structure assigns varying levels of importance to safety factors in the decision-making process, meaning that each factor has a different relative significance based on its assigned weight value. The FAHP is employed to determine the weight of these safety factors, and it involves the following steps:

Perform pairwise comparisons of the safety factors using a geometric mean method to consolidate the judgments of decision-makers under uncertainty. The geometric mean integrates the perspectives of experts as follows:

P = (l, m, u), K = 1, 2, …, k

(1)

where P represents the triangular fuzzy number, while K signifies the total number of decision-makers involved, and

L = (l1 × l2 × … × lk)1/k, m = (m1 × m2 × … × mk)1/k, u = (u1 × u2 × … × uk)1/k

(2)

Furthermore, Figure 3 illustrates the membership function representing a triangular fuzzy number. To clarify, the pairwise comparisons of safety factors are carried out by leveraging the fuzzy scale provided in

Table 3. Fuzzy importance scale using triangular fuzzy numbers.

Linguistic Variable	Fuzzy Numbers
Equally important	(1, 1, 1)
Weakly important	(2, 3, 4)
Fairly important	(4, 5, 6)
Strongly important	(6, 7, 8)
Absolutely important	(9, 9, 9)
The intermittent values between two adjacent scales	(1, 2, 3)
	(3, 4, 5)
	(5, 6, 7)
	(7, 8, 9)

. Pairwise comparisons between factors are conducted, and the fuzzy comparison matrix is built using fuzzy numbers, as demonstrated in

Table 4. Fuzzified pair-wise comparison matrix.

	HF 1	HF 2	HF 3	HF 4	HF 5	HF 6	HF 7	HF 8	HF 9
HF 1	(1.0, 1.0, 1.0)	(5, 5.4, 5.8)	(2.4, 3, 3.6)	(4, 4.6, 5.2)	(3.2, 4.0, 4.8)	(5.3, 6.0, 6.7)	(4.3, 5.0, 5.7)	(3.6, 4.2, 4.8)	(3.1, 3.8, 4.5)
HF 2	(2.1, 2.8, 3.5)	(1.0, 1.0, 1.0)	(2.9, 3.6, 4.3)	(2.5, 3.0, 3.5)	(4.4, 5.4, 6.4)	(4.3, 4.8, 5.3)	(4.3, 4.8, 5.3)	(3.8, 4.8, 5.8)	(3.0, 3.8, 4.6)
HF 3	(3.8, 4.2, 4.6)	(3.6, 4.2, 5)	(1.0, 1.0, 1.0)	(6.0, 6.2, 6.4)	(4.1, 4.6, 5.1)	(6.0, 6.4, 6.8)	(5.1, 5.6, 6.1)	(4.0, 4.4, 4.8)	(4.5, 5.0, 5.5)
HF 4	(2.5, 3.2, 3.9)	(2.8, 3.2, 3.6)	(2.1, 2.8, 3.5)	(1.0, 1.0, 1.0)	(2.7, 3.4, 4.1)	(4.3, 4.8, 5.3)	(4.2, 4.8, 5.4)	(3.6, 4.4, 5.2)	(2.6, 3.2, 3.8)
HF 5	(3.6, 4.4, 5.2)	(4.2, 5, 5.8)	(1.8, 2.4, 3)	(3.3, 4.0, 4.7)	(1.0, 1.0, 1.0)	(7.8, 8.2, 8.6)	(6.1, 6.8, 7.5)	(5.2, 5.8, 6.4)	(4.4, 5.0, 5.6)
HF 6	(3, 3.8, 4.6)	(2.5, 3.2, 3.9)	(1.7, 2.4, 3.1)	(2.5, 2.4, 3.1)	(2.0, 3.0, 4.0)	(1.0, 1.0, 1.0)	(3.4, 3.8, 4.2)	(3.3, 4.2, 5.1)	(3.0, 3.8, 4.6)
HF 7	(2.8, 3.6, 4.4)	(3.1, 3.8, 4.5)	(1.7, 2.4, 3.1)	(2.3, 3.0, 3.7)	(1.9, 2.8, 3.7)	(1.9, 2.4, 2.9)	(1.0, 1.0, 1.0)	(3.8, 4.8, 5.8)	(4.4, 5.2, 6.0)
HF 8	(3.4, 4, 4.6)	(4.5, 5.4, 6.3)	(2.2, 2.8, 3.4)	(3.2, 4.0, 4.8)	(2.2, 3.0, 3.8)	(4.1, 5.0, 2.9)	(4.2, 5.2, 6.2)	(1.0, 1.0, 1.0)	(5.4, 5.8, 6.2)
HF 9	(3.9, 4.6, 5.3)	(4.1, 4.8, 5.5)	(2.4, 3.2, 4)	(3.0, 3.6, 4.2)	(2.1, 2.8, 3.5)	(3.8, 4.6, 5.4)	(3.3, 4.2, 5.1)	(1.7, 2.4, 3.1)	(1.0, 1.0, 1.0)
SUM	(26.1, 31.6, 37.1)	(30.8, 36,41.2)	(18.2,23.6, 29)	(27, 32.6, 37.4)	(23.6,30, 36.4)	(38.5,43.2,47.9)	(35.9,41.2,46.5)	(30, 36, 42)	(31.4,36.6,41.8)

. The process involves the following:

-

B is an n × n dimensional decision matrix.

$$\mathrm{B}=\left[\begin{array}{ccc}\mathrm{B}11& & \mathrm{B}1\mathrm{n}\\ & & \\ \mathrm{B}\mathrm{n}1& & \mathrm{B}\mathrm{n}\mathrm{n}\end{array}\right]$$

(3)

-

[B_ij], where I, J = 1, 2, …, n, B_ij is the fuzzy number (l, m, u).

-

For reciprocal B⁻¹ = (l, m, u)⁻¹ = ( ${\displaystyle \frac{1}{\mathrm{l}}},{\displaystyle \frac{1}{\mathrm{m}}},{\displaystyle \frac{1}{\mathrm{u}}})$ and B_ij = 1 for i = j.

-

The steps to calculate weights using fuzzy geometric mean are as follows:

-

Fuzzy geometric mean value (r_i): B₁ Θ B₂ Θ B_n

-

=(l₁, m₁, u₁) Θ (l₂, m₂, u₂) Θ (l_n, m_n, u_n) = (l₁ × l₂ × … × l_n, m₁ × m₂ × … × m_n, u₁ × u₂ × … × u_n)^1/n. Where n is the number of criteria.

-

Fuzzy weights W_i = r_i Θ (r₁ Θ r₂ Θ r_n)⁻¹.

-

The center of area (COA) of weights W_i = (l + m + u)/3.

-

Normalized weights = ${\displaystyle \frac{{\mathrm{w}}_{\mathrm{i}}}{\sum _{\mathrm{n}}^{\mathrm{i}-1}{\mathrm{w}}_{\mathrm{i}}}}$

The normalized weights obtained using the fuzzy geometric mean are presented in

Table 5. The weight of road safety factors using fuzzy geometric mean method.

Risk Factor Code	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wj
HF 1	(3.237, 3.739, 4.226)	(0.090, 0.119, 0.159)	0.123	0.119
HF 2	(2.891, 3.447, 3.984)	(0.080, 0.110, 0.150)	0.113	0.110
HF 3	(3.8489, 4.188, 4.521)	(0.107, 0.133, 0.170)	0.137	0.133
HF 4	(2.662, 3.162, 3.646)	(0.074, 0.101, 0.137)	0.104	0.101
HF 5	(3.585, 4.119, 4.633)	(0.099, 0.131, 0.175)	0.135	0.131
HF 6	(2.345, 2.951, 3.529)	(0.065, 0.094, 0.133)	0.097	0.094
HF 7	(2.333, 2.942, 3.529)	(0.065, 0.094, 0.133)	0.097	0.094
HF 8	(3.038, 3.630, 4.201)	(0.084, 0.116, 0.158)	0.119	0.116
HF 9	(2.585, 3.178, 3.749)	(0.072, 0.101, 0.141)	0.105	0.102
Total	(26.525, 31.356, 36.020)		1.031	1
Inverse	(0.038, 0.032, 0.028)
Increasing Order	(0.028, 0.032, 0.038)

.

Phase Three: The weight of each safety factor in various hazard conditions is determined using the FAHP. As a result, the FAHP can be utilized for all safety factors to obtain their respective weights in different road conditions [C1, C2, C3, C4].

Table 6. The weight of the safety factor [HF1] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.557, 2.797, 3.028)	(0.230, 0.279, 0.340)	0.283	0.279
C2	(2.466, 2.634, 2.796)	(0.222, 0.263, 0.314)	0.266	0.262
C3	(1.679, 2.121, 2.534)	(0.151, 0.211, 0.285)	0.215	0.212
C4	(2.201, 2.80, 2.748)	(0.198, 0.247, 0.309)	0.251	0.247
Total	(8.902, 10.031, 11.106)		1.016	1
Inverse	(0.112, 0.099, 0.090)
Increasing Order	(0.090, 0.0996, 0.1123)

,

Table 7. The weight of the safety factor [HF2] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.144, 2.402, 2.648)	(0.197, 0.244, 0.303)	0.248	0.244
C2	(2.860, 3.0489, 3.233)	(0.263, 0.31, 0.36709)	0.314	0.309
C3	(1.651, 2.031, 2.385)	(0.152, 0.207, 0.271)	0.210	0.207
C4	(2.095, 2.354, 2.601)	(0.193, 0.239, 0.297)	0.243	0.239
Total	(8.750, 9.835, 10.867)		1.016	1
Inverse	(0.1142, 0.1016, 0.092)
Increasing Order	(0.092, 0.101, 0.114)

,

Table 8. The weight of the safety factor [HF3] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.413, 2.683, 2.941)	(0.215, 0.262, 0.321)	0.266	0.262
C2	(2.640, 2.811, 2.977)	(0.235, 0.274, 0.325)	0.278	0.274
C3	(1.714, 2.149, 2.554)	(0.152, 0.21, 0.279)	0.214	0.211
C4	(2.402, 2.592, 2.773)	(0.214, 0.253, 0.302)	0.256	0.253
Total	(9.170, 10.235, 11.24)		1.014	1
Inverse	(0.109, 0.098, 0.088)
Increasing Order	(0.088, 0.098, 0.109)

,

Table 9. The weight of the safety factor [HF4] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.343, 2.640, 2.923)	(0.201, 0.252, 0.3176)	0.256	0.252
C2	(2.967, 3.179, 3.385)	(0.254, 0.303, 0.837)	0.308	0.302
C3	(1.867, 2.302, 2.708)	(0.158, 0.219, 0.129)	0.224	0.220
C4	(2.045, 2.367, 2.672)	(0.175, 0.226, 0.2897)	0.230	0.226
Total	(9.222, 10.487, 11.687)		1.019	1
Inverse	(0.108, 0.095, 0.085)
Increasing Order	(0.086, 0.095, 0.108)

,

Table 10. The weight of the safety factor [HF5] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.619, 2.847, 3.068)	(2.225, 0.269, 0.325)	0.273	0.269
C2	(2.707, 2.876, 3.039)	(0.232, 0.272, 0.322)	0.276	0.271
C3	(2.037, 2.459, 2.856)	(0.175, 0.233, 0.303)	0.237	0.233
C4	(2.066, 2.387, 2.695)	(0.177, 0.226, 0.286)	0.230	0.226
Total	(9.429, 10.568, 11.658)		1.015	1
Inverse	(0.106, 0.095, 0.086)
Increasing Order	(0.086, 0.0945, 0.1060)

,

Table 11. The weight of the safety factor [HF6] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.330, 2.554, 2.771)	(0.216, 0.265, 0.327)	0.269	0.264
C2	(2.221, 2.493, 2.753)	(0.206, 0.258, 0.325)	0.263	0.258
C3	(1.749, 2.180, 2.582)	(0.162, 0.226, 0.304)	0.231	0.227
C4	(2.182, 2.428, 2.664)	(0.203, 0.252, 0.314)	0.256	0.251
Total	(8.482, 9.655, 10.769)		1.019	1
Inverse	(0.117, 0.104, 0.092)
Increasing Order	(0.092, 0.103, 0.117)

,

Table 12. The weight of the safety factor [HF7] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.457, 2.688, 2.909)	(0.220, 0.268, 0.330)	0.273	0.268
C2	(2.321, 2.551, 2.772)	(0.208, 0.255, 0.314)	0.259	0.254
C3	(1.787, 2.219, 2.621)	(0.160, 0.222, 0.297)	0.226	0.222
C4	(2.250, 2.556, 2.850)	(0.202, 0.255, 0.323)	0.260	0.255
Total	(8.816, 10.013, 11.151)		1.018	1
Inverse	(0.1134, 0.099, 0.089)
Increasing Order	(0.089, 0.099, 0.113)

,

Table 13. The weight of the safety factor [HF8] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.158, 2.370, 2.575)	(0.203, 0.247, 0.304)	0.252	0.247
C2	(2.513, 2.773, 3.021)	(0.237, 0.290, 0.357)	0.294	0.289
C3	(1.828, 2.220, 2.590)	(0.172, 0.231, 0.306)	0.237	0.233
C4	(1.972, 2.207, 2.424)	(0.186, 0.231, 0.287)	0.234	0.230
Total	(8.471, 9.570, 10.613)		1.017	1
Inverse	(0.118, 0.104, 0.094)
Increasing Order	(0.094, 0.104, 0.118)

and

Table 14. The weight of the safety factor [HF9] for each hazard cross-section.

Code of Hazard Conditions	Fuzzy Geometric Mean Value (gi)	Fuzzy Weights Wi	Center of Area (COA)	Normalized Wi
C1	(2.2676, 2.423, 2.574)	(0.212, 0.250, 0.298)	0.253	0.249
C2	(2.505, 2.769, 3.022)	(0.234, 0.286, 0.350)	0.290	0.285
C3	(1.935, 2.316, 2.672)	(0.181, 0.239, 0.309)	0.243	0.239
C4	(1.938, 2.190, 2.425)	(0.181, 0.2261, 0.281)	0.229	0.225
Total	(8.644, 9.696, 10.693)		1.0151	1
Inverse	(0.115, 0.103, 0.093)
Increasing Order	(0.093, 0.104, 0.116)

present the normalized weight of each safety factor for the cross-section cases.

Phase Four: The technique for order preference by the TOPSIS was developed by [38] as a practical method for solving MCDM problems. The TOPSIS helps decision-makers rank safety hazard locations based on their distances from an ideal solution and a negative ideal solution. The key steps in the TOPSIS method are as follows:

The first step of the TOPSIS method involves the construction of a decision matrix (A): In the TOPSIS method, a decision matrix A is constructed where x_ij represents the performance value of alternative j with respect to criterion i. The matrix has m criteria (i = 1…m) and n alternatives (j = 1…n). The elements x_ij refer to the safety factor values for each alternative under each hazard condition. Thus, decision matrix A encapsulates the performance data of the alternatives across the safety criteria. The TOPSIS then uses this decision matrix to systematically quantify and rank the hazard cross-sections based on their geometric distances from an ideal solution that maximizes criteria values and a negative ideal solution that minimizes criteria values. The closer an alternative is to the ideal solution and farther from the negative ideal solution, the higher it is ranked by the TOPSIS.

$$A=\begin{array}{cc}\begin{array}{ccccccccc}\mathrm{H}\mathrm{F}1& \mathrm{H}\mathrm{F}2& \mathrm{H}\mathrm{F}3& \mathrm{H}\mathrm{F}4& \mathrm{H}\mathrm{F}5& \mathrm{H}\mathrm{F}6& \mathrm{H}\mathrm{F}7& \mathrm{H}\mathrm{F}8& \mathrm{H}\mathrm{F}9\end{array}& \\ \left[\begin{array}{ccccccccc}0.28& 0.24& 0.26& 0.25& 0.27& 0.26& 0.27& 0.25& 0.25\\ 0.26& 0.31& 0.27& 0.30& 0.27& 0.26& 0.25& 0.29& 0.29\\ 0.21& 0.21& 0.21& 0.22& 0.23& 0.23& 0.22& 0.23& 0.24\\ 0.25& 0.24& 0.25& 0.23& 0.23& 0.25& 0.26& 0.23& 0.23\end{array}\right]& \begin{array}{c}\mathrm{C}1\\ \mathrm{C}2\\ \mathrm{C}3\\ \mathrm{C}4\end{array}\end{array}$$

(4)

The second step: The second step in the TOPSIS is to normalize decision matrix A [NA] to transform the various criteria scales into comparable units. This step is achieved by dividing each element x_ij by the squared sum of the criterion values as follows:

$$\overline{{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}={\displaystyle \frac{{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}{\sqrt{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}}^2}}}$$

(5)

$$\mathrm{NA}=\begin{array}{cc}\begin{array}{ccccccccc}\mathrm{H}\mathrm{F}1& \mathrm{H}\mathrm{F}2& \mathrm{H}\mathrm{F}3& \mathrm{H}\mathrm{F}4& \mathrm{H}\mathrm{F}5& \mathrm{H}\mathrm{F}6& \mathrm{H}\mathrm{F}7& \mathrm{H}\mathrm{F}8& \mathrm{H}\mathrm{F}9\end{array}& \\ \left[\begin{array}{ccccccccc}0.55& 0.48& 0.52& 0.50& 0.54& 0.53& 0.53& 0.49& 0.50\\ 0.52& 0.61& 0.55& 0.60& 0.54& 0.52& 0.51& 0.58& 0.57\\ 0.42& 0.41& 0.42& 0.44& 0.46& 0.45& 0.44& 0.46& 0.48\\ 0.49& 0.47& 0.50& 0.45& 0.46& 0.50& 0.51& 0.46& 0.45\end{array}\right]& \begin{array}{c}\mathrm{C}1\\ \mathrm{C}2\\ \mathrm{C}3\\ \mathrm{C}4\end{array}\end{array}$$

(6)

The third step: The condition ratings for the various safety factors may not be equally important in determining the overall hazard ranking. Therefore, weights were previously assigned to each safety factor to represent their relative importance in the ranking. To incorporate these weighting into the decision matrix, each element of the normalized decision matrix is multiplied by the corresponding safety factor weight. This action creates a weighted normalized decision matrix, where the columns have been scaled to account for the differential importance of the safety factors. Specifically, each element $\overline{{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}$ of the normalized matrix is multiplied by the weight wj of its corresponding safety factor j, as obtained from the FAHP in

Table 15. The ranking of safety hazard location by preference order.

	HF 1	HF 2	HF 3	HF 4	HF 5	HF 6	HF 7	HF 8	HF 9	Si+	Si−	Pi	Rank
C1	0.066	0.053	0.069	0.050	0.070	0.050	0.050	0.057	0.050	0.02	0.03	0.572	2
C2	0.062	0.067	0.072	0.060	0.071	0.049	0.048	0.067	0.058	0.00	0.04	0.896	1
C3	0.050	0.045	0.056	0.044	0.061	0.043	0.042	0.054	0.048	0.04	0.00	0.074	4
C4	0.059	0.052	0.067	0.045	0.059	0.047	0.048	0.053	0.046	0.03	0.02	0.352	3
V+	0.066	0.067	0.072	0.060	0.071	0.050	0.050	0.067	0.058
V−	0.050	0.045	0.056	0.044	0.059	0.043	0.042	0.053	0.046

. This action results in the weighted normalized value Vij = wj × ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$. Constructing this weighted matrix integrates the relative ranking of the safety factors into the decision analysis, beyond just their normalized condition ratings.

$$\mathrm{V}=\begin{array}{cc}\begin{array}{ccccccccc}\mathrm{H}\mathrm{F}1& \mathrm{H}\mathrm{F}2& \mathrm{H}\mathrm{F}3& \mathrm{H}\mathrm{F}4& \mathrm{H}\mathrm{F}5& \mathrm{H}\mathrm{F}6& \mathrm{H}\mathrm{F}7& \mathrm{H}\mathrm{F}8& \mathrm{H}\mathrm{F}9\end{array}& \\ \left[\begin{array}{ccccccccc}0.66& 0.53& 0.69& 0.50& 0.70& 0.50& 0.57& 0.50& 0.50\\ 0.62& 0.67& 0.72& 0.60& 0.71& 0.49& 0.67& 0.58& 0.58\\ 0.50& 0.45& 0.56& 0.44& 0.61& 0.43& 0.54& 0.48& 0.48\\ 0.59& 0.52& 0.67& 0.45& 0.59& 0.47& 0.53& 0.46& 0.46\end{array}\right]& \begin{array}{c}\mathrm{C}1\\ \mathrm{C}2\\ \mathrm{C}3\\ \mathrm{C}4\end{array}\end{array}$$

(7)

The fourth step: The next step in the TOPSIS is to determine the ideal and negative ideal solutions based on the weighted decision matrix V. The positive ideal solution (B⁺) represents the best possible alternative, with the maximum weighted normalized value for each criterion:

$${\mathrm{B}}^{+}=\{{{\mathrm{V}}_1}^{+}, {{\mathrm{V}}_1}^{+}, {{\mathrm{V}}_1}^{+}, \dots , {{\mathrm{V}}_{\mathrm{n}}}^{+}\} {\mathrm{V}}_{\mathrm{j}}^{+}=\left\{\left({\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{i}}\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}\right) \mathrm{i}\mathrm{f} \mathrm{j}\in \mathrm{j}\right)\right.,\left({\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathrm{i}}\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}\right) \mathrm{i}\mathrm{f} \mathrm{j}\in \mathrm{j}\mathrm{\prime }\right)\}$$

The negative ideal solution (B⁻) represents the worst possible alternative, with the minimum weighted normalized value for each criterion:

$${\mathrm{B}}^{-}=\{{{\mathrm{V}}_1}^{-}, {{\mathrm{V}}_1}^{-}, {{\mathrm{V}}_1}^{-}, \dots , {{\mathrm{V}}_{\mathrm{n}}}^{-}\} {\mathrm{V}}_{\mathrm{j}}^{-}=\left\{\left({\mathrm{m}\mathrm{i}\mathrm{n}}_{\mathrm{i}}\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}\right) \mathrm{i}\mathrm{f} \mathrm{j}\in \mathrm{j}\right)\right.,\left({\mathrm{m}\mathrm{a}\mathrm{x}}_{\mathrm{i}}\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}\right) \mathrm{i}\mathrm{f} \mathrm{j}\in \mathrm{j}\mathrm{\prime }\right)\}$$

The fifth step: Determine the distance of each competing option from both the ideal and non-ideal solutions as shown in Table 14.

$${\mathrm{S}}_{\mathrm{i}}^{+}={\left[\sum _{\mathrm{j}=1}^{\mathrm{m}}{\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}-{\mathrm{v}}_{\mathrm{j}}^{+}\right)}^2\right]}^{0.5}$$

(8)

$${\mathrm{S}}_{\mathrm{i}}^{-}={\left[\sum _{\mathrm{j}=1}^{\mathrm{m}}{\left({\mathrm{v}}_{\mathrm{i}\mathrm{j}}-{\mathrm{v}}_{\mathrm{j}}^{-}\right)}^2\right]}^{0.5}$$

(9)

The sixth step: Assess the proximity of each location to the ideal solution by calculating the relative closeness. The relative closeness of each potential location, in relation to the ideal solution, is determined using the following equation:

$${\mathrm{P}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{S}}_{\mathrm{i}}^{-}}{{\mathrm{S}}_{\mathrm{i}}^{+}+{\mathrm{S}}_{\mathrm{i}}^{-}}}$$

(10)

The seventh step: Establish a preference order based on rankings. The ranking order is determined by the value of P_i, where a higher value of relative closeness corresponds to a higher ranking order and indicates better performance of the alternative. By arranging the preference rankings in descending order, it becomes possible to compare relatively better performances. Figure 4 shows the ranking of safety hazard conditions.

According to Figure 4, the ranking of hazard conditions indicates that curve sections and the narrow bridge possess the highest priority among hazard safety factors when compared to other types of cross-sections. Consequently, decision-makers should take this into account to ensure that safety requirements are met, thereby proving effective in reducing the frequency and severity of accidents, as well as mitigating economic losses arising from such incidents. There are several reasons why curves and intersections may require heightened safety considerations:

• Curves: On curved sections of a road or highway, vehicles need to navigate a change in direction, which can be challenging, especially at higher speeds. Factors like insufficient super elevation, inadequate curve radius, poor sight distance, and a lack of proper signage or markings can increase the risk of vehicles leaving the intended path, leading to collisions or run-off-road accidents.
• Narrow Bridge present a compounded set of challenges by combining the inherent difficulties of navigating a curve with the additional constraint of a narrow cross-section width. These sections often have limited space for maneuvering, reduced shoulder widths and potential sight distance issues, further exacerbating the hazards typically associated with curves. With less room for error or recovery in case of deviation from the intended path, vehicles traversing narrow bridge curves face an increased likelihood of collisions with bridge rails or other vehicles, as the margin for corrective action is significantly diminished.

This study’s findings reveal significant implications for road safety in Egypt, particularly highlighting the critical nature of curves and narrow bridge curves as primary hazard factors. The analysis indicates that these sections pose substantially higher risks compared to other road configurations, necessitating immediate attention from transportation authorities and decision-makers. This heightened risk can be attributed to several complex factors; curved sections demand sophisticated vehicle control mechanisms as drivers navigate directional changes, often at varying speeds, while contending with challenges such as inadequate super elevation, suboptimal curve radius, and restricted sight distances. The situation becomes particularly critical in narrow bridge curves, where these challenges are compounded by limited cross-sectional width, reduced shoulder space, and minimal recovery zones for corrective maneuvers. These findings have substantial implications for road safety strategies in Egypt, suggesting the need for comprehensive safety enhancements, including improved geometric design, advanced warning systems, and enhanced lighting at critical locations. The economic dimension of these safety improvements is particularly relevant, as investing in appropriate safety measures could significantly reduce accident-related costs, healthcare expenses, and overall economic losses. This understanding should guide policymakers and engineers in prioritizing safety improvements, with a particular emphasis on curved sections and narrow bridge curves, ultimately contributing to a more resilient and safer transportation infrastructure in Egypt.

On the other hand, the hazard of intersections can be attributed to the points where multiple traffic streams intersect, creating potential conflict points and higher chances of vehicle-to-vehicle collisions or collisions with pedestrians or cyclists. Factors like obstructed sight lines, inadequate signalization, poor lighting, and confusing or non-standard intersection designs can contribute to increased safety hazards.

From FAHP-TOPSIS, the ranking of safety factors are assessed for each location condition to prioritize their importance in mitigating accidents and damages. This goal can be achieved by obtaining the weighted normalized value Vij for each safety factor, as indicated in the provided

Table 16. The ranking of safety factors for each cross-section.

	C1	C2	C3	C4
HF 1	3	5	4	3
HF 2	5	3	6	5
HF 3	2	1	2	1
HF 4	8	6	7	9
HF 5	1	2	1	2
HF 6	9	8	8	7
HF 7	7	9	9	6
HF 8	4	4	3	4
HF 9	6	7	5	8

and Figure 5. According to Table 16 and Figure 5, it is evident that the priority ranking of safety factors varies across different cross-sections, and these rankings are not uniform. The prioritization of safety factors is contingent upon the specific conditions and characteristics of each road cross-section. For the narrow bridge section [C1], the top priorities are road barriers, light and utility poles, and illuminated signs. In the case of curve cross-sections [C2], the most crucial safety factors are light and utility poles, road barriers, and guideposts. As for non-intersection sections, road barriers, light and utility poles, and surface conditions take precedence. Ultimately, for intersection cross-sections, light and utility poles, road barriers, and illuminated signs emerge as the highest-ranking priorities among other safety factor categories. In general, the key takeaway is that a one-size-fits-all approach to prioritizing safety factors may not be effective. Instead, a context-specific and statistical analysis approach that considers the unique characteristics and conditions of each cross-section type is necessary to implement targeted and effective safety countermeasures. By tailoring safety interventions to the specific needs of each cross-section, decision-makers can optimize resource allocation and maximize the impact on reducing accidents, improving overall road safety.

5. Conclusions

Road accidents result in significant economic losses, mainly due to expenses related to hospitalization, medical treatment, vehicle repairs, and property damages. To tackle this issue, it is crucial to promptly implement corrective measures that give priority to safety factors, particularly in high-risk areas of the road network, with the aim of reducing both the frequency and severity of accidents. However, resource limitations often make it impractical to address all identified safety factors for hazardous road locations. Hence, it becomes necessary to prioritize safety factors based on the available budget. Nevertheless, it is important to note that many existing approaches for ranking hazardous locations rely on comprehensive road accident data, which are frequently scarce or unavailable. The main objective of this study was to develop a methodology for ranking both the safety factors and the road safety hazardous locations. Comprehensive road accident data are rarely available, making it challenging to assess and prioritize hazardous locations using traditional methods. This study has yielded the following conclusions:

• A statistical model called the FAHP-TOPSIS was developed to determine the rankings of both safety factors and hazardous locations. This model serves as a tool to address ambiguity by incorporating fuzzy logic, allowing for the ranking of safety factors through the FAHP. Additionally, the combination of the FAHP and TOPSIS enables the ranking of safety hazard conditions. The integration of FAHP and TOPSIS methodologies is considered a decision-making framework.
• This study introduces a four-stage methodology for ranking road safety hazardous locations. It begins with the identification of safety factors and safety hazard conditions. Subsequently, the relative importance of these factors is determined using the FAHP. This step is followed by the creation of various stages with the TOPSIS method, aimed at identifying the ranking of hazard conditions.
• The FAHP-TOPSIS methodology enables the ranking of safety hazard locations based on their proximity to an optimal and worst-case scenario. Curve hazards were found to be the top priority when considering safety factors. Narrow bridges posed the next greatest hazard according to the analysis. This study could assist in allocating limited budgets to locations in greatest need of road safety enhancements. The FAHP-TOPSIS approach put forth here quantifies road safety audit findings to categorize locations as high, medium, or low risk. Thus, this technique may prove valuable for targeting improvements to the most hazardous areas.
• Curves and narrow bridges warrant heightened safety considerations due to their inherent challenges and increased risk factors. On curved road sections, vehicles must navigate changes in direction, which becomes especially demanding at higher speeds. Insufficient super elevation, tight curve radii, poor sight distances, and inadequate signage can heighten the risk of vehicles departing the intended path, leading to collisions or run-off-road accidents. On the other hand, narrow bridge curves compound these risks by combining the difficulties of curved sections with the constraints of narrow cross-section widths, limited maneuvering space, reduced shoulders, and sight distance issues. This finding exacerbates hazards, leaving vehicles with less margin for error or recovery, increasing the likelihood of collisions with bridge rails or other vehicles.
• The ranking of safety factors for each cross-section was obtained using FAHP-TOPSIS, which can be determined by the calculation of the weighted normalized value V_ij for each safety factor. The FAHP-TOPSIS analysis revealed the most critical safety factors for each cross-section type. And the findings revealed that the priority ranking of safety factors is not uniform across different cross-sections, exhibiting variations. The prioritization of these safety factors hinges upon the unique conditions and characteristics inherent to each specific road cross-section typology. In the context of narrow bridge sections [C1], the top-ranking priorities encompass road barriers, lighting and utility poles, and illuminated signage. When considering curved cross-sections [C2], the most critical safety factors are lighting and utility poles, road barriers, and guideposts. For non-intersection sections [C3], road barriers, lighting and utility poles, and surface conditions assume precedence. Ultimately, at intersection cross-sections [C4], lighting and utility poles, road barriers, and illuminated signs emerge as the highest-ranked priorities among the other safety factor categories under consideration.

In general, the consistency between the conclusions and evidence is further reinforced by the systematic analytical process employed, which accounts for uncertainty through fuzzy logic while providing clear prioritization of hazard factors. The significance of the results is evident in their practical applicability, offering clear identification of priority areas for road safety improvement, evidence-based recommendations for policymakers, and a replicable methodology for future assessments. This comprehensive approach ensures that the conclusions not only address the research questions posed but also provide valuable insights into practical road safety management and policy implementation.

The next step currently under consideration is providing an online decision-making tool toward enhancing the practical application of the proposed methodology and offering an interactive element of our research to help with applying the proposed approach in other contexts. Future research opportunities in road safety hazard assessments could explore additional critical factors and emerging criteria that complement the current study. Specifically, the integration of technological factors such as smart traffic systems, connected vehicle infrastructure, and real-time monitoring systems could provide new dimensions to safety assessments.