Expanding the Fine-Kinney Methodology Using Fuzzy Logic: A Case Study in an Energy Linemen Workshop

Abstract

This paper investigates the effectiveness and limitations of the traditional Fine-Kinney method for occupational risk assessment, emphasizing its shortcomings in addressing complex and dynamic work environments. To overcome these challenges, two advanced methodologies, Fine-Kinney10 (FK10) and Fuzzy Fine-Kinney10 (FFK10), are introduced. The FK10 employs a symmetric scaling system (1–10) for probability, frequency, and severity indicators, providing a more balanced quantification of risks. Meanwhile, FFK10 incorporates fuzzy logic to handle uncertainty and subjectivity in risk assessment, significantly enhancing the sensitivity and accuracy of risk evaluation. These methodologies were applied to a linemen workshop in an energy production and distribution company, analyzing various types of accidents such as falls from heights, exposure to electric currents, slips on surfaces, and more. The applications highlighted the practical benefits of these methods in effectively assessing and mitigating risks. A significant finding includes the identification of risks related to falls from heights of <2.5 m (SH1) and road traffic accidents (SH6), where all three methods yielded different verbal outcomes. Compared to the traditional Fine-Kinney method, FK10 and FFK10 demonstrated superior ability in distinguishing risk levels and guiding targeted safety measures. The study underscores that FK10 and FFK10 represent significant advancements in occupational risk management, offering robust frameworks adaptable across various industries.

1. Introduction

Occupational health and safety constitute critical parameters for the functioning of every organization or enterprise, as they directly affect both productivity and long-term sustainability. From the employers’ perspective, ensuring the well-being and protection of their human resources represents a strategic priority, aligned with the principles of corporate responsibility and sustainable development. Correspondingly, employees’ compliance with established standards and regulatory frameworks of occupational health and safety not only safeguards their physical integrity but also contributes to the reduction in occupational accident risks. Moreover, the systematic implementation of such practices enables organizations to avoid legal sanctions and financial liabilities associated with compensation from insurance providers, thereby reinforcing business stability and competitiveness. Despite technological advancements and safety measures implemented worldwide by both workers and employers, it is estimated that over 100 million working days are lost annually due to occupational accidents [1].

Furthermore, research in 2024 reported that approximately 2.3 million people die each year from occupational accidents [1], with the International Labour Organization (ILO) estimating nearly 3 million such deaths annually [2]. In Peru, for instance, 1508 occupational accidents were recorded in the electrical sector, accounting for 4.6% of all workplace incidents nationwide [3]. In Brazil, an accident occurs every 49 s on average, with a fatality approximately every 4 h among formally employed workers (representing only 56% of the total workforce). The direct cost for Brazil’s National Institute of Social Security is 125 USD per second [4].

Occupational accidents and diseases pose a significant challenge to workplaces and society, accompanied by severe negative consequences [5]. These include employee injuries, equipment damage, reduced productivity, financial losses due to absenteeism, and premature retirements [6]. Additional repercussions involve negative publicity and reduced competitiveness for organizations where accidents occur [7]. Moreover, the World Health Organization estimates that poor occupational health and safety results in economic losses of 4% to 6% of gross national product for countries. Thus, strengthening workplace safety is imperative, achievable through Occupational Health and Safety Risk Assessment (OHSRA) models [8].

It is deemed essential to make specific reference to workplace risk management. Risk management and occupational safety constitute a systematic process used to identify, assess, and control hazards in order to minimize workplace accidents as much as possible [9]. The primary objective is to reduce both the likelihood and severity of workplace injuries and accidents. This is achieved by identifying hazards, which may be either natural in origin or result from human activity [1]. Following hazard identification, a risk assessment must be conducted, and the severity of potential harm should be prioritized. Subsequently, appropriate measures should be implemented to mitigate or eliminate the risks. Risk management is an ongoing process. Therefore, continuous monitoring and periodic review of both the implemented control measures and the methodologies used are essential to ensure effective and sustained workplace safety [9,10].

One of the most hazardous tasks in the energy sector is the work performed by aerial linemen. These workers primarily operate at significant heights, with the primary risk being the potential for falls and resulting injuries [11]. This study focuses on the largest and oldest electricity company in Greece, which has extensive departmental structures for task distribution. One of its primary departments manages the electricity distribution network, comprising approximately 5000 employees. This workforce includes both office staff and numerous field crews dedicated to ensuring the continuous and uninterrupted supply of electricity throughout the country’s grid.

This research specifically examines the team of aerial linemen, consisting of 198 individuals. To ensure the continuous operation of the network, this team works year-round, 24/7, without interruptions for holidays or weekends. Furthermore, their work environment is one that cannot undergo significant technological advancement, relying primarily on personal protective equipment (PPE) [12] and the integration of new materials into PPE. The hazard analysis for this team is conducted using the Fine-Kinney method. Additionally, two other methods—FK10 and FFK10—are proposed, which build upon the Fine-Kinney methodology.

The risk index is calculated by multiplying three component indices: probability, frequency, and severity. The product of these indices provides a result that is interpreted to determine whether measures should be taken in the workplace. The Fine-Kinney method quantifies risk through the assessment of probability, severity, and exposure. Developed in 1976, it has been widely used for occupational risk assessment [13]. For decades, this method has been employed by various businesses and organizations as an initial approach to understanding workplace hazards. Safety professionals favor it due to its simplicity and rapid results. However, the method’s low sensitivity has often been a limitation, as it provides only a preliminary estimation of workplace risks [6,14,15,16,17,18,19,20].

In recent years, efforts have been made to improve the Fine-Kinney method, enhancing its precision and comparing it with other occupational health and safety models. Modern extensions include the use of fuzzy systems, neural networks, and machine learning to address uncertainty and subjectivity, as proposed by several researchers [19,21]. A hybrid model incorporating multi-criteria decision-making (MCDM) [22] methods with Fine-Kinney has been developed to tackle complex risk assessment challenges [23]. Other examples include integrating Fine-Kinney with hierarchical process analysis (AHP) and other multi-criteria analysis tools [24] for more effective risk evaluation [25,26]. Consequently, combining Fine-Kinney with fuzzy systems and advanced technologies, such as machine learning and Bayesian analysis [9], can significantly enhance the accuracy and efficacy of risk management.

However, no researcher to date has attempted to increase the sensitivity of the method by expanding its three key parameters: probability, severity, and frequency. The two new methods proposed in this study address this gap. Specifically, the probability index, originally comprising seven parametric values, is expanded to ten, while the severity and frequency indices, initially having six values, are also extended to ten. Similarly, the risk index, previously limited to five combinations and verbal outcomes, is expanded to ten.

This study makes a notable contribution to the advancement of occupational risk assessment methodology based on the Fine-Kinney model, by introducing the following innovations and improvements:

• Expansion of the three core indicators (probability, frequency, and severity), both numerically and linguistically, allowing for greater accuracy and sensitivity in distinguishing between different risk levels.
• Restructuring of the Risk Priority Number (R) through the numerical extension of the scale and the enrichment of verbal descriptions for each risk level, offering a more comprehensive reflection of the urgency and necessity of implementing control measures.
• Adoption of a unified ten-point scale (1–10) across all indicators, eliminating the use of sub-unitary values. This approach prevents the underestimation of the overall risk score and enhances the comparability and interpretability of the assessment outcomes.
• Integration of fuzzy logic into the methodology, aiming to normalize calculations and improve the consistency and reliability of final risk estimates—especially in environments characterized by increased subjectivity and uncertainty.
• Application of the revised methods in a real high-risk work environment (aerial linemen workshop), demonstrating their superiority over the traditional Fine-Kinney model in terms of hazard ranking and prioritization of safety interventions.

The remainder of this paper is structured as follows: Section 2 reviews the relevant literature, presenting recent scientific efforts to enhance the Fine-Kinney method in combination with other techniques. Section 3 introduces the upgraded FK10 and FFK10 methods, which offer improved sensitivity and accuracy in risk classification. Section 4 applies these methods to a real high-risk working environment (aerial technician crew), with the corresponding results presented. Section 5 discusses the verbal interpretation of the outcomes derived from the application of the methods.

Finally, Section 6 presents the conclusions, while Section 7 outlines future research directions.

2. Literature Review

For the purposes of the literature review, individual databases provided by major publishers such as SpringerLink, ScienceDirect, IEEE, MDPI, or Taylor & Francis were not accessed directly. Instead, Scopus was employed as the sole search platform, owing to its broad and comprehensive coverage, which already incorporates the content of the aforementioned publishers. This approach ensured consistent and systematic access to the relevant body of literature.

The search strategy involved the combined use of the keywords “Occupational Risk Assessment”, “Fuzzy Logic”, “Risk Assessment”, and “Workplace Hazard”, together with the term “Fine-Kinney Method”. The initial search retrieved 85 articles. Subsequently, a second screening was performed, with the sole criterion being the inclusion of studies presenting improved versions of the classical Fine-Kinney method. The search was conducted in January 2025, and a total of 22 articles were ultimately selected for inclusion in the literature review.

According to Kokangul and colleagues [27], the Fine-Kinney method assigns equal weight to its three parameters. This method is widely employed in practice for risk assessment. The authors examine risk assessment by integrating the Fine-Kinney method with the Analytic Hierarchy Process (AHP). They acknowledge that the Fine-Kinney method generates risk scores for each hazard, whereas the AHP method provides a singular, aggregated risk score. In a novel approach combining the two methods, experts conducted a risk determination study in a large construction company. The findings indicated that the risk category intervals of the Fine-Kinney method could be utilized in conjunction with the AHP results. However, they also highlighted that such a combined risk assessment method might not be universally applicable across all workplaces due to varying risk levels in different occupational sectors [27].

Gul and co-authors argue that a fundamental limitation of the Fine-Kinney method is its equal weighting of the three indices: the probability of occurrence, the frequency of occurrence, and the severity of the event. To address this, they propose a new method incorporating Fuzzy Analytic Hierarchy Process (FAHP) and Fuzzy VIKOR (FVIKOR), designed to overcome the limitations of the classic Fine-Kinney method in occupational risk assessments. This approach enhances sensitivity and decision-making for occupational health and safety (OHS) risk evaluations by rebalancing the parameters. The proposed method enables group decision-making in risk assessment using linguistic terms rather than numerical values. Consequently, the FAHP-FVIKOR framework identifies more nuanced risk levels, organizing risks into seven categories instead of five, thereby improving prioritization [16].

In another study concerning occupational health and safety issues in railway transportation, researchers combined the Fine-Kinney method with fuzzy logic. They claim that incorporating a fuzzy rule-based empirical system manages inherent uncertainties, providing improved decision-making for stakeholders [28]. Risk assessment in railway transport is critical due to the high exposure of passengers and workers to hazards in workshops, stations, railway lines, and offices. Traditional methods like the 5×5 Matrix, Fault Tree Analysis (FTA), and Failure Modes and Effects Analysis (FMEA) struggle to handle uncertainties effectively. The dependence of the Fine-Kinney method on crisp values for probability (P), exposure (E), and consequence (C) limits its flexibility in incorporating expert judgment. The proposed fuzzy logic methodology addresses these limitations, offering improvements in sensitivity, accuracy, and practicality compared to the classic Fine-Kinney method. This hybrid approach overcomes traditional constraints, providing a more adaptable and reliable framework for risk assessment. Its applicability extends beyond railway transportation to industries such as construction and shipping, showcasing its potential for broader adoption [15].

In a further study by Gul and colleagues [29] the authors focus on enhancing the prioritization of control measures in risk assessments based on the Fine-Kinney method by employing a combined Bayesian Best-Worst Method (BBWM) and FVIKOR approach. This methodology addresses challenges in effectively implementing control measures by incorporating criteria such as feasibility, functionality, performance, and integrity. It proposes a novel multi-criteria decision-making (MCDM) framework for prioritizing control measures in Fine-Kinney-based risk assessments. The authors assert that combining BBWM with FVIKOR overcomes the limitations of traditional risk assessment prioritization methods. Additionally, BBWM, as an improved MCDM method, identifies the importance of criteria based on decision-makers’ evaluations, reducing information loss compared to traditional methods. This approach was applied to fuel storage tanks at oil stations. The case study demonstrated the practicality and effectiveness of the method in addressing critical risks. By integrating expert opinions and fuzzy logic, the proposed method enhances traditional approaches, offering a robust tool for occupational health and safety management [29].

In another study, efforts were made to enhance occupational health and safety (OHS) practices at a gas-filling facility by integrating the Fine–Kinney risk assessment method with fuzzy logic techniques and multi-criteria decision-making (MCDM) methods, such as AHP and TOPSIS. The objective was to improve the objectivity and sensitivity of risk assessments and prioritize actions considering operational constraints. This goal was achieved through a seven-step process: risk identification, classical risk analysis (using Fine–Kinney), fuzzy Fine–Kinney risk analysis, identification of impact groups, development of an action plan, action prioritization with TOPSIS, and integration of operational constraints. The model was applied to the gas-filling process, production, and transportation sectors, successfully identifying key risks such as fire hazards from greasy gloves, tank pressure increases, and electrical failures. The research integrates classical and fuzzy risk assessment with MCDM techniques to address subjectivity in traditional methods. By accounting for affected groups and company-specific constraints, the study offers a flexible and practical framework for action selection in industrial risk management [14].

While the Fine–Kinney model is widely used for risk assessment, it has limitations in addressing complex and uncertain environments, such as accounting for interactive effects of risk factors and subjective expert opinions. To overcome these challenges, an innovative hybrid framework combining the Fine–Kinney model with the Complex Spherical Fuzzy (CSF) CRADIS method was proposed. This approach allows precise risk prioritization in natural gas pipeline construction (NGPC) projects. The hybrid framework involves the following steps: data collection, CSF representation, formation of a group risk matrix, risk prioritization, and validation [30].

Wang and colleagues [31] introduced the extended Fermatean fuzzy MARCOS method combined with prospect theory. The proposed framework addresses the limitations of traditional Fine–Kinney methods by incorporating fuzzy logic for uncertain data representation, decision-makers’ prioritization, and psychological factors influencing risk assessments. The authors highlighted that the integration of Fermatean fuzzy sets (FFS) enables a broader and more flexible representation of uncertain risk data. The MARCOS method accounts for bounded rational behavior and reference points in decision-making. Additionally, a new Fermatean fuzzy prioritized weighted average (PWA) operator was introduced to effectively aggregate risk assessments from decision-makers, considering their priority levels. This operator also incorporates psychological biases, whereas traditional frameworks for risk prioritization overlook bounded rationality. The risk evaluation process involves four phases: risk data processing, aggregation using the PWA operator, risk prioritization with the extended MARCOS method, and validation through sensitivity and comparative analyses. The framework employs linguistic scales and fuzzy logic for processing risk data, making it suitable for uncertain environments. The hybrid Fermatean fuzzy Fine–Kinney with MARCOS model represents a significant advancement in occupational risk assessment, addressing limitations in traditional methods and providing a robust and adaptable framework for complex, uncertain environments [31].

In another study, an extended Fermatean fuzzy GLDS (Gained and Lost Dominance Score) method with CRITIC (Criteria Importance Through Inter-criteria Correlation) was adopted for risk classification and weight determination. The authors argued that the existing literature on the Fine–Kinney framework rarely considers collective and individual risk attitudes in ranking potential risks, particularly with Fermatean fuzzy-based risk scoring information. To bridge this gap, a novel ranking approach was proposed, integrating Fermatean fuzzy sets with the GLDS method. The findings indicate that the improved framework effectively ranks potential risks with complex risk information [32].

Kuleshov and his colleagues emphasize the utility of the Fine-Kinney method for assessing accident severity compared to other approaches. They highlight that occupational risk assessment is an integral component of workplace safety management, aiming to minimize injuries and illnesses. Additionally, the Fine-Kinney method, a quantitative risk assessment tool, was selected for its capability to analyze and control hazards by evaluating the probability, exposure frequency, and potential consequences of risks. The researchers applied this method to analyze three years of accident data from a coal mining company. The provided tables included standardized values for probability, exposure, and consequences, facilitating consistent scoring. The study underscores the practicality of the Fine-Kinney method for systematic risk evaluation, emphasizing its role in transforming qualitative risk data into reliable insights. The economic loss analysis further highlights the financial impact of accidents, drawing employer attention to the need for improved occupational safety standards. Finally, the authors present the method as a robust tool for workplace hazard mitigation [18].

Traditional risk assessment methods, such as Failure Mode and Effects Analysis (FMEA) and the Fine-Kinney method, consider risk parameters including probability, severity, detectability, and frequency. However, no approach simultaneously integrates all these parameters. To address this gap, a novel Safety and Critical Effect Analysis (SCEA) methodology employing Pythagorean fuzzy systems (PFS) has been proposed to enhance risk estimation accuracy. Essentially, SCEA calculates risk using Fine-Kinney standards while incorporating accident detectability. The authors argue that SCEA, as an advanced risk assessment approach, integrates probability, severity, detectability, and frequency parameters, and its extension with PFS enables better management of uncertainty and supports expert judgments [21].

Kuleshova and Pankov [33] investigate occupational risks within thermal energy engineering enterprises, focusing on personnel such as power unit drivers, repair technicians, and electricians responsible for machinery maintenance. Special attention is given to risk evaluation using various assessment methods and emphasizing critical occupational health factors. The study analyzes occupational morbidity and employs multiple risk assessment techniques, including the Fine-Kinney method, Matrix Method, Guide R 2.2.1766-03, and semi-quantitative risk estimations. The authors highlight the variability and subjectivity inherent in different risk assessment models, noting that while Fine-Kinney and semi-quantitative methods offer generalized frameworks, Guide R 2.2.1766-03 provides a more objective approach by correlating occupational exposures with health risks [33].

According to Oturakçi and colleagues [34], the Fine-Kinney method combines probability, frequency, and severity scores to compute an overall risk rating. However, it lacks sensitivity, especially for risks characterized by high probability and high frequency, leading to ambiguities in risk prioritization. This issue is addressed through the introduction of linear and quadratic interpolation techniques. Comparing the results with the classical method, risk scores were recalculated for each hazard, enhancing sensitivity, prioritization, ambiguity reduction, and action plan adjustments. Furthermore, quadratic interpolation was found to be the most effective for risk ranking in high-risk scenarios. These improvements overcome the limitations of the classical approach, such as insensitivity and ambiguity, and emphasize the importance of adapting traditional methods to evolving workplace safety challenges, ultimately contributing to safer and more efficient operations [34].

Güney and Kahraman [17] address occupational health and safety (OHS) risks in environmental research laboratories. The two methods employed—Analytic Hierarchy Process (AHP) and Fine-Kinney—were used for hazard assessment, determination of appropriate safety measures, and calculation of the overall implementation cost of these precautions. The results were noteworthy, highlighting the importance of applying structured risk assessment models to enhance safety, reduce accident likelihood, and ensure a safer work environment for personnel. Moreover, the study calculated the costs associated with implementing the proposed changes [17].

Ilbahar and colleagues [35] combine the Fine-Kinney method, Preference-based Fuzzy Analytic Hierarchy Process (PFAHP), and Fuzzy Inference Systems (FIS) into an integrated framework. This approach claims to provide a more accurate and informative risk assessment model. The method was applied to excavation operations at construction sites. Linguistic terms were converted into interval-valued Pythagorean fuzzy numbers (IVPFNs). Risks were categorized into five primary groups: Environmental Factors, Staff Management, Unsafe Behaviors, Heavy Equipment, and Construction Yard Management. The results demonstrated higher accuracy compared to the classical Fine-Kinney method [35].

In another study, the authors aim to address the lack of a robust and systematic framework for evaluating occupational health and safety risks in industrial environments. The fuzzy integrated assessment complements this approach by translating linguistic safety evaluations into numerical data using fuzzy logic. The findings demonstrated a more effective and improved categorization of risks associated with worker production safety. This approach bridges the gap between qualitative and quantitative risk assessment, thereby enhancing the reliability and practical utility of safety evaluations and ultimately contributing to safer workplace environments [36].

Furthermore, building on previous research in the construction sector, Bashary and colleagues [37] reinforce the Fine-Kinney method with the Building Demolition Safety Index (BDSI). Their study identifies the limited attention researchers have given to demolition projects, which are characterized by unique and high-risk tasks. To ensure safer and more reliable risk management, they propose a hybrid framework integrating the Delphi method, Fine-Kinney, Fuzzy Fault Tree Analysis (FTA), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and Fuzzy Inference System (FIS). This complex methodology combines leading workplace safety techniques. The results indicate satisfactory risk management through expert judgments and real project applications, highlighting the applicability and robustness of the BDSI model [37].

A recent study conducted in Turkey utilized a fuzzy model for managing occupational risks in the industry, specifically those arising from natural disasters. The authors highlight the issues with the Fine-Kinney method’s coefficients, as values smaller than one underestimate the severity of the problem, ultimately rendering the classic method inadequate for application in natural disaster scenarios, where it undermines the results. For instance, it categorizes the risk of earthquakes as a simple “potential risk,” whereas the fuzzy model classifies it as a “high-risk” situation. Additionally, the authors emphasize the fuzzy logic-based method as a supportive tool for planning and forecasting. Finally, the study concludes, as do many similar studies, that while the Fine-Kinney method offers a quick result, the fuzzy version provides superior outcomes and is applicable in more complex and dynamic natural disaster conditions [20].

In research conducted within the construction sector, the difficulty of finding personnel due to the numerous hazardous tasks involved is emphasized. The authors propose two models related to occupational risk assessment: the OHRAHM (Occupational Health Risk Assessment Hierarchy Model) and the OHHFRAM (Occupational Health Hazard Factor Risk Assessment Model). These models incorporate reliability analysis methods, superiority diagram techniques, and fuzzy sets with subjective linguistic judgments based on the Fine-Kinney model. The data for the study were collected from construction companies located along the Pearl River in China. The study concludes that the integration of fuzzy logic into the Fine-Kinney method significantly enhances its ability to assess chronic health risks in the workplace. The models not only differentiate between health and safety risks but also account for the subjective and often inaccurate nature of workers’ experiences. From a theoretical perspective, the models expand the scope of quantitative risk assessment tools, while practically providing construction managers and policymakers with a systematic approach for risk prioritization and mitigation. Furthermore, the authors argue that these models bridge critical gaps in worker safety, with fuzzy logic playing a key role in this improvement. Standardization of these models could potentially create a new dynamic protocol for hazardous industries [38].

A recent study conducted in the metallurgy industry found that the complexity of workplace processes and the high frequency of occupational accidents and illnesses underscore the need for well-documented risk assessment methods. To address this, the authors propose an enhanced risk assessment methodology that integrates fuzzy logic principles into the Fine-Kinney model. The ultimate goal of this method is to bypass the rigid scales of the classic method. As a result, the model uses ten linguistic levels compared to the original five, enabling a better analysis and classification of risks. Among the 86 cases evaluated by the authors, 26 saw the risk levels shift to higher tiers due to the application of fuzzy logic, whereas only a few were assessed at a lower risk category compared to the classic method. In this way, the authors demonstrate the superiority of the fuzzy approach in visualizing and improving safety and health management [39].

The literature review indicates that when the Fine-Kinney method is combined with other methodologies, the degree of subjectivity is substantially reduced, resulting in more accurate and targeted outcomes.

Beyond occupational health and safety, the Fine–Kinney method can be applied across a wide range of scientific domains. Indicative examples include the healthcare sector, the maritime industry. Recent literature highlights such applications, emphasizing that this method offers significant potential beyond traditional occupational risk assessment, supporting decision-making in diverse and complex environments.

Table 1. Overview of Fine–Kinney method applications beyond the field of OHS.

Article	Sector/Case Study	Method Applied	Key Findings/Practical Implications
[40]	Tertiary hospital, epilepsy patients	Fine–Kinney (FK) for assessing non-compliance with quality indicators	Identified high non-compliance rates in critical indicators (quality of life, folic acid intake, contraception). Integration of clinical pharmacists improved compliance and reduced risks.
[41]	Nursing homes in Istanbul	Fine–Kinney + ANFIS (hybrid)	Developed a new hybrid method for spatial risk assessment. Achieved 95.7% prediction accuracy. Provides faster, more objective assessments without requiring a large number of experts.
[42]	Oil/chemical tankers—gas freeing process	Fine–Kinney + Intuitionistic Fuzzy TODIM	The hybrid approach improved evaluation of critical risks (explosion, toxicity). Addressed uncertainty in decision-making and provided more accurate risk prioritization for operational safety.
[43]	Maritime operations—ship maneuvers in port	Fuzzy Fine–Kinney	Bridge simulator study of berthing maneuvers. FK helped determine which ships are suitable for maneuvers under varying environmental conditions, providing a tool for safer port planning.

summarizes these applications, offering a concise depiction of the method’s utilization across different scientific domains.

3. Description of Methods

In this section, the classical Fine-Kinney method is presented and analyzed, along with two advanced methodological extensions that are proposed, namely FK10 and FFK10.

3.1. Fine-Kinney Method

The Fine-Kinney method is a powerful tool for the assessment and mitigation of workplace risks. It is a widely used risk assessment technique that evaluates hazards based on probability, frequency, and severity. Through the systematic evaluation of these three factors, companies and organizations can prioritize risks and effectively strengthen safety measures.

3.1.1. Selection of Workplace

The initial step in the method, before determining the indicator values, is to select the workplace and identify its potential hazards. Tasks involving high-risk activities, such as operation of heavy machinery, handling of hazardous chemicals, or work at heights, should be prioritized over other tasks and activities conducted within the company or workplace. Furthermore, compliance with regulations must be considered to ensure that all hazardous activities meet occupational safety standards. Employee commitment is also a critical component, where workers directly involved in these activities are expected to adhere not only to expert guidance and company policies but also to the correct and proper use of personal protective equipment. Following these procedures, the safety experts or the company’s safety engineer proceed to determine the three indicators of the method.

3.1.2. Probability Index

The probability index represents the likelihood of occurrence of a hazardous event. To assign a probability value, the safety technician or expert must refer to the company’s or organization’s historical data, established industry standards, their own assessment, as well as direct observations in the workplace (

Table 2. Probability Index.

Probability Level	Description	Score
Virtually impossible	The event is highly unlikely to occur and can almost be excluded from consideration in risk assessments due to extreme improbability.	0.1
Practically impossible	The event has such a low likelihood that its occurrence is negligible under normal operating conditions.	0.2
Conceivable but very unlikely	While theoretically possible, the event’s occurrence would require extraordinary or unusual circumstances.	0.5
Only remotely possible	The event could happen under specific, albeit rare, conditions or due to external factors.	1
Unusual but possible	The event does not occur frequently but could arise under less common situations or moderate deviations.	3
Quite possible	The event is plausible and could occur in standard operations or reasonably anticipated conditions.	6
Might well be expected	The event is highly probable and is likely to occur with regularity based on current trends or existing data.	10

).

3.1.3. Frequency Index

The frequency index reflects how often an individual is exposed to a hazard. To determine this index, the frequency of repetition of a task or hazardous activity must be examined, the duration of exposure to the risk each time, as well as the number of individuals exposed to the specific hazard (

Table 3. Frequency Index.

Frequency Index	Description	Score
Vary Rare	Less than once per year	0.5
Rare	A few times per year	1
Frequent	Monthly occurrence	2
Occasional	Weekly occurrence	3
Frequent	Daily or more frequent	6
Continuous	Unstoppable	10

).

3.1.4. Severity Index

The severity index represents the seriousness of the potential harm that may result from an incident. To determine the severity, the type of injury or damage is evaluated (e.g., ranging from minor cuts to fatality), the extent of the damage (i.e., whether it affects one or multiple individuals), and finally, whether it causes costly equipment damage or completely disrupts work operations (

Table 4. Severity Index.

Severity Index	Description	Score
Noticeable	Minor first aid accident, or >$100 damage	1
Important	Disability, or >$103 damage	3
Serious	Serious injury, or >$104 damage	7
Very Serious	Fatality, or >$105 damage	15
Disaster	Few fatalities, or >$107 damage	40
Catastrophic	Many fatalities, or >$107 damage	100

).

Once the three indices—probability, frequency, and severity—are defined, they are subsequently multiplied together to yield a final result (Risk Score = P × F × S). This result is then decoded using linguistic terms based on the risk interpretation table.

3.1.5. Risk Index

The risk index is derived from the product of the three aforementioned indices. The values used on a predefined scale assist in identifying the level of risk and determining the necessary actions to mitigate risk in the workplace (

Table 5. Risk Index.

Risk Level	Action Required	Risk Score
Risk	Perhaps acceptable	<20
Possible risk	Attention indicated	20–70
Substantial risk	Correction needed	70–200
High risk	Immediate correction required	200–400
Very high risk	Consider discontinuing operation	>400

).

3.2. Proposed Extensions of Fine-Kinney Method

The fundamental concept behind the FK10 and FFK10 methods is the creation of symmetrical values for the probability, frequency, and severity indices. Each of these three indices is scored on a scale from 1 to 10. This approach extends the probability level from 7 to 10 values, the frequency level from 6 to 10 values, and the severity level from 6 to 10 values. Each level differs from the previous one by only a single unit, in contrast to the classical Fine-Kinney method, which exhibits asymmetry in its values—a concern that has been highlighted by various authors [6,17,19,29,31,35,36].

The fuzzy scale of Fine-Kinney for the team of aerial workers, along with the design and implementation of the FFK10 method, was coded using the fuzzy toolbox in Matlab 24b. During the design phase, probability, frequency, and severity are selected as input variables, while the risk index is defined as the output using the Mamdani inference method.

3.2.1. Proposed Extensions of Input Indexes

Both newly proposed methods utilize the same input indicators, expanded to a ten-point scale.

As a result, the indices of frequency, probability, and severity acquire, for the first time in the history of the method, a symmetric structure. More specifically, the probability index, as presented in Table 2, is reformulated into the structure shown in

Table 6. Probability Index FK10 and FFK10.

Probability Index (P)	Description of Undesirable Event
10	Unavoidable, h < 10
9	Almost assured h < 102
8	Very probable, h < 103
7	Probable, h ≈ 103
6	Probability slightly greater than 50%, 104 < h < 105
5	Probability 50%, 105 < h < 106
4	Probability slightly less than 50%, 106 < h < 107
3	Improbable, h < 107
2	Very improbable, h ≈ 107
1	Impossible, h > 107

.

For the calculation of the probability index, the following formulas are used:

$$h={\displaystyle \frac{Total person - hours}{Total number of accidents per accident category }}$$

(1)

The frequency index, as outlined in Table 3 for both new methods, is transformed accordingly and presented in

Table 7. Frequency Index FK10 and FFK10.

Frequency Index (F)	Description of Undesirable Event
10	Permanent presence of damage
9	Presence of damage every 30 s
8	Presence of damage every 1 min
7	Presence of damage every 30 min
6	Presence of damage every 1 h
5	Presence of damage every 8 h
4	Presence of damage every 1 week
3	Presence of damage every 1 month
2	Presence of damage every 1 year
1	Presence of damage every 5 years

.

For the calculation of the frequency index, the following formulas are used:

$$f={\displaystyle \frac{Number of accidents in the category under investigation}{w\times d\times s}}$$

(2)

where f represents the number of accidents occurring over three shifts. Subsequently, linear interpolation is applied to determine the frequency index F. The formula used is as follows:

$${\displaystyle \frac{f-f_1}{f_1-f_2}}={\displaystyle \frac{F-F_1}{F_1-F_2}}$$

(3)

where

f₁ is the integer accident value immediately before f.

f₂ is the integer accident value immediately after f.

F₁ and F₂ are the integer frequency indices corresponding to f₁ and f₂, respectively.

w: The number of weeks within the examined time period. Typically, workplace evaluations are conducted on an annual basis. Therefore, w = 48 in cases where the workplace closes for certain periods, such as holidays or summer breaks, and w = 52 when the workplace operates continuously throughout the entire year.

d: The number of working days within a week. The value d = 5 applies if the workplace operates on a five-day workweek, whereas the maximum value is d = 7 if the activity takes place every day of the week.

s: The number of shifts within one day. For the specific crew under study, s = 3, as the daily working hours total 8 h, resulting in three shifts per 24 h period.

The severity index, initially presented in Table 4, is adapted to a ten-level scale. This revised scale does not solely account for the number of days of absence from work but also considers whether the incident leads to lasting health effects for the workers. Thus, the severity index is reformulated as depicted in

Table 8. Severity Index FK10 and FFK10.

Severity Index (S)	Description of Undesirable Event
10	Death
9	Permanent total disability
8	Permanent serious disability
7	Permanent slight disability
6	Absence from work > 3 weeks, and return with health problems
5	Absence from work > 3 weeks, and return after full recovery
4	Absence from work > 3 days and <3 weeks, and return after full recovery
3	Absence from work < 3 days, and return after full recovery
2	Slight injury without absence from the work, and with full recovery
1	No human injury

.

3.2.2. Risk Index

The risk index, as in the classic Fine-Kinney method, is derived from the product of the three indices: frequency, probability, and severity. The difference in this case lies in the maximum value, which is no longer the asymmetrical 400 but rather the number 1000.

3.3. Implementation Steps of the Fine-Kinney 10 (FK10) Method

To implement the Fine-Kinney 10 (FK10) method, as with the classical approach, data is required for the job positions under examination.

• Step 1: Identification of recorded accidents in the workplace being evaluated.
• Step 2: Determination of the probability and frequency indices based on the expanded ten-point scale, using mathematical formulas 1, 2, and 3, as presented earlier.
• Step 3: Identification of the severity index. For each job task, the highest possible damage that occurred during the assessment period is selected.
• Step 4: Multiplication of the three indices (R = P × F × S) to compute the overall risk index. Based on the resulting value, the appropriate verbal risk description is selected, in accordance with the risk level ranges presented in

  Table 9. Risk Index FK10 and FFK10.

  Risk Index (R)	Urgency Level of Required Actions
  900–1000	Immediate action
  800–900	Action during 1 days
  700–800	Action during 3 days
  600–700	Action during 1 week
  500–600	Action during 2 weeks
  400–500	Action during 1 month
  300–400	Action during 3 months
  200–300	Action during 6 months
  100–200	Action during 1 year
  0–100	Immediate action is not necessary but event surveillance is required

  .

3.4. Implementation Steps of the Fuzzy Fine-Kinney 10 (FFK10) Method

The implementation of the Fuzzy Fine-Kinney 10 (FFK10) method is carried out using MATLAB R2025a. Within MATLAB’s Fuzzy Toolbox, the three indices—probability, frequency, and severity—are used as input variables, while the risk index serves as the output.

Between the input values and the output value, the Mamdani-type fuzzy inference system is employed, as it is suitable for human intervention and provides more interpretable, rule-based outputs (see Figure 1).

The Mamdani fuzzy inference method is among the most widely adopted approaches in fuzzy logic systems, owing to its interpretability and suitability for decision-making problems under uncertainty. It is particularly significant in the field of occupational risk assessment, where the evaluation of hazards often relies on linguistic variables and subjective expert judgments.

The primary advantage of the Mamdani method lies in its linguistic transparency, as the rules are expressed in natural language and remain easily understandable by engineers and safety managers. Furthermore, it can capture nonlinear interactions among indicators, thereby ensuring more realistic and reliable outcomes compared to classical “crisp” methods. Within the framework of the FFK10 methodology, the adoption of the Mamdani system enhances the model’s sensitivity, enables smoother transitions between risk categories, and mitigates distortions caused by rigid thresholds. As a result, it supports a more accurate, interpretable, and reliable assessment of occupational risks in complex working environments.

The next step involves the correct assignment of indicator values according to the extended numerical scale.

In fuzzy logic systems, membership functions constitute the fundamental mechanism through which linguistic variables are quantitatively represented. Among the different types of membership functions implemented in the MATLAB Fuzzy Toolbox, the triangular (trimf), Z-shaped (zmf), and S-shaped (smf) functions are particularly significant due to their simplicity, interpretability, and computational efficiency. In the present study, the triangular membership function (trimf) was adopted, with its peak corresponding to the indices of frequency, severity, probability, and the overall risk analysis index, while the neighboring integer values of the respective indices were assigned as the lower and upper bounds. For the extreme numerical values (1 and 10), the Z-shaped (zmf) and S-shaped (smf) membership functions were employed, since no adjacent values exist beyond these boundary points. This methodological approach ensures the continuity of the fuzzy scale, reduces the likelihood of distortions during the fuzzification process, and enhances the accuracy and reliability of the risk assessment procedure, particularly at the boundary conditions of the value range.

Subsequently, for the fuzzification of the probability index in Matlab, the membership functions zmf, trimf, and smf were used (

Table 10. Membership Functions of Probability.

Probability Index	Membership Funtion Type	Name of MF	Params
1	zmf	mf1	[1 2]
2	trimf	mf2	[0 1 2]
3	trimf	mf3	[1 2 3]
4	trimf	mf4	[2 3 4]
5	trimf	mf5	[3 4 5]
6	trimf	mf6	[4 5 6]
7	trimf	mf7	[5 6 7]
8	trimf	mf8	[6 7 8]
9	trimf	mf9	[7 8 9]
10	smf	mf10	[6.5 8]

and Figure 2).

For the fuzzification of the probability index in Matlab, the membership functions zmf, trimf, and smf were used (

Table 11. Membership Functions of Frequency.

Frequency Index	Membership Funtion Type	Name of MF	Params
1	zmf	mf1	[0.125 1.125]
2	trimf	mf2	[0 0.7 1.3 2]
3	trimf	mf3	[1 1.7 2.3 3]
4	trimf	mf4	[2 2.7 3.3 4]
5	trimf	mf5	[3 3.7 4.3 5]
6	trimf	mf6	[4 4.7 5.3 6]
7	trimf	mf7	[5 5.7 6.3 7]
8	trimf	mf8	[6 6.7 7.3 8]
9	trimf	mf9	[7 7.7 8.3 9]
10	smf	mf10	[6.5 9]

and Figure 3).

For the fuzzification of the severity index in Matlab, the membership functions zmf, trimf, and smf were employed (

Table 12. Membership Functions of Severity.

Severity Index	Membership Funtion Type	Name of MF	Params
1	zmf	mf1	[0 1]
2	trimf	mf2	[0 1 2]
3	trimf	mf3	[1 2 3]
4	trimf	mf4	[2 3 4]
5	trimf	mf5	[3 4 5]
6	trimf	mf6	[4 5 6]
7	trimf	mf7	[5 6 7]
8	trimf	mf8	[6 7 8]
9	trimf	mf9	[7 8 9]
10	smf	mf10	[6.5 9]

and Figure 4).

For the fuzzification of the risk index in Matlab, the membership functions zmf, trimf, and smf were utilized (

Table 13. Membership Functions of Risk.

Risk Index	Membership Funtion Type	Name of MF	Params
1	zmf	mf1	[50 150]
2	trimf	mf2	[0 100 200]
3	trimf	mf3	[100 200 300]
4	trimf	mf4	[200 300 400]
5	trimf	mf5	[300 400 500]
6	trimf	mf6	[400 500 600]
7	trimf	mf7	[500 600 700]
8	trimf	mf8	[600 700 800]
9	trimf	mf9	[700 800 900]
10	smf	mf10	[800 900]

and Figure 5).

After defining the range of values for severity, probability, frequency, and risk index, the next step involves establishing rules to derive the corresponding relationships that control the behavior of the dependent variable. These rules will be defined for both the input variables and the output variable. The RulerView functionality enables the input of values for independent variables and provides the corresponding dependent variables based on the rules and commands defined within the FFK10 model. In the development of the proposed FFK10 model, a set of fuzzy logic rules was established to describe the relationship between the input and output variables. The rules follow the IF–THEN structure and are grounded in the philosophy underlying the Fine-Kinney methodology. For instance, one representative rule can be expressed as follows: IF the probability index is 5 AND the frequency index is 2 AND the severity index is 3, THEN the risk index takes the value 100 (see Figure 6). This formulation captures the complex interactions among parameters and enables a more realistic assessment of risk. In total, 1000 rules were generated, covering all possible combinations of the variables and ensuring the consistency and completeness of the system.

4. Application

As previously mentioned, the methods are applied within an electricity distribution company in Greece. The total number of employees in the aerial maintenance team is 198. These employees work in three shifts, operating 12 months a year, 30 days a month, and 24 h a day. The product of these values provides 1,710,720 total work hours annually (calculated as 198 × 12 × 30 × 24 = 1,710,720).

The total number of workplace accidents reported for 2022 was 73. Of these, 34 accidents occurred during work hours and resulted in sick leave exceeding three days. An additional 15 accidents happened during commuting to and from the workplace.

4.1. Work Environment

The aerial maintenance team primarily operates in outdoor environments under various weather conditions to ensure the continuous and uninterrupted supply of electricity to consumers. Consequently, most accidents occurred in environments typically encountered outdoors.

These accidents have been grouped into 13 main categories, which reflect the nature of the incidents. These categories are detailed in

Table 14. Recording of Occupational Accidents in the Overhead.

Code (A)	Nature of Accident (B)	Number of Accidents (C)	Work Hours Between Accidents by Nature (D)
SH1	Fall < 2.5 m	20	85,536
SH2	Fall > 2.5 m	5	342,144
SH3	Collapse/Subsidence/Landslide	2	855,360
SH4	Hit by/against an object	2	855,360
SH5	Overexertion/Fatigue	1	17,100,720
SH6	Exposure to electric current	3	570,240
SH7	Slips on floors	6	285,120
SH8	Traffic accidents	15	114,048
SH9	Compression by objects	1	1,710,720
SH10	Natural factors	4	427,680
SH11	Animal or insect bites	2	855,360
SH12	Overexertion during pulling or pushing objects	6	285,120
SH13	Other	6	285,120

. The acronym SH stands for Safety Hazard (Column A, Table 14). The third column (C) presents the number of incidents that occurred during 2022. In Column D, the average number of hours between two workplace accidents is displayed.

To comprehend the methodology for calculating risk levels in the subsequent Tables (Table 15, Table 16 and Table 17), the formulas and reference tables provided in the previous sections are utilized. Specifically, for Table 15 and the task coded as SH1, the risk level is calculated using the probability, frequency, and severity tables from the classical Fine-Kinney method.

More precisely, the probability index was assigned a value of 1, which is interpreted as “Happens frequently.” The frequency index was given a value of 2, indicating an occurrence rate of more than one incident per month (“Monthly occurrence”). For the severity index, a value of 15 was selected, corresponding to the verbal description “Major injury, lost workdays.” The final column of Table 15 displays the verbal output derived from the classical Fine-Kinney method (Table 15).

4.2. Application of the Classical Fine-Kinney Method

Table 15. Risk Analysis Using the Fine-Kinney Method.

Code	Probability	Frequency	Severity	Risk	Verbal Description
SH1	1	2	15	30	Attention is recommended
SH2	0.5	1	40	20	Attention is recommended
SH3	0.5	1	7	3.5	Acceptable risk, monitoring required
SH4	0.5	1	3	1.5	Acceptable risk, monitoring required
SH5	0.5	1	7	3.5	Acceptable risk, monitoring required
SH6	0.5	1	15	7.5	Acceptable risk, monitoring required
SH7	0.5	1	15	7.5	Acceptable risk, monitoring required
SH8	1	2	15	30	Attention is recommended
SH9	0.5	1	15	7.5	Acceptable risk, monitoring required
SH10	0.5	1	3	1.5	Acceptable risk, monitoring required
SH11	0.5	1	3	1.5	Acceptable risk, monitoring required
SH12	0.5	1	7	3.5	Acceptable risk, monitoring required
SH13	0.5	1	15	7.5	Acceptable risk, monitoring required

Table 15. Risk Analysis Using the Fine-Kinney Method.

Code	Probability	Frequency	Severity	Risk	Verbal Description
SH1	1	2	15	30	Attention is recommended
SH2	0.5	1	40	20	Attention is recommended
SH3	0.5	1	7	3.5	Acceptable risk, monitoring required
SH4	0.5	1	3	1.5	Acceptable risk, monitoring required
SH5	0.5	1	7	3.5	Acceptable risk, monitoring required
SH6	0.5	1	15	7.5	Acceptable risk, monitoring required
SH7	0.5	1	15	7.5	Acceptable risk, monitoring required
SH8	1	2	15	30	Attention is recommended
SH9	0.5	1	15	7.5	Acceptable risk, monitoring required
SH10	0.5	1	3	1.5	Acceptable risk, monitoring required
SH11	0.5	1	3	1.5	Acceptable risk, monitoring required
SH12	0.5	1	7	3.5	Acceptable risk, monitoring required
SH13	0.5	1	15	7.5	Acceptable risk, monitoring required

4.3. Application of Proposed Approach FK10

For the determination of the probability, frequency, and severity indices in the new approximate Fine-Kinney 10 (FK10) method, where the index values are uniformly distributed, the values presented in Table 18 were used. Specifically, for the calculation of the probability index, the values shown in Table 6 were employed. For instance, regarding SH1, since an accident occurs every 85,536 h according to the values in Table 6, the probability index is assigned the value 6 (10⁴ < h < 10⁵). In the same manner, the remaining probability indices in column B of Table 18 are completed.

To derive the frequency values in column C of Table 18, the criterion of linear interpolation (Equation (3)) was used to assign the most appropriate frequency value. Subsequently, the result was rounded to the second decimal place, as further decimal places do not significantly affect the risk index values. Specifically, Equation (2) was utilized, setting w = 52, since the crew operates continuously throughout the year; d = 7, as operations occur seven days per week; and s = 3, since there are three shifts per day. For the accident type SH1, the frequency value is calculated as f = 20/(52 × 7 × 3) = 0.018315 (column C, Table 16). Then, column D of Table 16 is completed using the reciprocal 1/f, specifically for SH1 yielding 1/0.018315 = 54.6. This value of 54.6 indicates the number of shifts between two accidents.

In Table 8, the frequency index value F₁ = 4 corresponds to one accident occurring once per week, that is, 7 × 3 = 21 shifts. Accordingly, f₁ = 1/21 = 0.047619 is calculated. Similarly, the frequency index F₂ = 3 corresponds to one accident occurring once per month, i.e., 30 × 3 = 90 shifts, with f₂ = 1/90 = 0.011111. Substituting these values into Equation (3) yields:

$${\displaystyle \frac{f-f_1}{f_1-f_2}}={\displaystyle \frac{F-F_1}{F_1-F_2}}\underset{0}{\Rightarrow }{\displaystyle \frac{0.018315-0.047619}{0.047619-0.011111}}={\displaystyle \frac{F-4}{4-3}}\underset{0}{\Rightarrow }F=3.2$$

The remaining entries in the frequency column (column C) of Table 16 are completed in the same manner.

Table 16. Auxiliary table for calculating shifts.

Code (A)	Nature of Accident (B)	Frequency Index (F) (C)	Number of Shifts Per Accident (D)
SH1	20	0.018315	54.6
SH2	5	0.004579	218.4
SH3	2	0.001832	546
SH4	2	0.001832	546
SH5	1	0.000916	1092
SH6	3	0.002747	364
SH7	6	0.005495	182
SH8	15	0.013736	72.8
SH9	1	0.000916	1092
SH10	4	0.003663	273
SH11	2	0.001832	546
SH12	6	0.005495	182
SH13	6	0.005495	182

Table 16. Auxiliary table for calculating shifts.

Code (A)	Nature of Accident (B)	Frequency Index (F) (C)	Number of Shifts Per Accident (D)
SH1	20	0.018315	54.6
SH2	5	0.004579	218.4
SH3	2	0.001832	546
SH4	2	0.001832	546
SH5	1	0.000916	1092
SH6	3	0.002747	364
SH7	6	0.005495	182
SH8	15	0.013736	72.8
SH9	1	0.000916	1092
SH10	4	0.003663	273
SH11	2	0.001832	546
SH12	6	0.005495	182
SH13	6	0.005495	182

For the determination of the severity index (column C, Table 17), the description of the most severe adverse event that has occurred for each specific type of accident provides the corresponding severity index value. Specifically, for SH1 (column A), the average total number of sick leave days was 66, and upon the worker’s return to work, the individual suffered permanent disability. Therefore, the severity index was assigned the value of 8. Furthermore, for the severity index, values greater than 6 are associated with physical injuries or impairments that persist upon the employee’s return to work and are of a permanent nature. For this reason, in the second column (column B, Table 17), alongside the number of recovery days, there is an additional indication of physical injury (Table 17).

Table 17. Auxiliary table for determining severity based on accident outcomes.

Code (A)	Total Sick Leave Days and Health Status (B)	Severity Index (C)
SH1	66 + physical injury	8
SH2	80 + physical injury	8
SH3	0	3
SH4	18	4
SH5	10	4
SH6	52 + physical injury	8
SH7	27	5
SH8	44 + physical injury	8
SH9	30	5
SH10	30	6
SH11	25	5
SH12	22	5
SH13	11	4

Table 17. Auxiliary table for determining severity based on accident outcomes.

Code (A)	Total Sick Leave Days and Health Status (B)	Severity Index (C)
SH1	66 + physical injury	8
SH2	80 + physical injury	8
SH3	0	3
SH4	18	4
SH5	10	4
SH6	52 + physical injury	8
SH7	27	5
SH8	44 + physical injury	8
SH9	30	5
SH10	30	6
SH11	25	5
SH12	22	5
SH13	11	4

Table 18 presents the probability (column B), frequency (column C), and severity indices (column D) for the FK10 model. Column E displays the risk number, calculated as the product of the three indices, while column F provides the corresponding verbal risk assessment.

Table 18. Risk analysis using the FK10 method.

Code (A)	Probability (B)	Frequency (C)	Severity (D)	Risk (E)	Recommendation (F)
SH1	6	3.2	8	153.6	Measures to be taken within 1 year
SH2	6	2.36	8	113.28	Measures to be taken within 1 year
SH3	5	2.09	3	31.35	Immediate measures not required
SH4	5	2.09	4	41.8	Immediate measures not required
SH5	4	2	4	32	Immediate measures not required
SH6	5	2.18	8	87.2	Immediate measures not required
SH7	5	2.27	5	56.75	Immediate measures not required
SH8	6	3.07	8	147.36	Measures to be taken within 1 year
SH9	4	2	5	40	Immediate measures not required
SH10	6	2.27	6	81.72	Immediate measures not required
SH11	5	2.07	5	51.75	Immediate measures not required
SH12	5	2.45	5	61.25	Immediate measures not required
SH13	5	2.45	4	49	Immediate measures not required

Table 18. Risk analysis using the FK10 method.

Code (A)	Probability (B)	Frequency (C)	Severity (D)	Risk (E)	Recommendation (F)
SH1	6	3.2	8	153.6	Measures to be taken within 1 year
SH2	6	2.36	8	113.28	Measures to be taken within 1 year
SH3	5	2.09	3	31.35	Immediate measures not required
SH4	5	2.09	4	41.8	Immediate measures not required
SH5	4	2	4	32	Immediate measures not required
SH6	5	2.18	8	87.2	Immediate measures not required
SH7	5	2.27	5	56.75	Immediate measures not required
SH8	6	3.07	8	147.36	Measures to be taken within 1 year
SH9	4	2	5	40	Immediate measures not required
SH10	6	2.27	6	81.72	Immediate measures not required
SH11	5	2.07	5	51.75	Immediate measures not required
SH12	5	2.45	5	61.25	Immediate measures not required
SH13	5	2.45	4	49	Immediate measures not required

4.4. Application of Proposed Fuzzy Approach FFK10

Similarly, for the determination of the probability, frequency, and severity indices in the FFK10 model, the same values are used; however, a fuzzy approach is applied, which is computed through Matlab as explained in the previous section. The column for risk presents the new risk value, followed by the corresponding verbal explanation for this index (

Table 19. Risk analysis using the FFK10 method.

Code	Probability	Frequency	Severity	Risk	Recommendation
SH1	6	3.2	8	228	Measures to be taken within 6 months
SH2	6	2.36	8	167	Measures to be taken within 1 year
SH3	5	2.09	3	50.8	Immediate measures not required, but event monitoring advised
SH4	5	2.09	4	56.6	Immediate measures not required, but event monitoring advised
SH5	4	2	4	45	Immediate measures not required, but event monitoring advised
SH6	5	2.18	8	122	Measures to be taken within 1 year
SH7	5	2.27	5	103	Measures to be taken within 1 year
SH8	6	3.07	8	213	Measures to be taken within 6 months
SH9	4	2	5	49	Immediate measures not required, but event monitoring advised
SH10	6	2.27	6	105	Measures to be taken within 1 year
SH11	5	2.09	5	101	Measures to be taken within 1 year
SH12	5	2.45	5	113	Measures to be taken within 1 year
SH13	5	2.45	4	85.6	Immediate measures not required, but event monitoring advised

).

5. Discussion and Results Analysis

The analysis and modeling of accidents face obstacles beyond methodological limitations. One significant barrier is the insufficient access researchers have to comprehensive databases [9,44,45,46], which could accelerate the understanding and modeling of various risk mitigation techniques. Consequently, many variations of models—whether based on Fine-Kinney or other techniques—are applied to workplaces or accident cases with limited data availability.

In recent years, various modifications of the Fine-Kinney model have been proposed in the literature. The majority of these aim either to improve the methodology or to compare it with alternative approaches [6,14,19,29,31,35]. The present study modified the indices of probability, frequency, and severity by increasing their precision and sensitivity, scaling them uniformly from 1 to 10. Similarly, the risk index was expanded from five parameter levels to ten, thereby doubling the range of numerical and verbal categories and shortening the time intervals considered. This adjustment enhanced both the sensitivity and accuracy of the results.

The analysis based on the classical Fine-Kinney methodology, as presented in Table 15, provides a satisfactory overview of accident risks in the tower maintenance workshop. For example, fall incidents under 2.5 m (SH1) yield a risk score of 30, indicating an immediate need for control measures. This reflects the high frequency and relative severity of such incidents according to the classification in Table 5. Conversely, incidents related to overexertion or fatigue (SH5) yield a lower risk score of 3.5, categorized as an acceptable risk requiring monitoring. However, the method exhibits limitations, notably its reliance on clear and accurate input data, and the fact that several indices have values below one, which diminishes and dilutes the product. Furthermore, the lack of differentiation among low risk scores may undermine risk perception for certain events. Overall, the application of the Fine-Kinney method, as demonstrated in Table 15, provides a quantitative basis for risk assessment in the tower maintenance workshop.

In contrast, the FK10 method differs from the traditional Fine-Kinney approach through its symmetric distribution of index values and more detailed risk analysis. Specifically, Table 18 shows that fall incidents under 2.5 m (SH1) receive a risk score of 153.6, signifying the necessity for action within one year. This difference compared to the classical Fine-Kinney method allows for a more balanced risk evaluation based on the parameters considered. Similarly, traffic accidents (SH8) record a risk score of 147.36, reinforcing the need for immediate intervention. The FK10 method offers greater precision in risk estimation by employing symmetrical index values and applying linear interpolation to calculate frequency indices. This approach reduces subjectivity and provides a more quantitative basis for decision-making. Nevertheless, the method retains some limitations, such as the requirement for accurate input data and dependence on the precision of linear interpolation. Nonetheless, cases like SH6 (87.2) and SH10 (81.72) highlight the importance of medium-term measures, as these values approach 100, marking a change in verbal risk categorization. FK10 thus delivers a more comprehensive and balanced risk evaluation framework, enhancing decision-making and improving risk categorization across different action levels. By adopting this method, organizations can achieve more efficient resource allocation and strengthen workplace safety.

The Fuzzy Fine Kinney 10 Method (FFK10), as applied in Table 19, introduces an innovative framework for risk assessment by incorporating fuzzy logic to manage uncertainties. The indices of probability, frequency, and severity are derived from Table 5, Table 7, Table 9, Table 15 and Table 16, while the risk index is calculated using MATLAB’s fuzzy toolbox, as illustrated in Figure 2, Figure 3, Figure 4 and Figure 5.

The results presented in Table 19 reveal a more nuanced categorization of risk compared to previous methods. For instance, fall incidents below 2.5 m (SH1) receive a score of 228, indicating the need for intervention within six months. This score, higher than that computed by the FK10 method, reflects the enhanced sensitivity of FFK10 to uncertainty and small data fluctuations.

FFK10 achieves greater accuracy through the fuzzification of input values and the use of fuzzy membership functions such as zmf, trimf, and smf to represent uncertainty. This approach provides a more realistic and dynamic picture of risk by accounting for subjectivity in expert assessments. Specifically, traffic accidents (SH8) register a score of 213, emphasizing the need for faster interventions within six months, compared to the one-year deadline indicated by the FK10 method.

The overall results of all three methods, as presented in

Table 20. Summary results table for Fine-Kinney, FK10, and FFK10 methods.

Code	Classical FK	FK10	FFK10
SH1	Implementation of control measures	Measures to be taken within 1 year	Measures to be taken within 6 months
SH2	Implementation of control measures	Measures to be taken within 1 year	Measures to be taken within 1 year
SH3	Acceptable risk, monitoring	Immediate measures not required	Immediate measures not required, but event monitoring advised
SH4	Acceptable risk, monitoring	Immediate measures not required	Immediate measures not required, but event monitoring advised
SH5	Acceptable risk, monitoring	Immediate measures not required	Immediate measures not required, but event monitoring advised
SH6	Acceptable risk, monitoring	Immediate measures not required	Measures to be taken within 1 year
SH7	Acceptable risk, monitoring	Immediate measures not required	Measures to be taken within 1 year
SH8	Implementation of control measures	Measures to be taken within 1 year	Measures to be taken within 6 months
SH9	Acceptable risk, monitoring	Immediate measures not required	Immediate measures not required, but event monitoring advised
SH10	Acceptable risk, monitoring	Immediate measures not required	Measures to be taken within 1 year
SH11	Acceptable risk, monitoring	Immediate measures not required	Measures to be taken within 1 year
SH12	Acceptable risk, monitoring	Immediate measures not required	Measures to be taken within 1 year
SH13	Acceptable risk, monitoring	Immediate measures not required	Immediate measures not required, but event monitoring advised

, highlight significant differences and improvements offered by the advanced FK10 and FFK10 methods compared to the traditional Fine-Kinney approach. Each method has distinct advantages and limitations, which render them appropriate for different risk environments and assessment needs. (Cells highlighted in yellow indicate cases where the risk index increases by one level, while those in orange correspond to an increase of two levels compared to the classical Fine-Kinney method.)

The verbal outcomes of FFK10 in Table 19 demonstrate greater sensitivity to minor differences among indices and provide more realistic risk estimations. This method is ideal for environments with a high degree of complexity and uncertainty.

When comparing the methods under the perspective of the nature of the accident, certain incidents, such as falls from less than 2.5 m (SH1), show differing results across all three methods. Specifically, in the traditional Fine-Kinney method, the risk index for SH1 is 30, which corresponds to a “possible risk” level, indicating that caution is advised. In contrast, the FK10 method assigns a value of 153.64, which prescribes the implementation of safety measures within one year, thereby providing a clearer indication of the required action. Notably, in the FFK10 method, the risk score increases further to 228 due to the sensitivity of the fuzzy system and the high severity index. This result verbally translates to the recommendation of “taking measures within six months” to prevent the accident. Similar trends are observed for SH8 (traffic accidents).

Similar conclusions apply for SH2 (falls from heights greater than 2.5 m). In the Fine-Kinney method, the risk index is exactly 20, the threshold value marking a task as having a potential risk. However, FK10 clearly indicates that measures must be taken within one year, as the risk index significantly exceeds 100 (113.28). In the FFK10 method, the risk value rises to 167, which also corresponds to the recommendation to “take measures within one year.” This demonstrates the dynamic nature of the method and the sensitivity introduced by fuzzy logic, where a high severity index elevates the overall risk score.

An interesting finding emerges in the case of electrical accident risks (SH6). The Fine-Kinney method assigns a very low risk index (7.5), interpreted as “acceptable risk.” Likewise, FK10 does not indicate the need for intervention since the risk value approaches 100, the threshold for changing the verbal risk category. Conversely, despite the low accident frequency associated with electrical hazards, the FFK10 method, via its fuzzy system, recognizes the high severity and even higher probability, resulting in a risk score of 122. This corresponds to the recommendation of “taking measures within one year.”

A similar pattern is seen for SH7, SH10, SH11, and SH12. For these accident types, the first two methods do not recommend any actions, whereas the FFK10 suggests that measures should be taken within one year. It is worth noting that SH7 and SH11 are marginally above the 100 threshold.

A critical factor influencing the differences among the methods is the uneven scaling of parameters in the Fine-Kinney method. This asymmetry affects the method’s ability to distinguish between similar risks and reduces its overall sensitivity. While this approach may be useful for general risk estimation, it struggles to identify subtle differences or to provide a clear prioritization hierarchy. The imbalance of input values for probability, frequency, and severity, as well as the output risk values, generates inequalities in the overall evaluation. Furthermore, the risk results often do not adequately reflect the severity or frequency of the hazard, complicating decision-making for effective risk management.

In contrast, the FK10 and FFK10 methods introduce symmetrical and uniform scales for calculating the risk index, thereby enhancing accuracy and flexibility in risk assessment. The maximum risk index value is set at 1000, offering a broader range and finer granularity for distinguishing risks. This contrasts with the Fine-Kinney method, whose practical maximum is approximately 400 (since reaching a value of 10,000 would require a frequent and likely total catastrophe, such as continuous and repetitive natural disasters, which is practically impossible). Only in such extreme cases could mass repetitive fatalities occur. Therefore, FK10 and FFK10 are more sensitive to differentiating between similar risk levels, enabling more precise categorization and prioritization.

This sensitivity is particularly pronounced in the FFK10 method, which leverages fuzzy logic to address subjectivity and uncertainty, making it well suited for complex environments.

The divergence between FK10 and FFK10 results can be attributed to the intrinsic characteristics of fuzzy set modeling and the Mamdani inference process. In FK10, each index (probability, frequency, severity) is assigned a crisp numerical value on a symmetrical 1–10 scale, and the overall risk index is derived by direct multiplication. This approach, although more refined than the classical Fine-Kinney method, still produces rigid thresholds and does not account for the uncertainty or subjectivity in expert judgments.

In contrast, FFK10 incorporates fuzzy membership functions (trimf, zmf, smf), which introduce overlapping sets and smooth transitions between adjacent levels. The positioning of the triangular functions and the “shoulder” effects of Z- and S-shaped functions create areas of partial membership, meaning that a single input can simultaneously activate multiple rules. Consequently, the aggregated fuzzy output after Mamdani inference and defuzzification tends to yield higher or shifted values compared to the crisp FK10 model. This is not a methodological bias but rather a reflection of the fuzzy system’s increased sensitivity to uncertainty and its capacity to capture subtle variations in expert evaluations that crisp scoring schemes overlook.

6. Conclusions

Despite its long-standing use, the Fine-Kinney method exhibits limitations regarding the sensitivity and accuracy of risk assessment. The traditional indices of probability, frequency, and severity employed for the evaluation of occupational hazards provide an initial indication of the level of risk in workplace environments. However, the asymmetry in the values of these indices and the lack of a dynamic approach have resulted in the method’s limited applicability in complex settings.

To address these limitations, the FK10 and FFK10 methods were developed. These methods introduce symmetrical scales for the three indices, extending the values from 1 to 10. Moreover, the FFK10 method incorporates fuzzy logic, enhancing the capability to manage subjectivity and uncertainty. This does not, of course, entail the complete elimination of subjectivity; however, it does result in its substantial reduction. Consequently, the findings are considerably more reliable when compared to those produced by the classical method. These modifications render the methods more sensitive in differentiating risks, allowing for more precise categorization and prioritization.

The transition to a 10-point scale also impacts the calculation of the risk index, which now more clearly reflects the dynamics of the parameters involved. In contrast, FK10 employs the product of indices uniformly ranging from 1 to 10, providing a more realistic and comprehensive representation of risk. This enhancement improves risk managers’ ability to identify, categorize, and prioritize hazards with greater accuracy and flexibility, while also facilitating improved evaluation of control measures. In this way, the risk is clearly mitigated that the multiplication of values smaller than unity will drive the product towards excessively low risk estimates, thereby implying an unduly diminished level of hazard.

Comparative analysis of the results demonstrated that the advanced FK10 and FFK10 methods offer significant advantages over the classical Fine-Kinney approach. For instance, in the FFK10 method, the verbal descriptions of outcomes are more specific, enabling the implementation of more targeted measures to mitigate risk. These adjustments prove particularly valuable in environments characterized by complex and dynamic hazards, such as work involving aerial operations, where uncertainty and extreme conditions are routine.

The application of FK10 and FFK10 in the study of occupational hazards among aerial workers underscored their utility. The results indicated that the new methods are more sensitive in data analysis and provide more comprehensive assessments of risk levels. Particularly for hazards with high severity and frequency, such as falls from height or exposure to electrical current, these methods offer clearer guidance on implementing safety measures.

Overall, the FK10 and FFK10 methods contribute significantly to the advancement of risk management. By incorporating fuzzy logic and refining evaluation parameters, they better adapt to the requirements of modern occupational environments.

7. Future Research

Future research could focus on the evaluation of the FFK10 method in high-risk occupational environments with increased accident frequency. In such work settings, FFK10 values are expected to exhibit significant differentiation and higher measurements, clearly demonstrating its superiority over other methods. Investigating the method’s performance under more adverse conditions may enhance its overall acceptance, highlighting its utility across a broader range of applications. The outcomes of the proposed methodology could be further strengthened by applying it in diverse occupational settings beyond the energy sector. Such an extension would significantly contribute to enhancing the reliability of the approach and to establishing the FFK10 model as a widely recognized tool for risk assessment. Additionally, the development of a user-friendly application (app) is recommended to enable safety professionals to obtain results quickly and easily. Such a tool would bridge the gap between FFK10 and traditional methods, which provide immediate results, thereby improving the accessibility and usability of the new method. Finally, the integration of FFK10 into risk analysis platforms, such as PHAWorks, in conjunction with other assessment techniques like LOPA, HAZOP, and FMEA, is proposed. Through this interoperability, the method could enhance the accuracy and detail of outcomes while providing valuable insights for risk management. This combination of tools would further strengthen the contribution of the FFK10 method to decision-making processes and risk mitigation.