A Novel Risk Assessment Approach for Open-Cast Coal Mines Using Hybrid MCDM Models with Interval Type-2 Fuzzy Sets: A Case Study in Türkiye

Abstract

Mining is a high-risk industry where occupational accidents are common due to its complex nature. Therefore, providing a more holistic and dynamic risk assessment framework is essential to identify and minimize the potential risks and enhance safety measures. Unfortunately, traditional risk assessment methods have limitations and shortcomings, such as uncertainty, differences in experience backgrounds, and insufficiency to articulate the opinions of experts. In this paper, a novel risk assessment method precisely for such cases in the mining sector is proposed, applied, and compared with traditional methods. The objective of this study is to determine the risk scores of Turkish Coal Enterprises, based on non-fatal occupational accidents, which operates eight large-scale open-cast coal mine enterprises in Türkiye. The causes of the accidents were categorized into 25 sub-criteria under 6 main criteria. The risk scores for these criteria were computed using the Pythagorean fuzzy Analytical Hierarchy Process (PFAHP) method. The first shift (8–16 h) (0.6341) for the shift category is ranked highest out of the 25 sub-risk factors, followed by maintenance personnel (0.5633) for the occupation category; the open-cast mining area (0.5524) for the area category, the 45–57 age range (0.5279) for employee age category, and the mining machine (0.4247) for the reason category, respectively. The methodologies proposed in this study not only identify the most important risk factors in enterprises, but also provide a mechanism for risk-based rankings of enterprises by their calculated risk scores. The enterprises were risk-based ranked with the fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method and Paksoy approach based on interval type-2 fuzzy sets (IT2FSs). The findings indicate that the first three risk score rankings of enterprises are the same for both approaches. To examine the consistency of the applied methods, sensitivity analyses were performed. The results of the study also indicate that the proposed approaches are recommended for effective use in the mining sector due to their ease of application compared to other methods and their dynamic nature in the risk assessment process.

1. Introduction

In today’s world, coal continues to be a pivotal, indispensable, reliable, and non-renewable energy source in the generation of global electricity [1,2,3,4]. It is used as fuel to generate electric power and in the iron and steel industry. Additionally, it also has a myriad of other uses, such as in medicine, the production of carbon fibers and foams, cement production, synthetic petroleum-based fuels, tars, and home and commercial heating. The global increase in coal production is due to the high demand for low-cost energy. The World Energy Council (WEC) reports that the world’s proven and exploitable coal reserve is 891 billion tons. At current production rates, this reserve is expected to last for 115 years. Additionally, it is anticipated that renewable energy will overtake fossil fuels as the world’s primary energy source in the near future in many countries [4,5,6]. A total of 87% of the total energy requirement of the world is provided by fossil fuels, such as natural gas, fuel oil, and coal, while the rest comes from other sources, such as hydroelectric and nuclear power plants [7]. According to the last Energy Institute Statistical Review of World Energy records, the ratio of coal in the production of electricity was 35.51% in 2023 [6,8]. It is predicted that the nature of coal as the fuel used at the highest rate in electricity production will not change until 2025, and that by 2030, it will be on a par with oil, natural gas, and renewable energy sources (solar, offshore wind, onshore wind, and hydroelectric power). With the rapid growth of electricity production, renewable energy sources, including solar, wind, and hydroelectric power, are predicted to be the fastest growing major energy source by 2050 [9,10,11].

Coal is extracted by either surface mining or underground mining methods. In Türkiye, all hard coal is extracted only from the Zonguldak Basin, and lignite basins are spread over the Middle Anatolia and Aegean Regions. The coal mining industry is characterized by a high degree of labor intensity, which in turn gives rise to a high incidence of fatal and non-fatal occupational accidents. Furthermore, the industry is replete with a plethora of hazards and associated risks. The hazards and hazard potential inherent in a mine may trigger occupational accidents unless strong measures are taken to prevent them. Such hazards may have undesirable effects on employees in the form of injury, disability, or fatality, as well as on mining enterprises due to downtimes, equipment breakdowns, and interruptions in operations [12,13].

The human factors approach was used to gain insight into the causes of accidents and can be applied to mining safety [14]. The Human Factors Analysis and Classification System (HFACS) defines failure under four levels as in stated in Figure 1 (Unsafe Acts, Preconditions for Unsafe Acts, and Unsafe Supervision and Organizational Influences). This Reason’s “Swiss cheese” model of accident causation had a profound impact on the prevailing views of accident causation. Consequently, it is necessary to identify the specific system failures or “holes” that may contribute to accidents so that they can be detected and corrected during accident investigations, or preferably, before an accident occurs. It is possible for latent failures/conditions to manifest during the operation of a system, which can subsequently trigger errors by affecting the conditions. These types of failures/conditions can give rise to active failures, which occur as a result of interaction with a system that acts in an insecure manner. In contrast to active failures, it is possible to detect them in advance and eliminate them or reduce their effects [15,16].

Risk assessment is just one of many stages of the risk management process, and it starts with hazard identification [25,26]. According to current literature knowledge, risk is defined as the likelihood of something happening that will have negative impacts, such as injuries, disabilities, and fatalities on the health or safety of miners [27]. It is reliable and easy to demonstrate the potential risks by evaluating historical accident data. This helps estimate the characteristics of risk parameters in risk assessments, and the hazards inherent in mining operations can be easily identified by an expert’s evaluation of historical injury data on occupational accidents [28]. To assess risks based on accidents that are resultant from individual, occupational, and locational aspects, evaluations should be made by considering all factors that affect occupational accidents [29]. If the risk scores of areas in which occupational accidents occurred, shifts in which occupational accidents occurred, occupational accident reasons, affected occupational groups, affected part of the body, and workers’ ages affected by the occupational accidents are calculated, various hazards can be easily determined and workers’ risk of exposure to occupational accidents and catching occupational diseases can be easily controlled by permanent supervisors and occupational health and safety (OHS) experts.

Traditional probabilistic risk analysis techniques often rely on the availability and accuracy of previous data, making them ineffective when data are unavailable. Recently, there was a growing interest in applying risk assessment techniques in fuzzy environments to provide accurate solutions even when data are approximate or uncertain. When the latest state of the topic in the literature is compiled, in the risk assessment process, the traditional AHP method is insufficient for reflecting the human thinking style in real life because it uses a fixed value to articulate the decision-maker’s opinion in the pair-wise comparisons [30]. In the area of decision-making, decision-makers usually find that it is more reliable to make interval judgments rather than fixed-value judgments. Therefore, the AHP method is criticized for its inability to adequately handle the inherent uncertainty [31]. To be able to overcome all these uncertainties, Fuzzy Multi-Criteria Decision-Making (FMCDM) techniques were developed. The linguistic terms employed in FMCDM techniques are converted to numerical values by using fuzzy sets, which serve to eliminate ambiguities and inconsistencies commonly encountered in classical risk assessment processes, such as those observed in this study. This, in turn, affords decision-makers greater freedom to express their opinions in a realistic manner. Due to these deficiencies of literature and to overcome this uncertainty, innovative combinations of hybrid decision risk assessment methods with different FMCDM techniques using IT2FSs are proposed in this study.

The rest of this paper is organized as follows: In Section 2, a detailed literature review about the subject is presented. In Section 3, Pythagorean fuzzy sets, hybrid Pythagorean fuzzy AHP, fuzzy TOPSIS, and the Paksoy [32] approach using IT2FSs methods are illustrated and the information given about the Turkish Coal Enterprises (TCE) enterprises for the relevant period of occupational accident records, the proposed risk-based classification hierarchy, the detailed data information, and risk estimation studies are summarized. In Section 4, determination of the risk weights of the criteria is achieved by using the Pythagorean fuzzy AHP and coal mines were risk-based ranked by using the fuzzy TOPSIS method and Paksoy approach by using IT2FSs. Obtained final risk scores and comparisons of the two methods are given in this section. Sensitivity analyses and the main limitations of the existing study are conducted in Section 5. Finally, conclusions, recommendations for future application perspectives, and solutions are discussed in the last section of the paper.

2. Literature Review

In general, when the literature is examined, it is found that there were several studies about risk assessment in different sectors up to now. Some of these are studies conducted in the mining sector using the Fault Tree Analysis (FTA) technique to overcome the risk management process, the prediction of the risk of potential coal and gas outburst in underground mining, in assessing the condition of mining equipment, and roof fall accidents in coal mines by different researchers [33,34,35,36,37,38,39,40,41,42]. Researchers also used the Failure Mode and Effects Analysis (FMEA) technique to investigate different mining problems, such as minimizing the risks to acceptable levels [43,44,45,46]. In addition, in the mining sector, Hazard and Operability Studies (HAZOP) techniques were also used by different researchers [47,48].

In the construction sector, Aslan [49] used the Fine–Kinney technique; Lee and Kim [50], Singha and Debasis [51], Ardeshir et al. [52], and Uchoa et al. [53] used the FMEA technique; and Liu and Zhang [54] and Joubert et al. [55] used the HAZOP technique, and Rusli et al. [56] used the FTA technique in their research studies.

In energy sector, Ateş [57], and Efe and Efe [58] used the Fine–Kinney technique; Ghasemi et al. [59] and Keyghobadi et al. [60] used the FMEA technique; and Melani et al. [61], Choi and Byeon [62], Pandey et al. [63], and Suryadi et al. [64] used the HAZOP technique in different risk management processes.

FMCDM techniques are also used in risk management process research studies aimed at evaluating risk factors in the mining industry up to now. Mahdevari [12] determined the most risk factors for coal mines producing with the underground production method in Kerman, Iran, with a model they created. In this study, the hazards were investigated and the most significant risks with the greatest negative impact were identified based on eight main criteria, such as electrical, personal, environmental, geo-mechanical, geo-chemical, mechanical, chemical, social, cultural, and managerial risks using the fuzzy TOPSIS method. Nezarat et al. [25] used the fuzzy AHP method to investigate the geological risks of the Golab tunnel located 120 km northwest of Iran. According to their risk estimation-based hierarchy, the riskiest criterion scores are computed for squeezing and face stability. In addition to these results, gas emissions and clogging of clay criteria have the lowest risk score. In another study, Yılmaz and Alp [65] studied to determine the riskiest sectors by evaluating the factors that cause work accidents. They applied the fuzzy TOPSIS method with the survey studies that applied to the decision-makers with high experience working in five different sectors. They stated that the riskiest sectors are the construction sector and the coal mining sector in the model they created with seven main criteria, which they determined as the inadequacy of preventive OHS services, the inadequacy of inspection, inadequacy of labor inspection, inadequacy of training, the inadequacy of risk assessment, insufficiency of maintenance, and inadequacy of employees. Gul et al. [66] consulted decision-makers to assess the hazards of underground mining and proposed a new risk assessment methodology by conducting a case study in a copper and zinc mine, which they see as a gap in the literature. They pointed out that their study, in which they preferred Pythagorean fuzzy Vise Kriterijumsa Optimizacija I Kompromisno Resenje (PFVIKOR) as a method, is a study that was not conducted before in underground metal mining in the literature, and they also evaluated the model with sensitivity analysis.

Furthermore, upon examination of the literature, it is evident that various studies were conducted on the risk management process, utilizing comparable MCDM techniques in other sectors. Chen and Wu [67] proposed a revised failure mode and effect analysis approach to selecting new suppliers. They applied the fuzzy AHP method to prioritize and evaluate supplier selection criteria and sub-criteria. Gul and Ak [68] proposed a comparative methodology for quantifying risk ratings in OHS risk assessment. Researchers used linguistic terms and Pythagorean fuzzy sets, which provide greater independence in their evaluations. The fuzzy AHP-fuzzy VIKOR-integrated method in quantifying risk ratings is also provided. Bakıoglu and Atahan [69] prioritized risks in self-driving vehicles by using AHP-integrated TOPSIS and VIKOR methods with Pythagorean fuzzy sets. Çolak and Kaya [70] suggested a MCDM methodology based on these methods to evaluate renewable energy alternatives for Turkey. The interval type-2 fuzzy AHP method is applied to determine the weights of decision criteria, and the hesitant fuzzy TOPSIS method is applied to prioritize renewable energy alternatives. Norouzi Masir et al. [71] aim to assess the risk of flyrock in opencast mines in order to calculate the risk score and minimize the risk of flyrock. They combined the decision-making trial and evaluation laboratory (DEMATEL) method and the fuzzy analytic network process (FANP) technique. Maksimović et al. [72] described an attempt to select the most suitable transport system at the open pit mines from the safety and quality point of view. For that purpose, the Evaluation Based on Distance from Average Solution (EDAS) method was used. Wang and Zhang [73] present a comprehensive quantitative approach for managing safety in coal mines by using fuzzy AHP. A multi-criteria decision-making model for managing safety in coal mines based on fuzzy set is constructed, which includes 17 factors and was an assessment. Wang et al. [74] estimate and rank all of these factors to develop a management model and guide the safety managers in the mining process by using the fuzzy AHP. Li et al. [75] conducted a gas explosion risk assessment in Babao coal mine in China. They proposed evaluating the risk of gas explosion in underground coal mines using the Bayesian network and fuzzy AHP.

3. Methodologies

In this part of the study, Pythagorean fuzzy sets and IT2FSs properties are presented. Then, Pythagorean fuzzy AHP, fuzzy TOPSIS methods, and Paksoy approach steps are given, respectively. The set of all notations used throughout this research article is also summarized in

Table 1. Set of the notations used through this research article.

Notation	Description of Notation	Notation	Description of Notation
$\mathrm{X}$	a fixed set	${\tau }_{ik}$	the determinacy value
$\tilde{\mathrm{P}}$	a Pythagorean fuzzy set	$tik$	the weights matrix before normalization
${\mathsf{\mu }}_{\tilde{\mathrm{P}}}\left(\mathrm{x}\right)$	the degree of membership	$w_i$	the normalized priority weights
${\mathsf{\nu }}_{\tilde{\mathrm{P}}}\left(\mathrm{x}\right)$	the degree of non-membership	$\mathrm{K}$	decision-makers for fuzzy TOPSIS
${\pi }_{\tilde{P}}\left(x\right)$	the degree of indeterminacy	$i$	alternative’s criterion value
$\tilde{Q}$	an interval-valued Pythagorean fuzzy set	${\breve{\mathrm{x}}}_{\mathrm{ij}}$	the value of alternative’s criterion value
${\mu }_{\tilde{Q}}^L\left(X\right)$	lower the degree of membership	${\breve{\mathrm{w}}}_{\mathrm{j}}$	the importance weights of the criteria’s importance
${\mu }_{\tilde{Q}}^U\left(X\right)$	upper the degree of membership	$\tilde{D}$	fuzzy decision matrix
${\pi }_{\tilde{Q}}^L\left(X\right)$	lower the degree of non-membership	$\tilde{R}$	normalized fuzzy decision matrix
${\pi }_{\tilde{Q}}^U\left(X\right)$	upper the degree of non-membership	$R={\left(r_{ik}\right)}_{mXm}$	pairwise comparison matrix
$\widetilde{A_i}$	interval type-2 fuzzy set	$r_{ij}, \left(\forall i, j\right)$	normalized trapezoid fuzzy numbers
${\tilde{A}}_i^U$	the upper trapezoidal membership function	A	benefit criterion
${\tilde{A}}_i^L$	the lower trapezoidal membership function	B	cost criterion
$a_{i1}^U,a_{i2}^U,a_{i3}^U,a_{i4}^U,$ $a_{i1}^L,a_{i2}^L,a_{i3}^L,a_{i4}^L$	the references points of the IT2FS	$\tilde{\mathrm{V}}={\left[{\tilde{\mathrm{v}}}_{\mathrm{ij}}\right]}_{\mathrm{mxn}}$	the weighted normalized fuzzy decision matrix
$H_i\left(\widetilde{A_i^U}\right)$	states the membership estimation of the factor	FPIS $A^{+}$	the fuzzy positive-ideal solution
${\mathrm{u}}_{\mathrm{U}}$	the largest possible value of the upper membership function	FPIS $A^{-}$	the fuzzy negative ideal solution
${\mathrm{u}}_{\mathrm{L} }$	the largest possible value of the lower membership function	${\mathrm{d}}_{\mathrm{i}}^{+}$	distance of each alternative to the positive ideal solution
${\mathrm{l}}_{\mathrm{U}}$	the least possible value of the upper membership function	${\mathrm{d}}_{\mathrm{i}}^{-}$	distance of each alternative to the negative ideal solution
${\mathrm{l}}_{\mathrm{L}}$	the least possible value of the lower membership function	${\mathrm{CC}}_{\mathrm{i}}$	the closeness coefficient
${\mathrm{m}}_{1\mathrm{U}},{\mathrm{m}}_{2\mathrm{U}}$	the second and third parameters of the upper membership function	${\mathrm{P}}_{\mathrm{ij}}$	i. enterprise’s evaluation score according to j criteria
${\mathrm{m}}_{1\mathrm{L}},{\mathrm{m}}_{2\mathrm{L}}$	the second and third parameters of the lower membership function	${\mathrm{W}}_{\mathrm{i}}$	weight of j criterion
$D={\left(d_{ik}\right)}_{mXm}$	the differences matrix	${\mathrm{RS}}_{\mathrm{i}}$	enterprise risk score
${\mu }_{ikL}^2, v_{ikU}^2$	lower and upper values of the membership	Ei	alternatives
${\mu }_{ikU}^2, v_{ikL}^2$	lower and upper values of the non- membership	Cij	criteria
$S={\left(s_{ik}\right)}_{mXm}$	the interval multiplicative matrix	Di	decision makers

.

3.1. Pythagorean Fuzzy Sets (PFSs)

In the process of the fuzzy sets being proposed until today, many extensions of it were revealed, such as neutrosophic sets [76], Pythagorean fuzzy sets [77], orthopair fuzzy sets [78], hesitant fuzzy sets [79], and intuitionistic fuzzy sets [80,81].

This study utilized Pythagorean fuzzy sets to reduce uncertainty and address the uncertainty inherent in the decision-making process. This section outlines the basic process stages of Pythagorean fuzzy sets, IT2FSs, and the interval type-2 Pythagorean fuzzy AHP method.

Definition 1. 

If $X$ is a fixed set, a Pythagorean fuzzy set $\tilde{P}$ is an object with the form shown in Equation (1) [82]:

$$\tilde{P}\widetilde{=}\left\{x,{\mu }_{\tilde{P}}\left(x\right),{\nu }_{\tilde{P}}\left(x\right);x\mathsf{\epsilon }X\right\}$$

(1)

where the function ${\mathsf{\mu }}_{\tilde{\mathrm{P}}}\left(\mathrm{x}\right):\mathrm{X} \mapsto$ [0, 1] describes the degree of membership and ${\mathsf{\nu }}_{\tilde{\mathrm{P}}}\left(\mathrm{x}\right): \mapsto$ [0, 1] expresses the degree of non-membership of the element $\mathrm{x} \mathsf{\epsilon } \mathrm{X}$ to P, respectively, and, for every $\mathrm{x} \mathsf{\epsilon } \mathrm{X}$, it holds (Equation (2)):

$$0\le {\mu }_{\tilde{P}}{\left(x\right)}^2+{\nu }_{\tilde{P}}{\left(x\right)}^2\le 1$$

(2)

The formula for calculating the degree of indeterminacy is shown in Equation (3):

$${\pi }_{\tilde{P}}\left(x\right)=\sqrt{1-{\mu }_{\tilde{P}}{\left(x\right)}^2-{\nu }_{\tilde{P}}{\left(x\right)}^2 }$$

(3)

Definition 2. 

An interval-valued Pythagorean fuzzy set is defined as shown in Equation (4) [83]:

$$\tilde{Q}=\left\{x, {\mu }_{\tilde{Q}}\left(x\right), v_{\tilde{Q}}\left(x\right);\mathrm{x} \mathsf{\epsilon } X\right\}$$

(4)

where ${\mathsf{\mu }}_{\tilde{\mathrm{Q}}}\left(\mathrm{x}\right)=\left[{\mathsf{\mu }}_{\tilde{\mathrm{Q}}}^{\mathrm{L}}\left(\mathrm{X}\right),{\mathsf{\mu }}_{\tilde{\mathrm{Q}}}^{\mathrm{U}}\left(\mathrm{X}\right)\right]$ ⊂ [0, 1] and ${\mathrm{v}}_{\tilde{\mathrm{Q}}}\left(\mathrm{x}\right)=\left[{\mathrm{v}}_{\tilde{\mathrm{Q}}}^{\mathrm{L}}\left(\mathrm{X}\right),{ \mathrm{v}}_{\tilde{\mathrm{Q}}}^{\mathrm{U}}\left(\mathrm{X}\right)\right]\subset \left[0,1\right].$ For $\tilde{\mathrm{Q}}$, the following Equation (5) must be provided:

$$0\le {\mu }_{\tilde{Q}}^U{\left(X\right)}^2+v_{\tilde{Q}}^U{\left(X\right)}^2\le 1$$

(5)

Then, with the degree of indeterminacy, ${\mathsf{\pi }}_{\tilde{\mathrm{Q}}}\left(\mathrm{x}\right)=\left[{\mathsf{\pi }}_{\tilde{\mathrm{Q}}}^{\mathrm{L}}\left(\mathrm{X}\right),{\mathsf{\pi }}_{\tilde{\mathrm{Q}}}^{\mathrm{U}}\left(\mathrm{X}\right)\right]$, it can be computed as follows (Equations (6) and (7)) [83]:

$${\pi }_{\tilde{Q}}^L\left(X\right)=\sqrt{1-{\mu }_{\tilde{Q}}^U{\left(X\right)}^2-v_{\tilde{Q}}^U{\left(X\right)}^2 }$$

(6)

$${\pi }_{\tilde{Q}}^U\left(X\right)=\sqrt{1-{\mu }_{\tilde{Q}}^L{\left(X\right)}^2-v_{\tilde{Q}}^L{\left(X\right)}^2 }$$

(7)

3.2. Interval Type-2 Fuzzy Sets

In this section of the research paper, brief definitions of interval type-2 fuzzy sets are provided.

Definition 3. 

Let $\widetilde{A_i}$ be a non-negative interval type-2 trapezoidal fuzzy number (IT2TrFN).

$$\widetilde{A_i}=\left(\widetilde{A_i^U},A_i^L\right)=\left(a_{i1}^U,a_{i2}^U,a_{i3}^U,a_{i4}^U;H_1\left(\widetilde{A_i^U}\right),H_2\left(\widetilde{A_i^U}\right)\right),\left(a_{i1}^L,a_{i2}^L,a_{i3}^L,a_{i4}^L;H_1\left(\widetilde{A_i^L}\right),H_2\left(\widetilde{A_i^L}\right)\right)$$

In the following, the upper trapezoidal membership function ${\tilde{A}}_i^U$ and the lower trapezoidal membership function ${\tilde{A}}_i^L$ of the interval type-2 fuzzy set ${\tilde{A}}_i$ are provided in Figure 2 [84].

Where $\widetilde{A_i^U},A_1^L$ are type-1 fuzzy sets, $a_{i1}^U,a_{i2}^U,a_{i3}^U,a_{i4}^U,a_{i1}^L,a_{i2}^L,a_{i3}^L,a_{i4}^L$ are the references points of the IT2FSs $\widetilde{A_i}$ $H_1\left(\widetilde{A_i^U}\right)$; states the membership estimation of the factor $a_{j\left(j+1\right) }^U$ in the upper trapezoidal membership function $\widetilde{A_i^U},1\le j\le 2, H_j\left(\widetilde{A_i^L}\right)$; also it states the membership estimation of the factor $a_{j\left(j+1\right)}^L$ in the lower trapezoidal membership function $\widetilde{A_i^L},1\le j\le 2$,$H_1\left(\widetilde{A_i^U}\right)\in \left[0,1\right], H_2\left(\widetilde{A_i^U}\right)\in \left[0,1\right], H_1\left(\widetilde{A_i^L}\right)\in \left[0,1\right], H_2\left(\widetilde{A_i^L}\right)\in \left[0,1\right]$, and $1\le j\le n$ [85,86].

Defuzzification for Type-2 Fuzzy Sets

The defuzzification process for a type-2 fuzzy set involves two steps. In the first step, the type-2 fuzzy set is identified as a type-1 fuzzy set using the type reduction process. Then, one of the defuzzification methods for ordinary (type-1) fuzzy sets is used to find the equivalence of type-2 fuzzy sets [87]. The probability-based approach reduction method of [85], which is one of the reduction methods in the literature, is given in Equation (8).

$$\mathrm{DTriT}={\displaystyle \frac{\begin{array}{c}\frac{\left({\mathrm{u}}_{\mathrm{U}}-{\mathrm{l}}_{\mathrm{U}}\right)+\left({\mathsf{\beta }}_{\mathrm{U}}.{\mathrm{m}}_{1\mathrm{U}}-{\mathrm{l}}_{\mathrm{U}}\right)+({\mathsf{\alpha }}_{\mathrm{U}}.{\mathrm{m}}_{2\mathrm{U}}-{\mathrm{l}}_{\mathrm{U}}}{4}+\left[\frac{\left({\mathrm{u}}_{\mathrm{L}}-{\mathrm{l}}_{\mathrm{L}}\right)+\left({\mathsf{\beta }}_{\mathrm{L}}.{\mathrm{m}}_{1\mathrm{L}}-{\mathrm{l}}_{\mathrm{L}}\right)+\left({\mathsf{\alpha }}_{\mathrm{L}}.{\mathrm{m}}_{2\mathrm{L}}-{\mathrm{l}}_{\mathrm{L}}\right)}{4}+l_L\right]\end{array}}{2}}$$

(8)

The largest possible value of the upper membership function is ${\mathrm{u}}_{\mathrm{U}}$ and the largest possible value of the lower membership function is ${\mathrm{u}}_{\mathrm{L}}$; and the least possible value of the upper membership function is ${\mathrm{l}}_{\mathrm{U}}$ and the least possible value of the lower membership function is ${\mathrm{l}}_{\mathrm{L}}$. The second and third parameters of the upper membership function are ${\mathrm{m}}_{1\mathrm{U}}$ and ${\mathrm{m}}_{2\mathrm{U}}$; ${\mathrm{m}}_{1\mathrm{L}}$ and ${\mathrm{m}}_{2\mathrm{L}}$ are the second and third parameters of the lower membership function, respectively [86].

3.3. Pythagorean Fuzzy AHP

Pythagorean fuzzy sets are an improved variation of intuitionistic fuzzy sets [68] in some cases where intuitionistic fuzzy sets cannot resolve ambiguity [77]. Compared to other fuzzy sets, Pythagorean fuzzy sets are a more helpful and flexible tool in addressing vagueness and uncertainty in multi-criteria decision-making problems in the mining industry [88].

This subsection explains the steps of the interval-valued Pythagorean Fuzzy (IVPF) AHP.

Table 2. Interval-valued Pythagorean fuzzy AHP weighting scale [89].

Linguistic Terms	PFN Equivalents IVPF Numbers
	${\mathit{\mu }}_{\mathit{L}}$	${\mathit{\mu }}_{\mathit{U}}$	${\mathit{v}}_{\mathit{L}}$	${\mathit{v}}_{\mathit{U}}$
Certainly Low Importance (CLI)	0.00	0.00	0.90	1.00
Very Low Importance (VLI)	0.10	0.20	0.80	0.90
Low Importance (LI)	0.20	0.35	0.65	0.80
Below Average Importance (BAI)	0.35	0.45	0.55	0.65
Average Importance (AI)	0.45	0.55	0.45	0.55
Above Average Importance (AAI)	0.55	0.65	0.35	0.45
High Importance (HI)	0.65	0.80	0.20	0.35
Very High Importance (VHI)	0.80	0.90	0.10	0.20
Certainly High Importance (CHI)	0.90	1.00	0.00	0.00
Exactly Equal (EE)	0.1965	0.1965	0.1965	0.1965

provides the linguistic terms and Pythagorean Fuzzy Number (PFN) equivalents of IVPF numbers.

• Step 1. Construct the pairwise comparison matrix $R={\left(r_{ik}\right)}_{mXm}$ as provided in Table 2.
• Step 2. Calculate the differences matrix $D={\left(d_{ik}\right)}_{mXm}$ by applying Equations (9) and (10) to the lower and upper values of the membership and non-membership functions.

  $$d_{ikL}={\mu }_{ikL}^2-v_{ikU}^2$$

  (9)

  $$d_{ikU}={\mu }_{ikU}^2-v_{ikL}^2$$

  (10)
• Step 3. Calculate the interval multiplicative matrix $S={\left(s_{ik}\right)}_{mXm}$ using Equations (11) and (12):

  $$s_{i{k}_L}=\sqrt{1000{ }^{d_L}}$$

  (11)

  $$s_{i{k}_U}=\sqrt{1000{ }^{d_U}}$$

  (12)
• Step 4. Calculate the determinacy value $\tau ={\left(r_{ik}\right)}_{mXm}$ of the $r_{ik}$ using Equation (13):

  $${\tau }_{ik}=1-\left({\mu }_{ikU}^2-{\mu }_{ikL}^2\right)-\left(v_{ikU}^2-v_{ikL}^2\right)$$

  (13)
• Step 5. To obtain the weights matrix before normalization, multiply the determinacy values with the $S={\left(s_{ik}\right)}_{mXm}$ matrix, resulting in the $T={\left(t_{ik}\right)}_{mXm}$ matrix.

  $$t_{ik}=\left( {\displaystyle \frac{s_{i{k}_L}+s_{i{k}_U}}{2}} \right){\tau }_{ik}$$

  (14)
• Step 6. Calculate the normalized priority weights $w_i$ using Equation (15).

  $$w_i={\displaystyle \frac{{{\displaystyle \sum }}_{k=1}^m{t}_{ik}}{{{\displaystyle \sum }}_{i=1}^m{{\displaystyle \sum }}_{k=1}^m{t}_{ik}}}$$

  (15)

3.4. Fuzzy TOPSIS

The fuzzy TOPSIS method evaluates both the distance to the positive ideal solution and the distance to the negative ideal solution simultaneously to calculate the necessary proximity for the ideal solution. The order of preference to be made at the end is obtained by comparing the distances. In other words, it emerges as a method that ranks the alternatives by revealing the distances between the best (positive ideal) to the worst (negative ideal) points [90].

The coefficient of closeness for each alternative is calculated using transformed fuzzy numbers. Alternatives can be ranked with the help of the obtained closeness coefficients. In the conventional TOPSIS method, performance values and weights of criterion are given as exact numbers and therefore it does not take into account the uncertainty arising from human perception of determining the weights and qualitative measurements. Since precise data are insufficient to model real-life applications, subjective attributes and weights of attributes are often expressed in verbal variables [91]. The concept of [92] fuzzy TOPSIS, the most preferred technique, can be described as follows:

• Step 1: Consisting of $K$ decision-makers and shows the $i$.’rd. alternative’s criterion value of ${\breve{x}}_{ij}^K$. The values of the alternative criteria are calculated using an Equation (16).

  $${\breve{\mathrm{x}}}_{\mathrm{ij}}={\displaystyle \frac{1}{\mathrm{K}}} \left[{\breve{\mathrm{x}}}_{\mathrm{ij}}^1\left(+\right){\breve{\mathrm{x}}}_{\mathrm{ij}}^2 \left(+\right)\dots \left(+\right){\breve{\mathrm{x}}}_{\mathrm{ij}}^{\mathrm{K}}\right]$$

  (16)
  Hereby, using IT2FS alternatives were evaluated based on criteria (Table 3).

  Table 3. Definition and IT2FSs of the linguistic variables [85,93,94,95].

  Linguistic Terms	Interval Type-2 Fuzzy Sets
  Very Low (VL)	((0, 0, 0, 0.1; 1, 1),	(0, 0, 0, 0.05; 0,9 0,9))
  Low (L)	((0, 0.1, 0.1, 0.3; 1, 1),	(0.05, 0.1, 0.1, 0.2; 0.9, 0.9))
  Medium Low (ML)	((0.1, 0.3, 0.3, 0.5; 1, 1),	(0.2, 0.3, 0.3, 0.4; 0.9, 0.9))
  Medium (M)	((0.3, 0.5, 0.5, 0.7; 1, 1),	(0.4, 0.5, 0.5, 0.6; 0.9, 0.9))
  Medium High (MH)	((0.5, 0.7, 0.7, 0.9; 1, 1),	(0.6, 0.7, 0.7, 0.8; 0.9, 0.9))
  High (H)	((0.7, 0.9, 0.9, 1; 1, 1),	(0.8, 0.9, 0.9, 0.95; 0.9, 0.9))
  Very High (VH)	((0.9, 1, 1, 1; 1, 1),	(0.95, 1, 1, 1; 0.9, 0.9))

  Table 3. Definition and IT2FSs of the linguistic variables [85,93,94,95].

  Linguistic Terms	Interval Type-2 Fuzzy Sets
  Very Low (VL)	((0, 0, 0, 0.1; 1, 1),	(0, 0, 0, 0.05; 0,9 0,9))
  Low (L)	((0, 0.1, 0.1, 0.3; 1, 1),	(0.05, 0.1, 0.1, 0.2; 0.9, 0.9))
  Medium Low (ML)	((0.1, 0.3, 0.3, 0.5; 1, 1),	(0.2, 0.3, 0.3, 0.4; 0.9, 0.9))
  Medium (M)	((0.3, 0.5, 0.5, 0.7; 1, 1),	(0.4, 0.5, 0.5, 0.6; 0.9, 0.9))
  Medium High (MH)	((0.5, 0.7, 0.7, 0.9; 1, 1),	(0.6, 0.7, 0.7, 0.8; 0.9, 0.9))
  High (H)	((0.7, 0.9, 0.9, 1; 1, 1),	(0.8, 0.9, 0.9, 0.95; 0.9, 0.9))
  Very High (VH)	((0.9, 1, 1, 1; 1, 1),	(0.95, 1, 1, 1; 0.9, 0.9))

• Step 2: The importance weights of the criteria’s importance, determined by $K$ decision-makers ${\breve{\mathrm{w}}}_{\mathrm{ij}}^{\mathrm{k}}$ are calculated using Equation (17).

  $${\breve{\mathrm{w}}}_{\mathrm{j}}={\displaystyle \frac{1}{\mathrm{K}}} \left[{\tilde{\mathrm{w}}}_{\mathrm{j}}^1\left(+\right){\tilde{\mathrm{w}}}_{\mathrm{j}}^2\left(+\right)\dots \left(+\right){\tilde{\mathrm{w}}}_{\mathrm{j}}^{\mathrm{K}}\right]$$

  (17)

  In this paper, the weights for the criteria were obtained using the interval Pythagorean fuzzy AHP method.
• Step 3: Equation (18) shows the fuzzy decision matrix for a fuzzy multi-criteria decision-making problem with n criteria and m alternatives, presented in matrix format.

  $$\hat{\mathrm{D}}=\left[\left[\begin{array}{ccc}{\tilde{\mathrm{x}}}_{11}& \cdots & {\tilde{\mathrm{x}}}_{1\mathrm{n}}\\ ⋮& \ddots & ⋮\\ {\tilde{\mathrm{x}}}_{\mathrm{m}1}& \cdots & {\tilde{\mathrm{x}}}_{\mathrm{mn}}\end{array}\right]\right]\tilde{\mathrm{W}}=\left[{\tilde{\mathrm{w}}}_1{\tilde{\mathrm{w}}}_{21}\dots .{\tilde{\mathrm{w}}}_{\mathrm{n}}\right]$$

  (18)

  where ${\tilde{x}}_{ij}=\left(\forall \mathrm{i},\mathrm{j}\right)$ and ${\tilde{W}}_{j}j=\left(1,2,\dots .,n\right)$ are trapezoidal fuzzy numbers, and where $\tilde{D}$ denotes fuzzy decision matrix and $\tilde{W}$ denote fuzzy weights matrix.
• Step 4: After creating the fuzzy decision matrix, it is necessary to normalize it. The resulting normalized fuzzy decision matrix is denoted by $\tilde{R}$ and can be expressed as shown in Equation (19) below.

  $$\tilde{\mathrm{R}}={\left[{\tilde{\mathrm{r}}}_{\mathrm{ij}}\right]}_{\mathrm{mxn}}$$

  (19)

  Decision criteria come in two forms as benefit and cost criteria, where A is the benefit criterion and B is the cost criterion and is calculated as follows (Equations (20) and (21)):

  $${\tilde{\mathrm{r}}}_{\mathrm{ij}}=\left({\displaystyle \frac{{\mathrm{a}}_{\mathrm{ij}}}{{\mathrm{d}}_{\mathrm{j}}}}, {\displaystyle \frac{{\mathrm{b}}_{\mathrm{ij}}}{{\mathrm{d}}_{\mathrm{j}}}}, {\displaystyle \frac{{\mathrm{c}}_{\mathrm{ij}}}{{\mathrm{d}}_{\mathrm{j}}}}, {\displaystyle \frac{{\mathrm{d}}_{\mathrm{ij}}}{{\mathrm{d}}_{\mathrm{j}}}}\right), \mathrm{j}\in \mathrm{A},{ \mathrm{d}}_{\mathrm{j}}=\max {\mathrm{d}}_{\mathrm{ij}}, \mathrm{j}\in \mathrm{A}$$

  (20)

  $${\tilde{\mathrm{r}}}_{\mathrm{ij}}=\left({\displaystyle \frac{{\mathrm{a}}_{\mathrm{j}}^{-}}{{\mathrm{d}}_{\mathrm{ij}}}}, {\displaystyle \frac{{\mathrm{a}}_{\mathrm{j}}^{-}}{{\mathrm{c}}_{\mathrm{ij}}}}, {\displaystyle \frac{{\mathrm{a}}_{\mathrm{j}}^{-}}{{\mathrm{b}}_{\mathrm{ij}}}},{\displaystyle \frac{{\mathrm{a}}_{\mathrm{j}}^{-}}{{\mathrm{a}}_{\mathrm{ij}}}}\right), \mathrm{j}\in \mathrm{B},{ \mathrm{a}}_{\mathrm{j}}=\min {\mathrm{a}}_{\mathrm{ij}}, \mathrm{j}\in \mathrm{B}$$

  (21)

  Here, $r_{ij}, \left(\forall i, j\right)$ are normalized trapezoid fuzzy numbers.
• Step 5: Equation (22) is used to form the weighted normalized fuzzy decision matrix, taking into account the varying importance weight of each decision criterion. The elements of this matrix are calculated using Equation (23), based on the obtained normalized fuzzy decision matrix.

  $$\tilde{\mathrm{V}}={\left[{\tilde{\mathrm{v}}}_{\mathrm{ij}}\right]}_{\mathrm{mxn}} \mathrm{i}=1,2,\dots ..,\mathrm{m}\hspace{1em}\mathrm{j}=1,2,\dots ..,\mathrm{n}$$

  (22)

  $$\tilde{\mathrm{R}}={\left[{\tilde{\mathrm{r}}}_{\mathrm{ij}}\right]}_{\mathrm{mxn}}$$

  (23)
• Step 6: After creating the weighted normalized fuzzy decision matrix, the Fuzzy Positive Ideal Solution (FPIS $A^{+}$) and the Negative Ideal Solution (FNIS $A^{-}$) are calculated using Equations (24) and (25):

  $${\mathrm{A}}^{+}=\left({{\tilde{\mathrm{v}}}_1}^{+},{{\tilde{\mathrm{v}}}_2}^{+},\dots ..,{{\tilde{\mathrm{v}}}_{\mathrm{n}}}^{+}\right)$$

  (24)

  $${\mathrm{A}}^{-}=\left({{\tilde{\mathrm{v}}}_1}^{-},{{\tilde{\mathrm{v}}}_2}^{-},\dots ..,{{\tilde{\mathrm{v}}}_{\mathrm{n}}}^{-}\right)$$

  (25)

  Here, ${\widetilde{v_j}}^{+}=\left(1,1,1\right) \mathrm{ve} {\widetilde{v_j}}^{-}=\left(0,0,0\right) j=\left(1,2,\dots ..n\right)$. In other words, there are (1,1,1) and (0,0,0) represent the values for the decision criteria, respectively [92].
• Step 7: Equations (26) and (27) are used to calculate the distance of each alternative from $A^{+}$ to $A^{-}$ after assigning the (FPIS $A^{+}$) and the (FNIS $A^{-}$).

  $${\mathrm{d}}_{\mathrm{i}}^{+}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{d}}_{\mathrm{v}}({\tilde{\mathrm{v}}}_{\mathrm{ij}}, {\widetilde{{\mathrm{v}}_{\mathrm{j}}}}^{+}), \mathrm{i}=1,2,\dots ..\mathrm{m}$$

  (26)

  $${\mathrm{d}}_{\mathrm{i}}^{-}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{d}}_{\mathrm{v}}({\tilde{\mathrm{v}}}_{\mathrm{ij}},{{\tilde{\mathrm{v}}}_{\mathrm{j}}}^{-}), \mathrm{i}=1,2,\dots ..\mathrm{m}$$

  (27)

  Here, $d_v$ is the distance between the two fuzzy numbers. The distance measurement between two trapezoid fuzzy numbers can be calculated using the vertex method [96]. Equation (28) calculates the distance between two fuzzy numbers given as $d_v\left(\check{a }, \check{b}\right)$ and $\check{b}$.

  $$d_v\left(\check{\mathrm{a} }, \check{\mathrm{b}} \right)=\sqrt{{\displaystyle \frac{1}{4}}{\left[({\mathrm{a}}_1-{ \mathrm{b}}_1\right]}^2+{\left[({\mathrm{a}}_2-{ \mathrm{b}}_2\right]}^2+{\left[({\mathrm{a}}_3-{ \mathrm{b}}_3\right]}^2 {\left[({\mathrm{a}}_4-{ \mathrm{b}}_4\right]}^2}$$

  (28)
• Step 8: Equation (29) calculates the closeness coefficient $\left({\mathrm{CC}}_{\mathrm{i}}\right)$ using (FPIS ${\mathrm{A}}^{+}$), ${\mathrm{d}}_{\mathrm{i}}^{+}$ and (FNIS ${\mathrm{A}}^{-}$), ${\mathrm{d}}_{\mathrm{i}}^{-}$.

  $$\left({\mathrm{CC}}_{\mathrm{i}}\right)={\displaystyle \frac{{\mathrm{d}}_{\mathrm{i}}^{-}}{{\mathrm{d}}_{\mathrm{i}}^{+}+{ \mathrm{d}}_{\mathrm{i}}^{-}}} ,\hspace{1em}\mathrm{i}=1,2,\dots ..\mathrm{m}$$

  (29)

  If ${\mathrm{A}}_{\mathrm{i}}={\mathrm{A}}^{+}$, then ${\mathrm{CC}}_{\mathrm{i}}=1,$ and if ${\mathrm{A}}_{\mathrm{i}}={\mathrm{A}}^{-}$ then ${\mathrm{CC}}_{\mathrm{i}}=1$. In other words, as the ${\mathrm{CC}}_{\mathrm{i}}$ value approaches 1, the alternative $A_i$ moves closer to the positive ideal solution and further away from the negative ideal solution. Using ${\mathrm{CC}}_{\mathrm{i}}$, we can rank all alternatives and confidently select the best one [97]. Convergence coefficients take a value between 0 and 1, and the closer to 1, the higher the preference rate.

3.5. Determining the Risk Scores of Enterprises

The risk scores of coal mines were computed as follows using the weights obtained from Pythagorean fuzzy AHP in this section and the assessment scores obtained in Equation (30) with the Paksoy approach using interval type-2 fuzzy sets.

$${ \mathrm{RS}}_{\mathrm{i}}={\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{J}}\mathrm{Pij}.\mathrm{Wj}$$

(30)

• ${\mathrm{P}}_{\mathrm{ij}}$: i. enterprise’s evaluation score according to j criteria
• ${\mathrm{W}}_{\mathrm{i}}$: weight of j criterion
• ${\mathrm{RS}}_{\mathrm{i}}$: enterprise risk score

3.6. Introduction of Coal Mines, and Designing of the Robust Hybrid Top-Down Risk-Based Classification Hierarchy

The proposed methods were implemented to compute the risk scores (weights) of the main criteria, its sub-criteria, and risk scores of TCE enterprises and to risk-based rank according to computed risk scores. The proposed model comprises the following steps:

• Identifying the robust hybrid top-down risk-based classification decision hierarchy algorithm.
• Computing the risk scores of criteria by using interval-valued Pythagorean fuzzy AHP.
• Evaluating the enterprises according to computed risk scores with a combination of the fuzzy TOPSIS method and Paksoy approach by using IT2FSs and determining the final risk scores of the coal mines, comparing the two methods’ results with each other.
• Demonstrating the robustness of the applied methods by performing sensitivity analyses.

The proposed approaches applied in this study are all clearly delineated in the general step by step flowchart, as illustrated in Figure 3.

In the context of the present study, the proposed approach was implemented by evaluating the non-fatal occupational accident records of TCE enterprises over a six-year period. These records were kept in an exemplary manner by the top management of TCE, with meticulous attention to detail and regularity. Based on the occupational accident history, the main components contributing to occupational accidents were categorized and evaluated in the robust hybrid top-down risk-based classification decision hierarchy algorithm [98].

This study’s database was provided by TCE lignite mines. The data source is the official records of TCE, and TCE is a government-run enterprise. The records were provided in full, therefore our data source is reliable. The data include details for each accident, such as the detailed reason of the accident, location of the accident, employee’s information about the name, surname, birthday, the job conducted during the accident of the employees, and injured body parts due to the accidents. The inclusion and exclusion criteria of the robust hybrid top-down risk-based classification decision hierarchy were determined according to these records and the authors’ current knowledge of the literature [20,98,99]. Pairwise comparisons were conducted by taking into account these records by decision-makers. In addition, the experienced and highly educated managers who worked in the TCE were selected as decision-makers in this study.

According to these records, TCE’s enterprises (alternatives) are coded as E1, E2, E3, E4, E5, E6, E7, and E8 in the hierarchy (Figure 4). These enterprises are spread over the Aegean Regions, Marmara Regions, and Middle Anatolia in Türkiye. Coal is extracted by the open-cast mining method in E1, E2, E4, E6, E7, and E8, whereas it is extracted both by the open-cast mining method and underground mining method at E3 and E5 enterprises. From these enterprises, E7 was transferred to the private sector in 2012; E4 and E8 were transferred to the private sector in 2013 under the privatization policies of TCE’s top management. As shown in Figure 5, the non-fatal occupational accident records were categorized under 6 main criteria under 25 sub-criteria. The accident location (area) main criterion was categorized into four sub-criteria: open-cast mining area (C₁₁), workshops (C₁₂), social facilities area of surface installations (C₁₃), and coal handling plants–coal washing plants–storage bins (C₁₄). The open-cast mining area is defined as the area that extracted the coal using heavy-duty mining equipment (heavy-duty mining trucks, hydraulic mining shovels, draglines, excavators, large wheel loaders, large dozers, rotary drill rigs, rock drills, and motor graders). Maintenance of the mining equipment is conducted in workshops. They show similarities to many other service workshops, except that the powered mobile plant is increasingly larger. The area of surface installations is the facility areas except for the coal handling plants, workshop, and open-cast mining area. A facility that washes coal to remove waste material from coal is defined as a coal handling plant [99]. The accident type criterion (reason) was categorized into six sub-criteria as mining machine (C₂₁), manual and mechanical handling (C₂₂), slip/fall (C₂₃), hand tools-related (C₂₄), transporting (C₂₅), and machinery (C₂₆). The occupation main criterion has four sub-criteria: maintenance personnel (C₃₁), driver (C₃₂), worker (C₃₃), and mining machine operator (C₃₄). The part of the body main criterion has four sub-criteria: head (C₄₁), upper extremities (C₄₂), lower extremities (C₄₃), as well as torso and sundry (C₄₄). The age main criterion was categorized according to the ESAW criteria as 20–24 (C₅₁), 25–34 (C₅₂), 35–44 (C₅₃), and 45–57 (C₅₄) [100]. The last main criterion of the hierarchy is the shift criterion, which was categorized as first shift (8–16 h) (C₆₁), second shift (16–24 h) (C₆₂), and third shift (24–08 h) (C₆₃).

In the present study, the most important and innovative combinations of FMCDM techniques with current scales were used to compute the risk scores of TCE in Türkiye. Combinations of these hybrid decision risk assessment methods are used for the first time, according to the authors’ current knowledge through literature.

This study will be a technical guide for the top management and decision-makers of coal mines or other industries to assess the potential hazards inherent in their work environment, evaluate the risks, and ensure coal production sustainability for enterprises. Furthermore, this study will provide a foundation for evaluating the vagueness and impreciseness of subjective evaluations in existing literature studies on mining with different FMCDM techniques using IT2FSs.

4. Results and Discussion

4.1. Application of the Pythagorean Fuzzy AHP Method

After constructing the robust hybrid top-down risk-based classification hierarchy, the risk scores of the evaluation criteria were computed. In this stage of the study, the Pythagorean fuzzy AHP method was used to compute the sub-criteria risk scores.

Table 4. Pairwise comparisons for the area criterion.

Area	C11	C12	C13	C14
C11	-	AAI	HI	VHI
		AAI	VHI	VHI
		AI	VHI	VHI
C12		-	AAI	VHI
			HI	VHI
			HI	HI
C13			-	AAI
				AI
				AAI
C14				-

shows the pairwise comparisons of sub-criteria for area criterion. Such comparisons were conducted for every main criterion in the robust hybrid top-down risk-based classification hierarchy.

The application of the Pythagorean fuzzy AHP method applied to the area’s sub-criterion is given below. Sub-criterion weights were obtained by applying these implementation steps to all other sub-criteria. By using the weighting scale for the interval-valued Pythagorean fuzzy AHP method [89] (Table 2), the decision-maker’s unified agreed pairwise comparison matrix for the area sub-criterion was obtained (

Table 5. Decision-maker’s unified agreed pairwise comparison matrix for the area’s sub-criterion.

Area	C11	C12	C13	C14
C11	0.1965	0.5167	0.7500	0.8000
	0.1965	0.6167	0.8667	0.9000
	0.1965	0.3833	0.1333	0.1000
	0.1965	0.4833	0.2500	0.2000
C12	0.3833	0.1965	0.6167	0.7500
	0.4833	0.1965	0.7500	0.8667
	0.5167	0.1965	0.2500	0.1333
	0.6167	0.1965	0.3833	0.2500
C13	0.1333	0.2500	0.1965	0.5167
	0.2500	0.3833	0.1965	0.6167
	0.7500	0.6167	0.1965	0.3833
	0.8667	0.7500	0.1965	0.4833
C14	0.1000	0.1333	0.3833	0.1965
	0.2000	0.2500	0.4833	0.1965
	0.8000	0.7500	0.5167	0.1965
	0.9000	0.8667	0.6167	0.1965

). Then, by using Equations (9) and (10), the difference matrix was calculated. This matrix is demonstrated in

Table 6. The differences matrix.

	C11		C12		C13		C14
C11	0.0000	0.000	0.0333	0.2333	0.7333	0.6000	0.6000	0.8000
C12	−0.2333	−0.0333	0.000	0.0000	0.2333	0.5000	0.5000	0.7333
C13	−0.7333	−0.5000	−0.5000	0.0000	0.0000	0.0000	0.0333	0.2333
C14	−0.8000	−0.6000	−0.7333	−0.5000	−0.2333	−0.0333	0.0000	0.0000

.

Then, by using Equations (11) and (12), the interval multiplicative matrix was computed (

Table 7. Interval multiplicative matrix.

	C11		C12		C13		C14
C11	1.0000	1.0000	1.1220	2.2387	12.5893	7.9433	7.9433	15.8489
C12	0.4467	0.8913	1.0000	1.0000	2.2387	5.6234	5.6234	12.5892
C13	0.0794	0.1778	0.1778	1.0000	1.0000	1.0000	1.1220	2.2387
C14	0.0631	0.1259	0.0794	0.1778	0.4467	0.8913	1.0000	1.0000

).

In

Table 8. Determinacy value matrix.

	C11	C12	C13	C14
C11	1.0000	0.8000	0.7667	0.8000
C12	0.8000	1.0000	0.7333	0.7667
C13	0.7667	0.7333	1.0000	0.8000
C14	0.8000	0.7667	0.8000	1.0000

, by using Equation (13), the determinacy value matrix is presented. By using Equation (14), the weights matrix before normalization, and by using Equation (15), the normalized priority weights for sub-criteria were obtained (

Table 9. The weights matrix before normalization and the normalized priority weights.

	C11	C12	C13	C14	Wi
C11	1.0000	1.3443	7.8708	9.5169	0.5524
C12	0.5352	1.0000	2.8828	6.9815	0.3191
C13	0.0986	0.4319	1.0000	1.3443	0.0805
C14	0.0756	0.0986	0.5352	1.0000	0.0478

). These computed the final risk scores for the whole hierarchy and are presented in detail (

Table 10. Priority weights (risk scores) for area, reason, and occupation sub-criteria.

Area		Reason		Occupation
Sub-Criterion	Risk Scores	Sub-Criterion	Risk Scores	Sub-Criterion	Risk Scores
Open-cast mining area	0.5524	Mining machine	0.4247	Maintenance personnel	0.5633
Workshops	0.3191	Manual and mechanical handling	0.1162	Driver	0.2261
Social facilities area of surface installations	0.0805	Slip/fall	0.1253	Worker	0.0932
Coal handling plants–Coal washing plants–Storage bins	0.0478	Hand tools-related	0.0426	Mining machine operator	0.1173
		Transporting	0.1140
		Machinery	0.1772

and

Table 11. Priority weights (risk scores) for part of body, age, and shift sub-criteria.

Part of Body		Age		Shift
Sub-Criterion	Risk Scores	Sub-Criterion	Risk Scores	Sub-Criterion	Risk Scores
Head	0.0959	20–24	0.0314	First shift (8–16 h)	0.6341
Upper extremities	0.4030	25–34	0.1245	Second shift (16–24 h)	0.2371
Lower extremities	0.1915	35–44	0.3163	Third shift (24–08 h)	0.1288
Torso and sundry	0.3094	45–57	0.5279

).

According to Table 10 and Table 11, the highest risky area for TCE enterprises was found to be an open-cast mining area; for occupational accident reason it is a mining machine; and for occupational group, the highest risk score value was computed for maintenance personnel in TCE enterprises. As a result of these risk score values, the upper extremities are the most affected part of the body for mine employees. It was determined that the most hazard-prone group is the mine employees between 45 and 57 years old. Additionally, it was concluded that the first shift (8–16 h) in TCE enterprises has the highest risk score among all the hazard factors.

4.2. Application of the Fuzzy TOPSIS Method

The calculated criteria weights in the previous section using the Pythagorean fuzzy AHP method were integrated into the fuzzy TOPSIS method and the final risk scores of TCE enterprises were calculated using the fuzzy TOPSIS method. Fuzzy averages of alternatives for each decision-maker based on the sub-criterion evaluation chart by using Equation (17) are presented in an aggregated fuzzy decision matrix (

Table 12. Aggregated fuzzy decision matrix.

	C11	C12	C13	C14	C21	C22	... ...	C51	C52	C53	C54	C61	C62	C63
E1	0.1162	0.0512	0.0512	0.0512	0.0512	0.0512	... ...	0.0187	0.175	0.1162	0.1750	0.1162	0.2337	0.0187
E2	0.0837	0.0837	0.0512	0.0512	0.1162	0.0187	... ...	0.0187	0.3575	0.1162	0.1162	0.175	0.0512	0.1162
E3	0.9237	0.9562	0.8587	0.8587	0.8912	0.8912	... ...	0.0837	0.6825	0.8000	0.9237	0.9237	0.6175	0.4225
E4	0.3575	0.1162	0.0837	0.0837	0.2925	0.3575	... ...	0.0187	0.2925	0.2925	0.2925	0.3575	0.1750	0.2337
E5	0.4225	0.8000	0.1162	0.8000	0.3575	0.5525	... ...	0.0187	0.1162	0.6825	0.4225	0.6175	0.2925	0.4875
E6	0.0187	0.0187	0.0187	0.0512	0.0187	0.0187	... ...	0.0187	0.0187	0.0837	0.0187	0.0187	0.0837	0.0187
E7	0.1750	0.1750	0.8912	0.1162	0.2925	0.8000	... ...	0.0512	0.3575	0.4225	0.2337	0.4225	0.3575	0.0512
E8	0.4875	0.1162	0.5525	0.0187	0.4875	0.2925	... ...	0.0512	0.3575	0.3575	0.3575	0.4875	0.2337	0.1750

). Then, normalized fuzzy decision matrix using Equation (18) is presented in

Table 13. Normalized fuzzy decision matrix.

	C11	C12	C13	C14	C21	C22	... ...	C51	C52	C53	C54	C61	C62	C63
E1	0.1258	0.0535	0.0575	0.0596	0.0575	0.0575	... ...	0.2234	0.2564	0.1453	0.1895	0.1258	0.3785	0.0384
E2	0.0906	0.0875	0.0575	0.0596	0.1304	0.0210	... ...	0.2234	0.5238	0.1453	0.1258	0.1895	0.0829	0.2384
E3	1.0000	1.0000	0.9635	1.0000	1.0000	1.0000	... ...	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.8667
E4	0.3870	0.1215	0.0939	0.0975	0.3282	0.4011	... ...	0.2234	0.4286	0.3656	0.3167	0.3870	0.2834	0.4794
E5	0.4574	0.8366	0.1304	0.9316	0.4011	0.6200	... ...	0.2234	0.1703	0.8531	0.4574	0.6685	0.4737	1.0000
E6	0.0202	0.0196	0.0210	0.0596	0.0210	0.0210	... ...	0.2234	0.0274	0.1046	0.0202	0.0202	0.1355	0.0384
E7	0.1895	0.1830	1.0000	0.1353	0.3282	0.8977	... ...	0.6117	0.5238	0.5281	0.2530	0.4574	0.5789	0.1050
E8	0.5278	0.1215	0.6200	0.0218	0.5470	0.3282	... ...	0.6117	0.5238	0.4469	0.3870	0.5278	0.3785	0.3590

. By using Equation (19), a weighted normalized fuzzy decision matrix was obtained (

Table 14. Weighted normalized fuzzy decision matrix.

	C11	C12	C13	C14	C21	C22	... ...	C51	C52	C53	C54	C61	C62	C63
E1	0.0695	0.0171	0.0046	0.0029	0.0244	0.0067	... ...	0.0064	0.0296	0.0426	0.1066	0.0798	0.0897	0.0049
E2	0.0501	0.0279	0.0046	0.0029	0.0554	0.0024	... ...	0.0064	0.0604	0.0426	0.0708	0.1201	0.0197	0.0307
E3	0.5524	0.3192	0.0776	0.0478	0.4247	0.1162	... ...	0.0287	0.1153	0.2930	0.5627	0.6340	0.2370	0.1116
E4	0.2138	0.0388	0.0076	0.0047	0.1394	0.0466	... ...	0.0064	0.0494	0.1071	0.1782	0.2454	0.0672	0.0617
E5	0.2527	0.2671	0.0105	0.0445	0.1704	0.0720	... ...	0.0064	0.0196	0.2500	0.2574	0.4238	0.1123	0.1288
E6	0.0112	0.0062	0.0017	0.0029	0.0089	0.0024	... ...	0.0064	0.0032	0.0307	0.0114	0.0128	0.0321	0.0049
E7	0.1047	0.0584	0.0805	0.0065	0.1394	0.1043	... ...	0.0176	0.0604	0.1547	0.1424	0.2900	0.1372	0.0135
E8	0.2915	0.0388	0.0499	0.0010	0.2323	0.0381	... ...	0.0176	0.0604	0.1309	0.2178	0.3346	0.0897	0.0462

). The weights of alternatives were computed using Equation (20); then, according to ${\mathrm{CC}}_{\mathrm{i}}$, these alternatives were ranked (

Table 15. Fuzzy TOPSIS results.

Enterprises	di*	di-	$\mathbf{C}{\mathbf{C}}_{\mathbf{i}}$	Normalized Weights
E1	24.1134	0.8866	0.0355	0.0470
E2	24.1002	0.8998	0.0360	0.0477
E3	19.1544	5.6124	0.2266	0.3002
E4	22.5808	2.1388	0.0865	0.1146
E5	21.3495	3.6505	0.1460	0.1934
E6	24.7637	0.2363	0.0095	0.0125
E7	22.5431	2.4569	0.0983	0.1302
E8	22.0849	2.9151	0.1166	0.1545

). Based on seven linguistic expressions in Table 3, pairwise comparisons for all enterprises according to the twenty-five sub-criteria of the hierarchy were calculated. One of these pairwise comparison matrixes for the C₁₁ sub-criterion is demonstrated in the first line of

Table 16. Interval type-2 fuzzy sets for the pairwise comparison matrix of enterprises according to C₁₁ the sub-criteria.

Criteria	Enterprises	Decision Makers						Fuzzy Numbers		Crisp Number
		DM1		DM2		DM3
C11	E1	0	0.05	0	0.05	0	0.05	0	0.05	0.1162
		0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
		0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
		0.3	0.2	0.3	0.2	0.3	0.2	0.3	0.2
		1	0.9	1	0.9	1	0.9	1	0.9
		1	0.9	1	0.9	1	0.9	1	0.9
	…	.	.	.	.	.	.	.	.	…
		.	.	.	.	.	.	.	.
		.	.	.	.	.	.	.	.
	E8	0.3	0.4	0.3	0.4	0.3	0.4	0.3	0.4	0.4875
		0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5
		0.5	0.5	0.5	0.5	0.5	0.5	0.5	0.5
		0.7	0.6	0.7	0.6	0.7	0.6	0.7	0.6
		1	0.9	1	0.9	1	0.9	1	0.9
		1	0.9	1	0.9	1	0.9	1	0.9

.

4.3. Application of the Paksoy Approach

At this stage, to evaluate the alternatives under each criterion were used IT2FSs. Therefore, we obtained the assessment scores of the alternatives. The assessment scores of the alternatives by using IT2FSs for the pairwise comparison matrix according to the C₁₁ sub-criteria are given in Table 16 and the final results of the Paksoy approach are given in

Table 17. Final results of the Paksoy approach.

Sub-Criterion								Defuzzied Weights	Normalized Weights
C11 E1	C12 E1	C13 E1	C14 E1	... ...	C61 E1	C62 E1	C63 E1	Average	0.0481
0.1162	0.0512	0.0512	0.0512		0.1162	0.2337	0.0187	0.0280
C11 E2	C12 E2	C13 E2	C14 E2	... ...	C61 E2	C62 E2	C63 E2	Average	0.0471
0.0837	0.0837	0.0512	0.0512		0.1750	0.0512	0.1162	0.0274
C11 E3	C12 E3	C13 E3	C14 E3	... ...	C61 E3	C62 E3	C63 E3	Average	0.2980
0.9237	0.9562	0.8587	0.8587		0.9237	0.6175	0.4225	0.1734
C11 E4	C12 E4	C13 E4	C14 E4	... ...	C61 E4	C62 E4	C63 E4	Average	0.1135
0.3575	0.1162	0.0837	0.0837		0.3575	0.1750	0.2337	0.0660
C11 E5	C12 E5	C13 E5	C14 E5	... ...	C61 E5	C62 E5	C63 E5	Average	0.1988
0.4225	0.8000	0.1162	0.8000		0.6175	0.2925	0.4875	0.1157
C11 E6	C12 E6	C13 E6	C14 E6	... ...	C61 E6	C62 E6	C63 E6	Average	0.0121
0.0187	0.0187	0.0187	0.0512		0.0187	0.0837	0.0187	0.0070
C11 E7	C12 E7	C13 E7	C14 E7	... ...	C61 E7	C62 E7	C63 E7	Average	0.1305
0.1750	0.1750	0.8912	0.1162		0.4225	0.3575	0.0512	0.0759
C11 E8	C12 E8	C13 E8	C14 E8	... ...	C61 E8	C62 E8	C63 E8	Average	0.1520
0.4875	0.1162	0.5525	0.0187		0.4875	0.2337	0.1750	0.0885
wi1	wi2	wi3	wi4	... ...	wi23	wi24	wi25
0.5524	0.3192	0.0805	0.0478		0.6340	0.2370	0.1288

. Such pairwise comparisons were conducted for other sub-criteria in the robust hybrid top-down risk-based classification hierarchy.

4.4. Comparisons

According to the results that computed the final risk scores of enterprises, the enterprise with coded E3 has the highest risk score and is followed by E5 and E8, respectively. It was concluded that the first three risk score rankings were the same for both methods. The lowest risk score was computed for E2, E1, and E6 in the fuzzy TOPSIS method and for E1, E2, and E6 in the Paksoy approach, respectively. The detailed computed final risk scores for enterprises are presented in Figure 5.

5. Sensitivity Analyses

Sensitivity analyses were performed using different sub-criterion weights to examine the sensitivity of the results obtained at the last stage of the study. We changed the weight of the sub-criterion, which is the highest among each criterion’s sub-criterion weights, and the weights of the other sub-criterion. Under the area criterion, the open-cast mining area sub-criterion, under the reason criterion the mining machine sub-criterion, under occupation criterion maintenance personnel sub-criterion, under part of body torso and sundry sub-criterion, under age criterion 45–57 sub-criterion, and under shift criterion first shift sub-criterion have the highest criterion weight.

The importance weight of the open-cast mining area sub-criterion, the importance weight of the workshops sub-criterion, the social facilities area of surface installations sub-criterion, and coal handling plants–coal washing plants storage bins sub-criterion were replaced, respectively, and the importance weights of the alternatives were computed again. The same procedures are applied for reason, occupation, part of body, age, and shift sub-criteria. As a result, we obtained 18 different scenarios for all enterprises. The obtained results are illustrated in Figure 6 and Figure 7. When we examine Figure 6 and Figure 7, we see that the risk-based rankings of enterprises do not change according to the scenarios obtained. The difference between the computed risk scores of these enterprises is very low. This shows that the determined risk scores of the TCE enterprises are sensitive to the risk weights obtained.

The risk evaluation methods that are proposed in this study not only identify the most important risk factors in these open-cast coal mine enterprises, but also provide a mechanism for risk-based ranking of enterprises by their calculated risk scores. In this context, the highest risk factors of the 25 sub-risk factors in the robust hybrid top-down risk-based classification decision hierarchy algorithm are detected in Table 10 and Table 11 before. In this context, to determine the level of significance and type of risk, these risk factors were also evaluated and compared with the As Low As Reasonably Practicable (ALARP) diagram. The ALARP is the most widely used approach to establish risk tolerance and is a framework that guides the decision-making process in risk management. The structure is composed of three principal levels from top to bottom as unacceptable region (intolerable risks), ALARP region (tolerable risk), and broadly acceptable region (tolerable risks) [101,102,103]. In this study, according to the derived final risk weights of the hierarchy, the first shift (8–16 h) category (0.6341), the maintenance personnel category (0.5633), the open-cast mining area category (0.5524), and the age range category (0.5279) lie in the intolerable risk zone, respectively. The mining machine category (0.4247), the upper extremities category (0.4030), the workshops category (0.3191), the 35–44 age range (0.3163) category, and the torso and sundry category are also located in the ALARP region. In conclusion, The ALARP principle is a fundamental concept that guides decision-making in risk management, and is most commonly used to establish risk tolerance, helping organizations systematically identify, assess, and reduce risks to as low a level as is reasonably practicable. It is imperative that decision makers implement appropriate control measures without delay in order to reduce the risks identified in the intolerable risk region to the lowest reasonably practicable level. These risk levels should be moved to the ALARP region immediately. Furthermore, the efficacy of the implemented engineering control measures must be continuously evaluated.

It is recommended that all employees involved in repair and maintenance activities are trained in standard procedures, as this is an important element in accident prevention. Training programs should be used to raise awareness of the use of Personal Protective Equipment (PPE). The overall safety of equipment and protective devices should be developed and periodically reviewed by the manufacturer. The majority of occupational accidents can be prevented through the implementation of effective work planning, including the allocation of appropriate workloads, shift changes where necessary for older employees, and the establishment of an occupational health and safety culture.

The main limitations of the existing study were also pointed out. In this sense, the delineation of these limitations can be described as follows: The data set used in the robust hybrid top-down risk-based classification decision hierarchy algorithm includes only open-cast mine employees who had a non-fatal occupational accident. This study was carried out on the large-scale open-cast coal mine enterprises of TCE lignite mines in Türkiye. By updating the dataset in such future studies, this limitation can be eliminated by adding non-fatal occupational accidents and even fatal accidents in underground coal mining to the risk assessment algorithm that was designed within the scope of the study. Furthermore, the analysis can be extended to include administrative staff in future work. It is of paramount importance to note that the methodologies proposed in this study can be readily applied in a multitude of high-risk industries, including the coal mining sector.

6. Conclusions

Considering that occupational accidents occur as the result of a combination of many factors, evaluation of all these factors together to investigate the root causes of accidents provides convenience to permanent supervisors, top management, and OHS experts. In this paper, non-fatal occupational accidents that are the most common in open-cast mining were evaluated.

For this purpose, this study presented the hybrid methods of Pythagorean fuzzy AHP and the fuzzy TOPSIS method and the Paksoy approach using IT2FSs to analyze and assess the risk scores and the risk-based rank of all the Turkish Coal Enterprises in Türkiye. Pythagorean fuzzy AHP was used to obtain risk scores of the criteria and the sub-criteria and the fuzzy TOPSIS and Paksoy approach was used for risk-based ranking.

According to the author’s current knowledge through literature and accident records database, six criteria used as the main criteria and twenty-five sub-criteria were identified for the risk-based ranking hierarchy [20,98,99]. The results of the study show that, for TCE enterprises, the highest weight risk score was computed for E3 > E5 > E8 in the two methods. This was followed by the fuzzy TOPSIS method as E7 > E4 > E2 > E1 > E6; and for the Paksoy approach E7 > E4 > E1 > E2, respectively. The lowest risk score was computed for the E6 enterprise in both methods. Additionally, the risk scores of the main criterion and sub-criterion in the hierarchy were computed. In the last stage of this study, according to the results obtained in the sensitivity analyses, it was observed that the proposed risk assessment methods are quite consistent.

The results indicate that, open-cast mining areas for area criterion and mining machine reasons, OHS trainings should be made more effective to create a safety culture for employees. Additionally, these trainings should be increased according to the occupational accidents in the enterprises and the current needs, not only according to the minimum periods in the occupational and safety regulations. Studies (elimination, substitution, isolation, risk transfer, and engineering controls) should be carried out, and primary vocational training should be given to occupation groups. Precautions should be organized by considering protection principles for the source, environment, and individual, respectively. Special training education related to their profession areas for maintenance personnel should be conducted more frequently by the top management of enterprises.

It is of great importance to review the risk factors identified within the scope of the study and to plan the regulatory studies to be carried out to reduce the lost day accidents in the enterprises. A coherent and overall prevention policy should be developed that covers the impact of factors related to technology, work organization, working conditions, social relations, and the work environment. After all these studies, the risk management process should be continued by monitoring and controlling whether the implementations are carried out. To reduce the risks that cannot be adequately controlled at the source, regular use of appropriate PPEs should be ensured. The use of PPEs for all employees should be supervised and ensured. At this point, employers should also be sensitive to this issue and be aware that it is both human responsibility and a legal obligation.

This study will be a guide for the top management of enterprises and decision-makers with the goal of identifying the existing hazards and associated risks easily to improve enterprises’ conditions through OHS policy for ensuring production sustainability. Considering the complex structure of occupational accidents, decision-makers can easily handle a risk assessment in the mining sector or other industries by using the proposed methodologies in the presented study. The hybrid approaches can be used by integrating the methods used in this study with other multi-criteria decision-making techniques. For further studies, other MCDM approaches, such as VIKOR, Elimination and Choice Translating Reality English (ELECTRE), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), and the Best Worst Method (BWM) can be applied by integrating different fuzzy set extensions such as heuristic, neutrosophic, and spherical. The proposed robust hybrid top-down risk-based classification decision hierarchy algorithm in this study can be expanded to provide a more holistic risk assessment by adding new criteria for other operations in the mining sector. Additionally, these approaches can be diversified to other high-risk sectors.