Introduction

Anesthesiology plays a key role in the healthcare sector. An anesthesiologist’s role extends beyond the operating room to include managing postoperative pain, chronic cancer pain, labor analgesia, cardiac and respiratory resuscitation, blood transfusion therapies, and respiratory therapies1. The wide range of activities performed by anesthesiologists, along with the emergence of new anesthesia and surgery methods, the use of modern equipment and new drugs, and the increase in professional obligations and expectations from them, have caused the workers in this field to face various risks2,3.

The emergence of these risks in this work may cause financial and life-threatening damage, as well as interruptions in the treatment process. Based on past studies, the risks faced by anesthesiologists are diverse and have a high prevalence rate. Surveys indicate a 40% burnout rate among anesthesiologists. This is the highest rate among all specialists working in the hospital4. The estimated 12-month prevalence of musculoskeletal disorders in anesthesiologists is 71.6%5. Additionally, another study found that 46.6% of anesthesiologists experience back pain due to clinical practice6.

The costs associated with these incidents can be significant; for example, the cost of exposure to body fluids in hospital operating rooms is estimated at $271 per 1,000 employees per year7. In addition to affecting the health and performance of anesthesiologists, these risks can negatively impact patient care. In this context, awareness of these occupational hazards and implementation of appropriate precautions are crucial for creating a safer work environment8,9. Identifying and controlling these risks by enhancing the quality of care, improving communication between employees and patients, and reducing complaints of medical errors, brings numerous benefits. As a result, risk assessment in this job is important to keep the potential safety risks within acceptable limits10. Risk assessment involves identifying possible risks caused by hazards and determining their acceptability. This process is a key tool for determining the appropriate risk control strategies and providing mitigation measures11.

So far, many different authors have introduced and used various techniques to identify workplace risks. These methods include Failure Mode and Effects Analysis (FMEA), Fault Tree Analysis (FTA), Event Tree Analysis (ETA), Fine-Kinney (FK), and Hazard and Operability Study (HAZOP), which are referred to as classical risk assessment methods in this study.

Despite their widespread use in risk assessment, classical methods have several limitations that reduce their effectiveness in complex and uncertain environments. These include: (1) the inability to fully capture system complexity, often focusing on limited aspects and a small set of criteria, which can overlook important risk factors11 (2) a lack of capability to handle uncertainty, which may lead to incorrect analysis and decision-making12 (3) evaluation of criteria using fixed or equal weights, without reflecting their true importance13 (4) the use of predefined tables and static data, which may not reflect unique or evolving conditions (5) the subjectivity of assessments, as different individuals may perceive and interpret risk differently based on their experience. These limitations can lead to inconsistent and unreliable assessments when using methods like FMEA14.

In recent years, the use of multi-criteria decision-making systems and fuzzy logic for risk assessment and prioritization in workplace environments has become widespread. Numerous studies have confirmed the advantages of these methods over classical approaches10,15,16,17,18. Research indicates that multi-criteria decision-making systems and fuzzy logic address the shortcomings of classical methods by offering more precise uncertainty management, comprehensive analysis, and adaptability to changing conditions and data19. This study aims to develop a hybrid model for risk assessment in anesthesiology by considering multiple criteria, including consequence (C), probability (P), detectability (D), exposure (E), risk capacity (RC), and their analysis for accurate risk estimation; utilizing fuzzy logic, which allows analysts to better address uncertainty; assigning weights to criteria using the Ordinal Priority Approach (OPA), helping analysts evaluate risks more precisely and make optimal decisions; employing a multi-criteria decision-making system to resolve disagreements and differing analyses among experts, allowing for the structured and systematic collection of diverse opinions for group decision-making; and using the Evaluation Based on Distance from Average Solution (EDAS) method to prioritize risks with higher accuracy.

Based on our knowledge and review, despite numerous studies on risk assessment for anesthesiologists20,21no study has yet employed the EDAS and OPA methods for evaluating the risks associated with this profession. The features of the proposed method make it a safe approach for risk assessment by enabling more precise and detailed risk analysis, along with the capability of sensitivity analysis.

Material and method

Research planning

To ensure a structured approach, the research was planned in sequential phases. First, a comprehensive literature review was conducted to identify occupational risks relevant to anesthesiologists and extract appropriate evaluation criteria. Subsequently, expert interviews were arranged based on a purposive sampling strategy, selecting participants with clinical experience and familiarity with fuzzy decision-making methods. A panel of six experts participated in data collection and prioritization activities. Participants were selected based on certain criteria such as experience, expertise, and informed consent to participate in the study. Risk scores were collected using interval type-2 fuzzy linguistic terms. The OPA method was then used to assign criteria weights, followed by the EDAS method for final risk prioritization. Finally, a sensitivity analysis was conducted using four distinct weight vectors to examine the robustness of the results. The planning ensured traceability, repeatability, and methodological coherence throughout the study. The methods employed in this study are described in the following sections. The main steps of the present study are shown in Fig. 1.

Fig. 1
Fig. 1The alternative text for this image may have been generated using AI.
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Hybrid risk assessment model for anesthesiologists.

EDAS method

EDAS is one of the newest approaches to multi-criteria decision-making systems developed by Keshavarz et al. in 201522. EDAS method is a multi-criteria decision-making approach that evaluates alternatives based on their distances from an average solution. Several extensions of the EDAS have been developed to handle various types of data and uncertainty. These include stochastic EDAS for normally distributed data23interval-valued intuitionistic fuzzy EDAS for vague and incomplete information24and interval-valued neutrosophic EDAS that consider truthiness, falsity, and indeterminacy simultaneously25.

This method measures positive and negative distances according to the type of criterion, which might be positive (the greater the criterion, the better) or negative (the smaller the criterion, the better). The alternative with the highest PDA (positive distance from the average) or lowest NDA (negative distance from the average) is considered the best26. The order of EDAS steps is as follows:

Step 1: Create the decision-making matrix (X) as shown below:

$$\:X={\left[{X}_{ij}\right]}_{n\times\:m}=\left[\begin{array}{cccc}{X}_{11}& \:{X}_{12}&\:\cdots\:&\:{X}_{1m}\\\:{X}_{21}&\:{X}_{22}&\:\cdots\:&\:{X}_{2m}\\\:\vdots&\:\vdots&\:\vdots&\:\vdots\\\:{X}_{n1}&\:{X}_{n2}&\:\cdots\:&\:{X}_{nm}\end{array}\right]$$
(1)

where \(\:{X}_{ij}\) represents the performance value of \(\:ith\:\)alternative on \(\:jth\) criterion.

Step 2: Calculate the average solution based on all the criteria, shown as follows:

$$\:AV={\left[A{V}_{j}\right]}_{1\times\:m},$$
(2)

where,

$$\:A{V}_{j}=\frac{\sum\:_{i=1}^{n}\:\:{X}_{ij}}{n}$$
(3)

Step 3: Calculate the positive and negative distance from the average (PDA and NDA) matrices based on the type of criteria (benefit and cost), shown as follows:

If \(\:jth\:\)criterion is beneficial,

$$\:PD{A}_{ij}=\frac{max\left(0,\left({X}_{ij}-A{V}_{j}\right)\right)}{A{V}_{j}}$$
(4)
$$\:ND{A}_{ij}=\frac{max\left(0,\left(A{V}_{j}-{X}_{ij}\right)\right)}{A{V}_{j}}$$
(5)

And if \(\:jth\:\)criterion is negative (cost),

$$\:PD{A}_{ij}=\frac{max\left(0,\left(A{V}_{j}-{X}_{ij}\right)\right)}{A{V}_{j}}$$
(6)
$$\:ND{A}_{ij}=\frac{\left.max\left(0,\left({X}_{ij}-A{V}_{j}\right)\right)\right)}{A{V}_{j}}$$
(7)

where \(\:PD{A}_{ij}\) and \(\:ND{A}_{ij}\) represent the positive and negative distance of \(\:ith\) alternative from average solution in terms of \(\:jth\:\)criterion, respectively.

Step 4: Calculate the weighted sum of \(\:PD{A}_{ij}\:\)and \(\:ND{A}_{ij}\:\)for all alternatives, shown as follows:

$$\:S{P}_{i}=\sum\:_{j=1}^{m}\:{w}_{j}PD{A}_{ij}$$
(8)
$$\:S{N}_{i}=\sum\:_{j=1}^{m}\:{w}_{j}ND{A}_{ij}$$
(9)

where \(\:{w}_{j}\) is the weight of the \(\:jth\) criterion.

Step 5: Normalize the values of \(\:SP\) and \(\:SN\) for all alternatives, given as follows:

$$\:NS{P}_{i}=\frac{S{P}_{i}}{\underset{i}{max}\:\left(S{P}_{i}\right)}$$
(10)
$$\:NS{N}_{i}=1-\frac{S{N}_{i}}{\underset{i}{max}\:\left(S{N}_{i}\right)}$$
(11)

Step 6: Calculate the appraisal score \(\:\left(AS\right)\) for all alternatives, as shown below:

$$\:A{S}_{i}=\frac{1}{2}\left(NS{P}_{i}+NS{N}_{i}\right),\:\text{W}\text{h}\text{e}\text{r}\text{e}\:0 \le A{S}_{i} \le 1.$$
(12)

Step 7: Rank the alternatives based on decreasing Appraisal Score (\(\:A{S}_{i}\)) values. The alternative with the highest \(\:A{S}_{i}\:\)is the best choice among the alternatives, allowing us to classify them accordingly.

OPA method

OPA is considered one of the most recent methods for multi-criteria decision-making (MCDM) problems. This method was developed in 2020 by Ataei and colleagues to solve MCDM problems that can be structured through ordinal relationships27. Subsequently, the effectiveness of this method in grey and fuzzy environments was established28,29. Additionally, the applicability and accuracy of this approach have been confirmed in various studies30,31,32,33. Most MCDM systems prioritize alternatives using a ranking system without considering their relative superiority11,20. After determining the criteria weights, the second group ranks the alternatives by forming an expert panel and aggregating their opinions.

The OPA method takes a more comprehensive view by considering attributes, alternatives, and experts as the three key factors in any decision-making problem. By taking these three elements into account, it employs a linear programming-based approach to solve complex problems27.

Another merit of the OPA is that there is no need to construct a pairwise comparison matrix. It also allows for the simultaneous calculation of the weights of experts, criteria, and alternatives. There is no need to normalize input data (as the use of different normalization methods in various MCDM approaches can lead to varying results). This method supports group decision-making without requiring averaging, and it accommodates incomplete data if an expert lacks sufficient knowledge about a particular subject or alternative27. This means that if an expert does not have enough information about a specific alternative or criterion, they can leave it unanswered without disrupting the decision-making process, thus preventing judgments based on insufficient knowledge. The steps of the OPA method are summarized below. Table 1 shows the sets, parameters, and variables used in the proposed mathematical model for the OPA method.

Table 1 Sets, parameters, and variables of the OPA method34.
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Step 1: Identify the most important criteria and ensure that no significant criterion is overlooked in the decision-making process.

Step 2: Determine the experts and prioritize them based on their experience, educational background, and type of expertise.

Step 3: In this step, the criteria identified in Step 1 should be prioritized by the experts.

Step 4: Prioritize the alternatives by the experts, taking into account the criteria (if this method is also to be used for prioritizing alternatives).

Step 5: In this step, based on the information obtained from the previous steps, the following model is formed and solved.

$$\:\begin{array}{c}MaxZ\\\:\text{}\text{S}\text{.}\text{t}\text{:}\text{}\\\:Z\le\:i\left(j\left(r\left({W}_{ijk}^{r}-{W}_{ijk}^{r+1}\right)\right)\right)\forall\:i,j,k\text{}\text{a}\text{n}\text{d}\text{}r\\\:Z\le\:ijm{W}_{ijk}^{m}\forall\:i,j\text{}\text{a}\text{n}\text{d}\text{}k\\\:\sum\:_{i=1}^{p}\:\sum\:_{j=1}^{n}\:\sum\:_{k=1}^{m}\:{W}_{ijk}=1\\\:{W}_{ijk}\ge\:0\forall\:i,j\text{}\text{a}\text{n}\text{d}\text{}k\end{array}$$
(13)

where Z is Unrestricted in sign.

After solving Model 13, Eq. (14) can be used to compute the weight of the local alternatives, if needed.

$$\:{W}_{k}=\left[\underset{i}{min}\:\left\{{W}_{ik}\right\},\underset{i}{max}\:\left\{{W}_{ik}\right\}\right]\forall\:k$$
(14)

where \(\:{W}_{ik}=\sum\:_{j=1}^{n}\:{W}_{ijk}\forall\:k\text{\:and\:}i.\).

To determine the local weights of the criteria, Eq. (15) can be utilized:

$$\:{W}_{j}=\left[\underset{i}{min}\:\left\{{W}_{ij}\right\},\underset{i}{max}\:\left\{{W}_{ij}\right\}\right]\forall\:j$$
(15)

where \(\:{W}_{ij}=\sum\:_{k=1}^{m}\:{W}_{ijk}\forall\:j\text{\:and}\text{}i\).

Meanwhile, if necessary, the experts’ weights can be calculated using Eq. (16).

$$\:{W}_{i}=\sum\:_{j=1}^{n}\:\sum\:_{k=1}^{m}\:{W}_{ijk}\forall\:i$$
(16)

The OPA method was preferred over other MCDM techniques such as AHP and VIKOR because it allows handling ordinal input without requiring normalization or pairwise comparisons. It also accommodates incomplete expert judgments and enables simultaneous weighting of experts, criteria, and alternatives, which is essential for group-based decision-making under uncertainty27. Similarly, the EDAS method was preferred over methods like TOPSIS due to its stability in the presence of outliers and its ability to distinguish between benefit and cost criteria based on average values35. These features make OPA and EDAS particularly appropriate for our case, which relies on qualitative expert data in a complex and uncertain medical context.

Prioritizing experts

Based on individual expertise and experience, specific weights can be assigned considering factors including work experience, educational level, job title, and age36. An expert with a higher weight will have a greater influence on the outcomes. In other words, if expert A has an advantage over expert B in the mentioned factors, their opinions on the weighting of criteria will be more important. In the present study, Table 2 and Eq. (17) were used to determine the expert weights and to ensure the reliability of the expert prioritization using the OPA method37,38.

Table 2 Weighting scores of various experts.
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$$\:{W}_{i}=\frac{\text{\:The\:weigh\:score\:of\:}{i}^{th}\text{\:Expert\:}}{\sum\:_{i=1}^{n}\:\text{\:The\:weight\:score\:of\:Experts\:}}$$
(17)

Interval type-2 fuzzy set theory

Fuzzy sets were introduced by Zadeh in 196539. The use of these sets has a more appropriate performance in dealing with uncertainty and ambiguity compared to classical sets.

Interval type-2 fuzzy sets (IT2FS) are an extension of fuzzy sets that can better handle uncertainties in various applications. They can address uncertainties in input variables and system parameters40. IT2FS are a generalization of interval-valued fuzzy sets, offering a broader perspective and representation capabilities41. The use of this method has been proven by researchers in various studies42,43,44. In the following, we present some fundamental concepts related to interval type-2 fuzzy sets (IT2FS):

Definition 2.3.1

Interval type-2 fuzzy sets: Consider \(\:\stackrel{\sim}{\stackrel{\sim}{A}}\) as a type-2 fuzzy set in the universe of discourse \(\:X\) represented by the type-2 membership function\(\:\:{\mu\:}_{\stackrel{\prime }{A}}\). \(\:A\) is called an interval type-2 fuzzy set when all \(\:{\mu\:}_{\stackrel{\prime }{A}}=1\). An interval type- 2 fuzzy set \(\:\stackrel{\sim}{\stackrel{\sim}{A}}\) can be considered a special case of a type-2 fuzzy set, and can be represented as follows45:

$$\:\stackrel{\sim}{\stackrel{\sim}{A}}={\int\:}_{x\in\:X}\:{\int\:}_{u\in\:{J}_{x}}\:1/(x,u),$$
(18)

where\(\:{\:J}_{x}\subseteq\:\left[\text{0,1}\right]\) and ∫ ∫ denotes union overall admissible x and u.

Definition 2.3.2

the trapezoidal IT2FS is presented as shown below46:

$$\:{\stackrel{\sim}{A}}_{ij}=\left({\stackrel{\sim}{A}}_{ij}^{U},{\stackrel{\sim}{A}}_{ij}^{L}\right)=\left(\genfrac{}{}{0pt}{}{\left({a}_{ij1}^{U},{a}_{ij2}^{U},{a}_{ij3}^{U},{a}_{ij}^{U};{H}_{1}\left({a}_{ij}^{U}\right),{H}_{2}\left({a}_{ij}^{U}\right)\right),}{\left({a}_{ij1}^{L},{a}_{ij2}^{L},{a}_{ij3}^{L},{a}_{ij4}^{L};{H}_{1}\left({a}_{ij}^{L}\right),{H}_{2}\left({a}_{ij}^{L}\right)\right)}\right)$$
(19)

Here \(\:{\stackrel{\sim}{A}}_{ij}^{U}\) and \(\:{\stackrel{\sim}{A}}_{ij}^{L}\) are type 1 fuzzy sets, \(\:{a}_{ij1}^{L},{a}_{ij2}^{L},{a}_{ij3}^{L},{a}_{ij4,}^{L}{a}_{ij1}^{U},{a}_{ij2}^{U},{a}_{ij3}^{U},{and\:a}_{ij4}^{U}\:\)represent reference points for IT2F \(\:{\stackrel{\sim}{A}}_{ij}\),\(\:\:{H}_{2}\left({a}_{ij}^{U}\right)\) \(\:and\:\) \(\:{H}_{1}\left({a}_{ij}^{U}\right)\:\:\)are the minimum and maximum bounds for the HMF respectively; and \(\:{H}_{2}\left({a}_{ij}^{L}\right){\:and\:H}_{1}\left({a}_{ij}^{L}\right)\:\)are the minimum and maximum bounds for the LMF respectively.

Definition 2.3.3

If 1 and 2 are two trapezoidal ITF and display them as below47:

$$\:\begin{array}{c}{\stackrel{\sim}{\stackrel{\sim}{A}}}_{1}=\left({\stackrel{\sim}{A}}_{1}^{U},{\stackrel{\sim}{A}}_{1}^{L}\right)=\left(\genfrac{}{}{0pt}{}{\left({a}_{11}^{U},{a}_{12}^{U},{a}_{13}^{U},{a}_{14}^{U};{H}_{1}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{1}^{U}\right)\right)}{\left({a}_{11}^{L},{a}_{12}^{L},{a}_{13}^{L},{a}_{14}^{L};{H}_{1}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{1}^{L}\right)\right)}\right)\\\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{2}=\left({\stackrel{\sim}{A}}_{2}^{U},{\stackrel{\sim}{A}}_{2}^{L}\right)=\left(\genfrac{}{}{0pt}{}{\left({a}_{21}^{U},{a}_{22}^{U},{a}_{23}^{U},{a}_{24}^{U};{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{U}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right)}{\left({a}_{21}^{L},{a}_{22}^{L},{a}_{23}^{L},{a}_{24}^{L};{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{L}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right)}\right)\end{array}$$
(20)

Arithmetic operations can be performed between them as follows.

The addition operation48:

$$\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{1}\oplus\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{2}\&=\left({\stackrel{\sim}{A}}_{1}^{U},{\stackrel{\sim}{A}}_{1}^{L}\right)\oplus\:\left({\stackrel{\sim}{A}}_{2}^{U},{\stackrel{\sim}{A}}_{2}^{L}\right)=\left(\begin{array}{c}\left(\left({a}_{11}^{U}+{a}_{21}^{U},{a}_{12}^{U}+{a}_{22}^{U},{a}_{13}^{U}+{a}_{23}^{U},{a}_{14}^{U}+{a}_{24}^{U}\right.\right.\\\:,\\\:\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right)\right)\\\:\left({a}_{11}^{L}+{a}_{21}^{L},{a}_{12}^{L}+{a}_{22}^{L},{a}_{13}^{L}+{a}_{23}^{L},{a}_{14}^{L}+{a}_{24}^{L}\right.\\\:\left.\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right)\right)\right)\end{array}\right)$$
(21)

The subtraction operation49:

$$\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{1}\ominus\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{2}\&=\left({\stackrel{\sim}{A}}_{1}^{U},{\stackrel{\sim}{A}}_{1}^{L}\right)\ominus\:\left({\stackrel{\sim}{A}}_{2}^{U},{\stackrel{\sim}{A}}_{2}^{L}\right)=\left(\begin{array}{c}\left(\left({a}_{11}^{U}-{a}_{24}^{U},{a}_{12}^{U}-{a}_{23}^{U},{a}_{13}^{U}-{a}_{22}^{U},{a}_{14}^{U}-{a}_{21}^{U}\right.\right.\\\:,\\\:\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right)\right)\\\:\genfrac{}{}{0pt}{}{\left({a}_{11}^{L}-{a}_{24}^{L},{a}_{12}^{L}-{a}_{23}^{L},{a}_{13}^{L}-{a}_{22}^{L},{a}_{14}^{L}-{a}_{21}^{L};\right.}{\left.\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right)\right)\right)}\end{array}\right)$$
(22)

The multiplication operation48:

$$\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{1}\otimes\:{\stackrel{\sim}{\stackrel{\sim}{A}}}_{2}\&=\left({\stackrel{\sim}{A}}_{1}^{U},{\stackrel{\sim}{A}}_{1}^{L}\right)\otimes\:\left({\stackrel{\sim}{A}}_{2}^{U},{\stackrel{\sim}{A}}_{2}^{L}\right)=\left(\begin{array}{c}\left(\left({a}_{11}^{U}\times\:{a}_{21}^{U},{a}_{12}^{U}\times\:{a}_{22}^{U},{a}_{13}^{U}\times\:{a}_{23}^{U},{a}_{14}^{U}\times\:{a}_{24}^{U}\right.\right.\\\:,\\\:\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{U}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{U}\right)\right)\right)\\\:\genfrac{}{}{0pt}{}{\left({a}_{11}^{L}\times\:{a}_{21}^{L},{a}_{12}^{L}\times\:{a}_{22}^{L},{a}_{13}^{L}\times\:{a}_{23}^{L},{a}_{14}^{L}\times\:{a}_{24}^{L};\right.}{\left.\left.min\left({H}_{1}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{1}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right),min\left({H}_{2}\left({\stackrel{\sim}{A}}_{1}^{L}\right),{H}_{2}\left({\stackrel{\sim}{A}}_{2}^{L}\right)\right)\right)\right)}\end{array}\right)\:$$
(23)

Definition 2.3.4

Linguistic terms and their corresponding IT2F values ​​are reported in Table 3. In the present study, this table was used to convert the qualitative values ​​determined by experts for each risk into IT2F values.

Table 3 Linguistic terms and their corresponding interval type-2 fuzzy sets42.
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Validation of the proposed method through sensitivity analysis

To validate the effectiveness and reliability of the proposed risk assessment model, two complementary validation strategies were employed. Sensitivity analysis allows researchers to understand the effect of changing each variable on other variables.

In the first stage, a sensitivity analysis was conducted to examine how changes in the weights of the evaluation criteria affect the final risk rankings. To achieve this, four sets of weight combinations were formed by altering the weights of different criteria. The designed weight vectors are reported in Table 4.

Table 4 The weight vectors composed for the sensitivity analysis.
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In the second stage, expert feedback was gathered to further assess the practical relevance and logical consistency of the results. After completing the risk prioritization using the developed OPA–EDAS approach, the final ranking outcomes were presented to the same group of specialists involved in the initial evaluation process. They were asked to review the results and provide their opinions on the coherence, applicability, and alignment of the prioritization with their real-world experience in the field of anesthesiology. This second stage of validation, based on expert judgment, helped confirm the practicality and acceptability of the proposed model in a professional context.

Case study

In this section, the effectiveness of the developed risk assessment model was evaluated in a real-world environment to address the shortcomings of classical risk assessment methods. Anesthesiologists, due to the high-pressure nature of their work, are exposed to various occupational stresses and hazards, which, if not adequately addressed and controlled, may cause severe harm to them. Therefore, identifying, assessing, evaluating, and controlling these risks using precise methods is very importance. The proposed model was tested as follows.

Risks identification

In the first phase, hazards related to the activities of anesthesiologists were identified. Two primary methods were used to collect data and accurately identify these hazards. First, a comprehensive review of scientific articles and previous studies was conducted to compile a thorough list of common and reported hazards in the anesthesiology profession. These sources included reputable scientific articles, analytical reports, and relevant case studies. Subsequently, to update and complete the identified hazard list, specialized interviews were conducted with anesthesiologists and experienced staff in this field. These interviews aimed to gather expert opinions and practical experiences related to the hazards and risks present in anesthesiologists’ activities. The interview guide developed for this study is provided as a supplementary file (see Supplementary Material 1). The identified risks are shown in Table 5.

The criteria for experts participating in the study were as follows: (1) a bachelor’s degree with at least 6 years of work experience or a higher degree with a minimum of 3 years of work experience; (2) comprehensive knowledge of the duties and activities of anesthesiologists; (3) familiarity with the risk assessment process; (4) familiarity with fuzzy sets, the OPA method, and the EDAS method (necessary training was provided in person for each of these aspects). Ultimately, a comprehensive list of hazards that anesthesiologists encounter in the workplace was compiled and is presented in Table 5. Additionally, the details of the specialists who participated in this study are provided in Table 6.

Table 5 Identified risks.
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Table 6 Characteristics of experts.
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Identifying and defining assessment criteria

Classical risk assessment methods often rely on a limited number of criteria—such as consequence, probability, and detectability—which may not be sufficient to fully capture the complexities and unique demands of high-risk professions like anesthesiology. To address this shortcoming and provide a more comprehensive and tailored evaluation, five criteria were selected for this study based on expert consultation and a thorough analysis of anesthesiologists’ work environment: Consequence (C): refers to the severity of the outcome or harm that the risk may cause to the anesthesiology professional. Since anesthesiologists often work in high-risk environments with time-sensitive tasks and complex equipment, the severity of consequences resulting from overlooked hazards must be carefully assessed. Probability (P): indicates the likelihood of a risk occurring. Given the dynamic and unpredictable nature of surgeries and anesthesia procedures, understanding the probability of risks is essential for effective planning and mitigation. Exposure (E): denotes how frequently anesthesiologists encounter a particular risk. This is especially relevant in their profession, as repetitive exposure to hazards like sharp instruments, infectious materials, or prolonged stress can accumulate over time and increase the likelihood of incidents. Detectability (D): indicates the likelihood that the anesthesiologist can identify and eliminate a hazard before it causes harm. In this profession, the ability to quickly detect personal health threats—such as early symptoms of stress, fatigue, or unsafe exposure—plays a crucial role in preventing harm to the specialist and ensuring continued safe practice. Risk Capacity (RC): refers to the ability of an individual or system to continue functioning effectively under risk conditions. In the context of anesthesiology, this includes the professional’s mental, physical, and procedural resilience during high-pressure situations, such as emergency surgeries or extended shifts. By integrating these five criteria—each of which addresses a distinct yet essential dimension of risk in anesthesiology—the proposed model enables a more nuanced and accurate prioritization of hazards, ensuring that no critical aspect is overlooked.

Results

Formation of the initial risk matrix

Based on the knowledge and experience of the experts, qualitative scores were assigned to the risks using a range of values from very low to very high. Thus, a qualitative score was determined for each of the five different criteria for each risk, and a qualitative matrix was formed. This matrix is ​​given in the appendix section. Next, using the information from Table 2, the qualitative values were converted into fuzzy values, and after defuzzification of these values, the initial risk matrix was formed (Table 7). This table can then be used to prioritize the various risks.

Table 7 Initial risk matrix.
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Determination of weights for criteria involved in risk assessment

The OPA method was used to determine the weights of the different criteria. Initially, the experts’ preferences ranking was established. The weight assigned to each expert is reported in Table 8. As shown in this table, Expert 4 had the highest priority with a weight of 0.230. The judgment of each of the six experts regarding the prioritization of various criteria is presented in Table 9. Finally, using the data from Tables 8 and 9, the final weights of the criteria involved in the risk assessment process were calculated. The weights of these criteria are displayed in Fig. 2.

Table 8 Selected expert profiles and their weighting score.
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Table 9 Rating criteria by experts.
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Fig. 2
Fig. 2The alternative text for this image may have been generated using AI.
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Final weights of the criteria.

Prioritizing the risks of anesthesiologists

Table 10 presents the required values for risk prioritization using the EDAS method, based on the PDA and the NDA. These values are used to calculate the AS, which ultimately determines the risk prioritization. By employing this method, an accurate assessment of the importance of each risk and the urgency of addressing it can be achieved.

Figure 3 illustrates the most significant hazards in the field of anesthesiology, highlighting those that require more immediate control strategies. This figure demonstrates which risks need to be addressed promptly to prevent severe consequences.

Table 10 Results of the EDAS prioritization method.
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Fig. 3
Fig. 3The alternative text for this image may have been generated using AI.
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Prioritizing the risks of anesthesiologists.

Validation of the proposed method through sensitivity analysis

In the first step of sensitivity analysis, in order to comprehensively evaluate the efficiency and ensure the robustness of the proposed model, different weights were assigned to the criteria. The changes in the weights of the criteria and their effect on the results of risk prioritization were investigated. Table 4 lists the different weights given to the criteria, while Fig. 4 clearly displays the effect of these weight changes on the final risk prioritization results. This analysis provides a detailed assessment of the sensitivity of the results to changes in the weights of the criteria and shows the key role of each criterion in determining the final priority. With the help of these results, it is possible to comment on the accuracy and validity of the developed method.

Fig. 4
Fig. 4The alternative text for this image may have been generated using AI.
Full size image

the line chart of parameters’ sensitivity analysis.

In addition, the second stage of sensitivity analysis and the feedback collected from the participating experts confirmed the validity of the proposed model. Most of the experts agreed that the risk prioritization results were logical, consistent with their professional experiences, and practically applicable. They particularly emphasized that the top-ranked risks, such as needlestick injuries and exposure to infectious bodily fluids, accurately reflected the most critical hazards in anesthesiology practice. This expert validation reinforces the robustness and real-world relevance of the proposed approach.

Discussion

Anesthesiologists, due to the hazardous nature of their profession, are exposed to various work-related risks and incidents. Conducting a risk assessment is a critical strategy for preventing the occurrence of such dangers50. Classical risk assessment methods, due to certain limitations, may face challenges in providing a comprehensive, accurate, and all-encompassing evaluation of risks51. This study was conducted with the aim of addressing these limitations and presenting a novel approach to risk assessment.

The findings of the study indicated that the use of the proposed model, due to its consideration of the weights of various criteria, enhances the decision-making process regarding different risks. To establish the criteria weights, experts were ranked based on their job title, educational background, experience, and age. As reported in Table 8, Expert 4, with a weight of 0.230, held the highest priority among the experts. This indicates that when gathering opinions on the prioritization of criteria relative to each other, as shown in Table 9, the opinion of this expert carries more weight in determining the importance of various criteria compared to other experts.

Figure 2 illustrates the calculated weights of the criteria. As shown in this figure, Criterion C, with a weight of 0.445, was the most important criterion in the study. Additionally, Criteria P, E, D, and RC, with weights of 0.265, 0.112, 0.109, and 0.069 respectively, ranked second to fifth in importance. This suggests that risks with higher severity require special attention. While the other criteria are undoubtedly important, high-severity risks carry the potential for irreparable consequences that must be avoided at all costs52.

Another reason for the higher importance of the C criterion compared to other criteria could be that high-severity risks, in addition to affecting staff, may also have negative impacts on the healthcare system and patients53. These effects can range from damage to professional reputation to legal and ethical consequences. Moreover, in an environment like a hospital, patients’ health is highly dependent on the decisions and actions of the medical team. Any high-severity incident could quickly escalate into a critical situation. Therefore, controlling and preventing high-severity incidents is of great importance54. This finding aligns with similar studies in the field.

In Soltani et al.‘s study, which was conducted with the aim of assessing the risks of explosive material warehouses using the combined ARAS-Shannon Entropy method, it was found that Criterion C, with a weight of 0.61, was the most important criterion10. This result was also confirmed in the studies by Akbari et al. and Fatih et al.55,56.

Another outcome of this study was the prioritization of risks using the EDAS method. Due to its features, such as considering the distance from the average, simplicity of calculations, high accuracy in the separation of risks, and transparency in interpreting results, EDAS proved to be a suitable method for risk prioritization57.

As shown in Fig. 3, needlestick injuries (R22) were identified as the most significant risk in the work environment of anesthesiologists. Additionally, exposure to blood, semen, vaginal secretions, and other bodily fluids (R21) and transmission of infectious and contagious diseases such as tuberculosis, SARS-CoV-2, SARS-CoV-1, and H1N1 through the air (R10) were the second and third most critical risks, respectively. Meanwhile, exposure to static magnetic fields and time-varying magnetic fields (from MRI machines, which can cause transient vertigo, nausea, and dizziness) (R4) was ranked as the lowest priority risk.

The high risk of transmitting infectious diseases and potential fatal outcomes due to needlestick injuries among anesthesiologists likely explains why this risk was identified as the most critical in their profession58. This risk is even more pronounced in emergency situations, where rapid action is essential59. Furthermore, the high probability of infection transmission, the extensive use of sharp instruments, substantial work pressure, constant exposure to numerous patients, and the physical, psychological, and legal consequences of needlestick injuries all underscore the prioritization of this risk as the most significant challenge faced by anesthesiologists.

In the study by Yadav et al., needlestick injuries were highlighted as one of the most serious risks for anesthesiologists60. Borna et al. also concluded that needlestick injuries are a major concern, particularly among residents and fellows61. To validate the proposed method, a sensitivity analysis was performed, which is used in risk assessment to assess the stability and accuracy of the results62. Four different weight vectors were created to examine how changes in the weight of each criterion affect the prioritization of risks. The weights were carefully chosen to accurately reflect the impact of each criterion’s weight on the overall risk prioritization.

Table 3 displays the different weight vectors, and Fig. 4 illustrates the results of risk prioritization based on changes in the weights of the criteria. As shown in Fig. 4, the results indicated that altering the weights of the criteria impacted the risk prioritization. In other words, if criteria RC or D are assigned a higher weight than C, the risk prioritization will change accordingly. This finding highlights the precision, validity, and flexibility of the developed method, enabling more accurate and reliable managerial decision-making in risk assessment. In addition, the validity of the proposed method was further confirmed through expert feedback, which supported the logical consistency and practical applicability of the results.

The developed method in this study, with its precision and comprehensiveness in risk assessment, can serve as an effective tool for anesthesiologists in managing and prioritizing risks. By considering key criteria and utilizing multi-criteria decision-making tools, this method enhances the ability to identify and prioritize the most critical risks, helping to reduce the likelihood of accidents and adverse outcomes in the anesthesiologists’ work environment.

Despite the robustness of the proposed model, several limitations must be acknowledged. The findings are derived from a single-case study involving experts from a specific hospital setting, which may limit the generalizability of the results to other institutions or healthcare systems. Moreover, expert judgments, while valuable, are inherently subjective and context-dependent. Additionally, the five selected risk assessment criteria were specifically tailored to the context of anesthesiology. While these criteria are well-justified for this setting, their applicability may need to be re-evaluated for other medical professions or environments with different risk profiles. Future studies should validate this model in diverse healthcare settings and with larger, more heterogeneous expert panels to enhance the external validity of the results. Nonetheless, the methodological framework and analytical procedures developed in this study provide a solid foundation for adaptation and testing in broader healthcare contexts.

Conclusion

In this study, a novel approach was developed to assess the risks faced by anesthesiologists in their work environment. The hybrid model combining EDAS and OPA methods was employed. To address the limitations of classical risk assessment methods and reduce uncertainty and ambiguity, the present study utilized a greater number of criteria, linguistic terms, and fuzzy theory. The results of this study successfully identified and prioritized the most significant risks faced by anesthesiologists with a high level of accuracy. For future research, several additional aspects could be considered. These could include evaluating the efficiency and applicability of the proposed method in other hospital specialties or industries for comparison with the present study, validating the model in different hospitals and healthcare systems to examine the robustness and generalizability of the approach, and the conducting long-term evaluation of the control results of the risks identified in this study based on the statistics of incidents that occur in the work environment of anesthesiologists.