Selection of essential oil extraction methods using the analytic hierarchy process (AHP) and the preference ranking organization method for enrichment evaluations (PROMETHEE) approaches

2.1. Properties of EOs

2.2. Applications of essential oils

Due to their diverse chemical composition and unique properties, EOs have found applications across a wide range of industries, each benefiting from the specific attributes of these potent natural extracts (Aljaafari et al., 2021; Jugreet et al., 2020):

Pharmaceuticals: EOs are increasingly recognized in the pharmaceutical industry for their therapeutic properties, offering alternative or complementary treatments for various ailments. For instance, eucalyptus oil is used as an expectorant to treat respiratory conditions like coughs and bronchitis (Beraich, Dikici, et al., 2025; El Allaoui et al., 2025), while peppermint oil serves as an effective decongestant (El Ahmadi, El Allaoui, et al., 2025). Oils such as clove and tea tree exhibit antimicrobial and antiseptic properties, making them valuable for treating infections, particularly in dental and dermatological applications. Additionally, EOs are often used to enhance the flavor and aroma of pharmaceutical products, improving patient palatability and adherence to treatment regimens (Beraich, El Farissi, et al., 2025; Wińska et al., 2019).

Cosmetics: In the cosmetics industry, EOs are prized not only for their aromatic qualities but also for their beneficial effects on the skin and hair. They are commonly used in skincare products, such as soaps and shampoos. For example, Rosmarinus officinalis (rosemary) oil is widely recognized for its ability to stimulate hair growth and reduce hair loss. Rosemary oil improves circulation to the scalp, which promotes hair follicle health and combats conditions like androgenetic alopecia (male-pattern baldness). It is often included in shampoos, hair serums, and scalp treatments to strengthen hair and prevent premature hair fall (Lourith & Kanlayavattanakul, 2013). EOs also play a critical role in the fragrance industry, with oils derived from plants such as lavender, sage, and thyme being highly sought after for creating sophisticated and unique perfumes. Continuous innovation in extraction techniques and the sustainable sourcing of raw materials ensure the quality, appeal, and ecological responsibility of modern cosmetic products (Sharmeen et al., 2021).

Food Preservation and Culinary Uses: EOs are widely used in the food industry due to their natural antimicrobial and antioxidant properties, which make them effective as preservatives. For example, Thymus vulgaris (thyme) oil and Origanum vulgare (oregano) oil are well-known for their strong antimicrobial effects against foodborne pathogens, helping to extend the shelf life of perishable goods (Panova et al., 2025). Additionally, Citrus sinensis (orange) oil is commonly used for its antioxidant properties in food preservation, while Syzygium aromaticum (clove) oil is often incorporated for both its antimicrobial activity and its aromatic qualities (El Ahmadi, Haboubi, et al., 2025). These EOs are frequently added to food packaging materials to enhance preservation directly (Konfo et al., 2023). Furthermore, EOs serve as flavor enhancers in various food products. For instance, Mentha piperita (peppermint) oil is used in confectioneries and beverages to provide a refreshing mint flavor, and Citrus limon (lemon) oil adds a bright, zesty flavor to candies and baked goods. This innovative use of EOs highlights their growing importance in modern food technology, blending natural preservation and flavor enhancement with consumer demand for more natural products (Nayak et al., 2020; Salanță & Cropotova, 2022).

Aromatherapy: One of the most traditional and well-known applications of EOs is aromatherapy, where they are utilized for their psychological and physical benefits. For example, Lavandula angustifolia (lavender) oil is widely used in aromatherapy for its calming and relaxing properties. It is commonly inhaled through diffusers to reduce stress, anxiety, and insomnia, promoting a sense of tranquility and improving sleep quality. When mixed with carrier oils for massages, lavender oil also helps alleviate muscle tension and headaches. Additionally, EOs like lavender are incorporated into ointments and creams for direct application. Aromatherapy has gained significant global recognition for promoting holistic well-being, offering a non-invasive approach to health and wellness (Ke et al., 2022).

Agriculture: In agriculture, EOs are increasingly valued for their role in plant protection and crop enhancement. Their natural nematocidal, insecticidal, and fungicidal properties offer a more sustainable alternative to synthetic chemicals, supporting environmentally friendly and organic farming practices. For example, Thymus vulgaris (thyme) oil and Mentha piperita (peppermint) oil are used as natural insecticides to control pests, reducing the need for synthetic pesticides. EOs are also used as biostimulants, which enhance plant growth and resilience. Rosmarinus officinalis (rosemary) oil, for instance, is applied as a biostimulant to promote root growth, increase nutrient uptake, and improve plant stress tolerance. This not only helps in improving crop yields but also supports sustainable agricultural systems by reducing dependency on synthetic growth enhancers. Such practices contribute to healthier soils and ecosystems while maintaining agricultural productivity (Ootani et al., 2013) (Bouhout et al., 2024).

2.3. Challenges in extracting essential oils

Extracting EOs is a complex process fraught with numerous challenges. These range from the degradation of heat-sensitive compounds, which can reduce the oil’s therapeutic and aromatic qualities, to issues like oxidation, which can alter the oil’s fragrance and efficacy. As a result, selecting an appropriate extraction method becomes critical, requiring a balance between efficiency and the preservation of the oil’s complex blend of volatile compounds (Singh et al., 2020).

Chemical Stability Challenges: Maintaining the chemical stability of EOs during extraction is a key challenge. Many contain heat-sensitive compounds, which can degrade on exposure to high temperatures, compromising the oil’s therapeutic and aromatic properties. Therefore, temperature control during extraction is crucial to avoid damaging these delicate components. Another significant concern is oxidation. Prolonged exposure to air can lead to oxidation, which alters the color, fragrance, and efficacy of the oil. While antioxidants can be added during the extraction process to reduce oxidative damage, minimizing air exposure is essential for preserving the oil’s quality.

Furthermore, the complexity of EOs adds to these challenges. They often contain hundreds of different compounds, each with unique properties. To maintain the integrity of the oil, extraction methods must capture the full range of these compounds without causing degradation. Effective management of the extraction parameters is critical to achieving this balance (Mahanta et al., 2021).

Economic Factors: The economic challenges of EO extraction are considerable. Traditional extraction methods (TMs) tend to have lower upfront costs but are often inefficient, leading to longer processing times and higher energy consumption. These inefficiencies can drive up operational costs over time, making these methods less economically viable for large-scale production. In contrast, more modern extraction techniques, while initially more expensive due to the specialized equipment required, provide greater efficiency and higher quality yields. This efficiency can result in lower long-term costs despite the higher initial investment. Balancing these economic factors, including cost, quality, and production scale, is essential when selecting an extraction method (Olusegun et al., 2022).

Techno-Economic Challenges: Nonconventional extraction methods, while producing high-quality and solvent-free EOs, present significant technical and economic challenges. These methods often require specialized equipment that incurs high initial and operational costs. Moreover, scaling these techniques from a laboratory setting to industrial-scale production is complex, as it demands a thorough understanding of the extraction kinetics involved. Effective process design and optimization are essential to minimize energy use and reduce waste, ensuring the process is both cost-effective and environmentally sustainable. However, the need for precise control and significant upfront investment can pose substantial hurdles for large-scale adoption (Moncada et al., 2014).

2.4. Traditional and modern extraction techniques

To address the challenges of EO extraction, a variety of techniques have been developed, each offering distinct advantages and limitations. These methods can be broadly classified into traditional and modern techniques, with each affecting the yield, quality, and purity of the extracted oils (Beraich et al., 2024).

3.1. The AHP method

The AHP, developed by Saaty in 1980, is a widely used method for solving MCDM problems. It enables the evaluation of both measurable quantitative criteria and less tangible qualitative factors. AHP is based on three core principles: structuring the decision problem, making pairwise comparisons of choices and criteria, and synthesizing these comparisons to determine priorities.

The first step in AHP is to structure the decision problem into a hierarchy. This involves breaking down the complex decisions into interconnected elements, objectives, criteria, and alternative, arranged in a hierarchical structure, much like a family tree. The hierarchy typically consists of three levels: the primary goal or overall objective at the top, the criteria that influence the decision in the middle, and the possible alternatives or choices at the bottom. This structured approach helps decision-makers focus on the most important factors and make informed, consistent choices (Bohra & Anvari‐Moghaddam, 2022; Saaty, 1980).

Once the problem is organized into a structured hierarchy, the next step in the AHP involves evaluating the importance of the criteria at each level, starting from the second level down to the alternatives. This is done using a pairwise comparison matrix, where each criterion and sub-criterion is compared against the others with precise consistency. Each pair of criteria is weighed based on how it impacts the level above them, with comparisons typically made on a 9-point scale. This systematic process helps to prioritize and determine the most suitable option.

In this scale, a comparison of a criterion with itself is always assigned a value of 1, and this value is repeated diagonally in the matrix. For other comparisons, odd numbers between 3 and 9 are used based on expert judgments: 1 = equally important, 3 = moderately important, 5 = strongly important, 7 = very strongly important, and 9 = extremely important (Dağdeviren, 2008; Wang & Yang, 2007). In this study, we applied a pairwise comparison to weigh each criterion. The main criteria, yield (C1), quality (C2), cost (C3), environmental impact (C4), and safety (C5), were compared against each other, and the same approach was used for sub-criteria within each category. The result is a matrix that quantifies preferences and calculates ratios for each criterion. The Pairwise Comparison Matrix was developed using the following approach:

$A=\left[\begin{array}{ccccc}{a}_{11}& a_{12}& a_{13}& \cdots & a_{1n}\\ a_{21}& a_{22}& a_{23}& \cdots & a_{2n}\\ a_{31}& a_{32}& a_{33}& \cdots & a_{3n}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ a_{n1}& a_{n2}& a_{n3}& \cdots & a_{nn}\end{array}\right],a_{ii}=1,a_{ji}=\frac{1}{a_{ij}},a_{ij}\ne 0$

At the second step, the mathematical process commences to normalize and find the relative weights for each matrix. The normalized pairwise comparison matrix A_normalized is obtained by dividing each element a_ij by the sum of its column c_j. When c_j is calculated using the following formula:

$C_j={\sum }_{i=1}^n{a}_{ij}$

The a_ij in A_normalized equation is determined by applying the equation below:

$a_{ij}^{normalized}=\frac{a_{ij}}{c_j}$

and then, the structure of the normalized pairwise comparison matrix becomes:

$A_{\text{normalized}}=\left[\begin{array}{ccccc}\frac{a_{11}}{c_1}& \frac{a_{12}}{c_2}& \frac{a_{13}}{c_3}& \cdots & \frac{a_{1n}}{c_n}\\ \frac{a_{21}}{c_1}& \frac{a_{22}}{c_2}& \frac{a_{23}}{c_3}& \cdots & \frac{a_{2n}}{c_n}\\ \frac{a_{31}}{c_1}& \frac{a_{32}}{c_2}& \frac{a_{33}}{c_3}& \cdots & \frac{a_{3n}}{c_n}\\ ⋮& ⋮& ⋮& \ddots & ⋮\\ \frac{a_{n1}}{c_1}& \frac{a_{n2}}{c_2}& \frac{a_{n3}}{c_3}& \cdots & \frac{a_{nn}}{c_n}\end{array}\right]$

The priority vector for each criterion is calculated by averaging the rows of the normalized matrix using the equation below:

$w_i=\frac{1}{n}{\sum }_{j=1}^n\frac{a_{ij}}{c_j}$

Where:

- $w_i$ is the i-th element of the priority vector.

- $a_{ij}$ is the element in the i-th row and j-th column of the original pairwise comparison matrix.

- $c_j$ is the sum of the elements in the j_th column of the original pairwise comparison matrix.

- n is the number of criteria.

3.2. The PROMETHEE method

PROMETHEE is a popular decision-making method used in various fields. It was developed in 1982 by J. P. Brans and first presented at the University of Laval, Quebec, Canada. PROMETHEE is also a rather simple ranking method that is well-suited to problems where a finite number of alternatives have to be ranked according to several, sometimes conflicting, criteria (Verma, 2020). To carry out the PROMETHEE technique, the implementation requires two essential types of information: weights of the criteria and a preference function to estimate the contribution of each alternative with respect to each criterion. The weights indicate the relative importance of each criterion and can be established through various methodologies, such as the AHP, which we’ve used in this study. Moreover, the preference function considers how different choices measure up against each of these criteria. This function assigns a preference degree ranging from 0 to 1, as summarized in Table 1. with various forms available, such as usual, V-shape, level, Gaussian, U-shape, and linear, to suit different decision-making needs. These preference functions help to streamline the comparison process by eliminating scaling effects among criteria, simplifying the mathematical calculations required for ranking alternatives (Oubahman & Duleba, 2021). Overall, PROMETHEE stands out as the most straightforward, efficient, and fastest method among the MCDM techniques available. accessible, efficient, and quickest method among existing MCDM techniques (Deshmukh, 2013; El Abdouni, Haboubi, et al., 2024).

PROMETHEE’s ranking method involves a series of steps, which we have followed to rank oil extraction methods. We have ranked both traditional and modern techniques separately:

Step1: The initial step in applying the PROMETHEE method involves constructing a decision matrix, designated as matrix M_n×c where n is the number of alternatives and c is the number of criteria. In the decision matrix, each entry in the matrix quantifies the performance of a specific essential oil extraction method according to a designated criterion. Since these criteria can vary greatly in how they are measured. They can be meaningfully compared and aggregated by normalizing them to a unified scale from 0 to 1. For example, the Cost metric is measured in dollars, Yield in grams, and yet another in arbitrary units, as is the case for quality, environmental impact, and safety. This normalization ensures that each criterion contributes equitably to the overall assessment, preventing any single criterion from disproportionately skewing the results due to its measurement scale.

Step2: Normalize the Decision matrix M_n×c, which involves subtracting the minimum value from each criterion score and dividing by the range (maximum - minimum) for that criterion across all alternatives. The result is a matrix where the scores for each criterion are scaled between 0 and 1. The normalization equation for beneficial criteria, such as yield and quality, is applied to enhance comparative analysis.

$R_{ij}=\frac{\left[X_{ij}-min\left(x_{ij}\right)\right]}{\left[max\left(x_{ij}\right)-min\left(x_{ij}\right)\right]}$

Conversely, for non-beneficial criteria like cost, environmental impact, and safety, a different normalization equation is used to ensure that lower values indicate better performance.

$R_{ij}=\frac{\left[max\left(x_{ij}\right)-X_{ij}\right]}{\left[max\left(x_{ij}\right)-min\left(x_{ij}\right)\right]}$

Step3: Determination of deviation by pairwise comparison by subtracting the score of one alternative from the score of the other (e.g., M1 and M2) using the following equation:

$D_{(M1\text{\ }–\text{\ }M2)}=(R_{\left(ij\right)1}-\text{\ }{R}_{\left(ij\right)2})$

Step4: Determine the Preference Functions (P) for each criterion (c). This function quantifies the difference in evaluations between any two alternatives (e.g., M1 and M2) for a specific criterion into a preference degree ranging from 0 to 1. The preference function (P_j)​ translates how one alternative is preferred over another based on the calculated deviation (Oubahman & Duleba, 2021). The preference function is applied using the following conditions in the Table 2:

Condition 1 applies when M1 is not better than M2, thus showing no preference for M1 over M2. Condition 2 applies when M1 outperforms M2, with the degree of preference being proportional to the deviation multiplied by the weight of the criterion.

Step5: determine the multi-criteria preference index (π), which represents an overall preference of one alternative over another by aggregating the preference degrees from all criteria. The multi-criteria preference index π for a pair of alternatives M1 and M2 is given by:

${\pi }_{\left(M1,M2\right)}={\sum }_{j=1}^c{P}_j\left(M1,M2\right)$

Here, c represents the total number of criteria, j=1 indicates the starting point of an index for summation, ensuring that the aggregation begins with the first criterion. Importantly, the summation of the criteria weightages, which encompasses all criteria from the first to the last, always equals 1, maintaining a balanced and normalized evaluation across all considered factors.

Step6: Calculate the Outranking Flows for each alternative by summing the degrees of preference (π) of that alternative over all others. It indicates how much an alternative is preferred over others. Conversely, the negative flow is calculated by summing the degrees of preference (π) of all the other alternatives over the alternative under consideration. This indicates how much it is disfavored compared to the others. The Positive flow was calculated using the following formula:

${\varphi }^{+}\left(M_i\right)={\sum }_{j=1,j\ne i}^n{\pi }_{\left(Mi,Mj\right)}$

Here, π_{(Mi, Mj)} is the preference degree of M_i over M_j, and the summation excludes j=i to avoid self-comparison. And to calculate the Negative Flow the formula used is the following:

${\varphi }^{-}\left(M_i\right)={\sum }_{j=1,j\ne i}^n{\pi }_{\left(Mj,Mi\right)}$

Here, π_(Mj,Mi) represents the degree to which M_j is preferred over M_i, ensuring that j=i for meaningful external evaluations.

ϕ⁺(M_i): Represents the total preference given to alternative M_i ​ compared to all others, summing up the individual preferences where M_i ​is favored. ϕ⁻(M_i): Represents the total preference given to all other alternatives over M_i, aggregating instances where M_i is less preferred.

Step7: Calculate Net Flows and Rank the Alternatives. The net flow for each alternative is obtained by subtracting the negative flow from the positive flow. Alternatives are then ranked based on their net flows, from the highest to the lowest, to determine the most to least preferred methods for essential oil extraction, and this is done using the formula:

$\varphi \left(M_i\right)={\varphi }^{+}\left(M_i\right)-{\varphi }^{-}\left(M_i\right)$

A positive net flow indicates a generally preferred alternative, while a negative net flow suggests it is less favored. Once the net flows are calculated for all alternatives. Alternatives are ranked from the highest to the lowest net flow. The alternative with the highest net flow is ranked first as it is the most preferred overall, considering the sum of all evaluations against all other alternatives. This ranking helps in identifying the best option or prioritizing multiple options based on their overall effectiveness and acceptability in the decision-making context.

3.3. Sensitivity analysis approach

To assess the impact of changes in criteria weights on the ranking of EO extraction methods, a sensitivity analysis was conducted using the AHP and PROMETHEE methodologies. The analysis was performed in four distinct scenarios:

• 1.

  Baseline Scenario (Original Weights): The original weight distribution from the AHP analysis was used.

• 2.

  Scenario 1 – Emphasizing Cost & Environmental Impact: Increased the weights of cost (C3) and environmental impact (C4), while reducing the emphasis on yield (C1).

• 3.

  Scenario 2 – Prioritizing Quality & Safety: Increased the importance of quality (C2) and safety (C5) while reducing the influence of cost and environmental impact.

• 4.

  Scenario 3 – Balanced Approach: Distributed weights more evenly across all criteria to assess the robustness of ranking stability.

For each scenario, the weighted scores of both traditional and modern extraction methods (MMs) were recalculated using PROMETHEE. The ranking results from each scenario were compared to the baseline rankings to determine the degree of sensitivity to weight variations. If the rankings change significantly when weights are modified, it indicates that the choice of extraction method is highly dependent on the assigned criteria priorities. Conversely, if certain methods consistently rank highly across different scenarios, it confirms their overall effectiveness and adaptability.

4.1. Evaluation of criteria through AHP

The evaluation of EO extraction methods through the AHP in this study categorizes various criteria, namely (C1), (C2), (C3), (C4), and (C5), along with their respective sub-criteria, labelled from SC1.1 to SC1.3 for each criterion up to SC5.3. These criteria form a robust framework for assessing the effectiveness of different extraction techniques. Tables 3 and 4 present the results matrix of the pairwise comparison using the Saaty rating scale. The weighting of each criterion (Table 3) and sub-criterion (Table 4) was determined based on expert opinions, technical knowledge, and general sustainability criteria for selecting essential oil extraction methods. Additionally, the normalized outcomes are also presented.

Table 5 outlines the weights for each main criterion and its associated sub-criteria, along with their CR to ensure the reliability of the evaluations. Fig. 3 features a pie chart that offers a visual representation of each criterion’s weight, providing a quick and intuitive understanding of their relative importance in the decision-making process. The primary criteria weights underscore strategic priorities: Yield is paramount, commanding a dominant weight of 48.25%, reflecting its critical role in enhancing the efficiency and output of the extraction methods. Following closely is Quality, valued at 23.58%, which highlights the imperative for superior product standards. Safety is also emphasized, with a weight of 15.22%, reinforcing the focus on secure operational protocols. Conversely, Cost and Environmental Impact are deemed less pivotal yet necessary considerations within the decision-making framework, assigned weights of 8.7% and 4.3% respectively.

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Fig. 3.

Distribution of weights among various criteria and sub-criteria derived from an AHP analysis.

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In terms of sub-criteria, Efficiency within Yield stands out with a weight of 64.33%, prioritizing optimal production efficiency. Chemical Profile, crucial within the Quality criterion, holds a weight of 63.33%, stressing the retention of essential chemical characteristics. Moreover, Operator Safety leads the Safety criterion with a significant weight of 72.35%, underscoring a strong commitment to safety measures. The overall CR of 0.076 confirms that the pairwise comparisons are consistently made, suggesting the judgments in the AHP analysis are coherent and reliable. Sub-criteria matrices also maintain CR values below 0.1, further validating the consistency of the evaluation process.

4.2. Ranking alternatives through PROMETHEE

In this phase of the study, various MMs and TMs were assessed based on predetermined criteria critical to the extraction process. The assessment results are systematically organized into an evaluation matrix. This matrix quantitatively represents the performance of each method against the criteria of yield, quality, cost, environmental impact, and safety. The detailed evaluations of the eleven alternative extraction methods, as per the specified criteria, have been presented in Tables 6 and 7 below, providing a clear basis for comparison and further analysis.

Upon establishing the evaluation matrix and defining the preference functions, the alternative methods were assessed using the Decision Lab software. This analytical process yielded the positive flow (φ⁺), negative flow (φ⁻), and net flow (φ) values for each alternative. These values are crucial for determining the ranking and selection of the most suitable methods, are presented in Tables 8 and 9. This encapsulates the results from the PROMETHEE method, illustrating the comparative strengths and weaknesses of each method based on the calculated flows, thereby guiding the decision-making process.

By using the positive and negative flow values presented in Table 8, the partial ranking of TMs is initially determined using the PROMETHEE I methodology. PROMETHEE I is a Partial Ranking networking and Fig. 4 presents the graph network ranking for MMs of EOs.

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Fig. 4.

PROMETHEE I Partial Ranking for TMs of EO.

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4.3. Sensitivity analysis of criteria weights on ranking outcomes

Sensitivity analysis is a crucial step in MCDM as it evaluates how changes in criteria weights impact the final rankings of extraction methods (Liu & Liu, 2024). Given that different industries prioritize factors such as yield, cost, environmental impact, and safety differently, adjusting the weight distribution helps determine whether the preferred extraction method remains robust under varying conditions. This analysis strengthens the reliability of the findings by assessing the extent to which ranking outcomes shift when different priorities are emphasized. This study provides a more comprehensive understanding of which extraction methods are the most resilient and which ones may be optimal under specific constraints. Tables 10 and 11 present the results of the sensitivity analysis, showing how modern and TMs rank under different weighting scenarios.

The sensitivity analysis, evaluated through net flow variations (Fig. 9), confirms the robustness of SFE as the top-ranked MM in most scenarios. However, when cost and environmental impact are prioritized, SFME emerges as a cost-effective and sustainable alternative. MAE remains stable in mid-rank positions, reflecting its balanced performance across different evaluation criteria. For TMs (Fig. 8), SD proves to be the most adaptable, ranking highest in the original, cost-focused, and balanced scenarios. This suggests that SD is a preferred method for industries that balance efficiency, cost-effectiveness, and environmental concerns. However, CP outperforms other methods when quality and safety are prioritized, making it ideal for premium EO extraction. Conversely, HMD and Microwave Hydro Diffusion & Gravity (MHG) consistently rank lowest across all criteria, indicating their limited competitiveness in practical applications.

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Fig. 8.

Net flow variations of TMs across different weighing scenarios.

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Fig. 9.

Net flow variations of TMs across different weighing scenarios.

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4.4. Acknowledgment of study limitations

This study recognizes certain limitations that may impact the generalizability and applicability of its findings. First, the weighing of criteria and sub-criteria in the AHP analysis was based on expert judgments, which, while informed, may introduce subjective biases. The selection of experts and their individual experiences could influence the assigned weights, potentially reflecting preferences specific to certain industries or contexts. Additionally, data availability constrained the analysis to a finite number of extraction methods and criteria. While the study incorporated a range of both traditional and modern extraction techniques, emerging methods or less-documented techniques may not have been fully represented. Furthermore, reliance on available data may omit region-specific practices or recent innovations that could shift optimal extraction method recommendations. Future research could expand the scope of expert input and include a more diverse set of methods, thereby enhancing the robustness and applicability of the results across various industries and geographical contexts.