Integrating Fuzzy AHP-TOPSIS for Material Selection in Green Hydrogen and Ammonia Production

The transition to sustainable energy systems has placed green hydrogen and ammonia production at the forefront of global decarbonization efforts [19]. The efficiency, scalability, and environmental sustainability of these technologies are intrinsically linked to the materials employed in their production processes.

Efficiency is a cornerstone criterion in evaluating materials for green hydrogen and ammonia production [20]. Catalytic activity, energy conversion efficiency, selectivity, and reaction kinetics are pivotal sub-criteria. Qadeer et al. [21] demonstrated that ruthenium-based catalysts significantly enhance hydrogen evolution reaction (HER) rates, outperforming traditional platinum-based catalysts. Similarly, Ahmad et al. [22] emphasized the importance of high ionic conductivity in proton exchange membranes (PEMs), which are critical for efficient ion transport in electrochemical systems. Recent advancements in nanostructured materials, such as perovskite oxides, have shown promise in improving energy conversion efficiency by optimizing electronic structures [23]. However, challenges remain in balancing catalytic activity with cost and durability, as highlighted by Haque et al. [24], who noted the trade-offs between performance and material degradation under operational conditions.

The durability and stability of materials are essential for ensuring long-term performance in harsh operating environments [25]. Thermal stability, chemical stability, mechanical stability, and longevity are critical sub-criteria. Sajid et al. [26] explored the use of metal-organic frameworks (MOFs) and perovskites for their exceptional thermal and chemical resilience in ammonia synthesis. Irshad et al. [27] highlighted the degradation mechanisms in electrocatalysts used in high-temperature electrolysis, emphasizing the need for robust materials that maintain structural integrity. Advances in composite materials, such as carbon-supported catalysts, have shown potential in enhancing mechanical stability and extending material lifespan [28]. Despite these advancements, the development of materials that can withstand cyclic loading and extreme conditions remains a significant research focus.

The environmental sustainability of materials is increasingly prioritized in the context of green hydrogen and ammonia production [29]. Carbon footprint, recyclability, toxicity, and resource sustainability are key sub-criteria. Islam et al. [30] examined the environmental implications of various catalyst materials, advocating for the adoption of bio-based and recyclable options to minimize ecological harm. Bora et al. [31] highlighted the potential of renewable materials in reducing greenhouse gas emissions associated with ammonia synthesis. However, the reliance on rare-earth elements in some advanced materials poses challenges for resource sustainability, as noted by Dagwar et al. [32]. The integration of circular economy principles, such as material recycling and reuse, is gaining traction as a strategy to address these challenges.

Economic feasibility is a critical consideration in material selection, encompassing material cost, processing cost, maintenance cost, and economic scalability. Ren et al. [33] analyzed the cost-performance trade-offs of rare-earth elements in catalyst design, suggesting the use of abundant alternatives like iron-based catalysts to reduce costs. Kanth et al. [34] highlighted the high processing costs associated with advanced membranes, emphasizing the need for scalable manufacturing techniques. Recent studies have also explored the potential of low-cost materials, such as nickel and cobalt, in replacing expensive platinum-group metals (PGMs) without compromising performance [35]. However, achieving a balance between cost and efficiency remains a key challenge.

Scalability and innovation are essential for the widespread adoption of green hydrogen and ammonia technologies [19, 30]. Raw material availability, manufacturability, compatibility with emerging technologies, potential for innovation, and integration into circular economy models are critical sub-criteria. Bednarski et al. [36] reviewed the global supply chains for critical materials, highlighting the challenges posed by resource scarcity and geopolitical factors. Yang and Long [37] proposed the use of abundant and renewable materials to overcome these challenges, emphasizing the importance of resource sustainability. Recent advancements in nanotechnology and smart materials have opened new avenues for innovation, enabling the development of materials with enhanced properties and adaptability [38]. The integration of these materials into circular economy models further enhances their sustainability and scalability (Table 1).

Table 1. Hierarchical framework of criteria and sub-criteria for material evaluation in green hydrogen and ammonia production

In the pursuit of advancing green energy ambitions, selecting optimal materials for green hydrogen and ammonia production is paramount to ensuring efficiency, scalability, and sustainability. Nickel-based alloy is one of the alternatives considered for green hydrogen and ammonia production [39]. It is widely recognized for its cost-effectiveness and abundance, making it an attractive option for large-scale deployment [40]. This material exhibits high thermal and chemical stability, which is particularly advantageous for high-temperature electrolysis processes commonly used in hydrogen production [41]. These characteristics ensure that the material can maintain performance under the demanding operational conditions typical of industrial applications. However, nickel-based alloy has notable limitations in terms of its environmental impact. The production of nickel-based alloys is associated with a relatively high carbon footprint, and its recyclability is limited compared to other materials [42]. Furthermore, while it performs adequately in terms of catalytic activity, its efficiency may fall short when advanced properties are required for innovative and highly efficient technologies [43]. As a result, it may be better suited for conventional applications rather than cutting-edge advancements.

Cobalt-doped perovskite oxide offers a more balanced performance across multiple evaluation criteria [44]. Known for its exceptional ionic conductivity, this material is particularly well-suited for membrane applications in hydrogen separation and storage [45]. Its ability to facilitate efficient ion transport makes it a strong candidate for enhancing the overall efficiency of green hydrogen production systems. Additionally, cobalt demonstrates impressive durability, maintaining its structural and chemical integrity under cyclic operational conditions [46]. This durability aligns well with the long-term energy goals of Morocco, where consistent performance in diverse environmental conditions is essential. However, cobalt's limited availability and the environmental concerns associated with its extraction pose significant challenges [47]. Cobalt mining is often linked to ecological degradation and social issues, which could undermine Morocco's commitment to sustainability. Although this material presents a reliable option for advanced applications, these concerns about resource sustainability and environmental impact limit its scalability for large-scale production.

Innovative nanostructured platinum-free catalyst stands out for its groundbreaking catalytic activity, achieving unparalleled energy conversion efficiency in green hydrogen production [48]. The nanostructured design enhances its surface area, enabling faster reaction rates and reducing the energy requirements for hydrogen and ammonia synthesis [49]. This material also aligns closely with environmental criteria, as it is recyclable and has a minimal ecological footprint [50]. Unlike many traditional catalysts, it avoids reliance on scarce and costly platinum-group metals, making it a more sustainable choice. Furthermore, nanostructured catalyst's adaptability to emerging technologies and its potential for future innovation position it as a cornerstone for Morocco's ambitious Green Hydrogen Strategy [51]. While the initial cost of this catalyst is higher compared to other materials, its long-term benefits, including superior efficiency, sustainability, and compatibility with cutting-edge advancements, make it the most promising alternative for driving Morocco’s energy transition.

To establish a pairwise comparison matrix for sub-criteria, more detailed insights are incorporated into the process. These matrices reflect the relative importance of sub-criteria within each of the five main criteria based on nuanced expert judgments in the Moroccan context.

In evaluating sub-criteria, expert judgments were collected using linguistic terms to express preferences, such as "Very High Importance," "High Importance," "Equal Importance," "Low Importance," and "Very Low Importance." These linguistic terms were systematically transformed into triangular fuzzy numbers (TFNs) to address the inherent uncertainty and subjectivity in human judgment. TFNs capture the variability in expert opinions through three parameters: the lower bound (l), the most likely value (m), and the upper bound (u), which represent pessimistic, moderate, and optimistic evaluations, respectively [17]. The TFN scale used in this study is presented in Table 2.

Table 2. Triangular fuzzy number (TFN) scale used in pairwise comparisons

The resulting pairwise comparison matrices reflect the relative importance of each sub-criterion, with higher TFN values denoting greater importance and reciprocal TFNs indicating reduced importance in the context of material selection for green hydrogen and ammonia production. The pairwise comparison matrix for the sub-criteria under C1 is shown in Table 3.

Table 3. Comparison matrix of pairwise evaluations for sub-criteria under C1

Table 4. Hierarchical pairwise comparison matrix for criteria

C11 is consistently rated as significantly more important than other sub-criteria, showing its dominant role in optimizing reaction rates for green hydrogen production. C13 have relatively smaller TFNs, indicating their secondary but relevant roles in ensuring precision in chemical pathways and operational speed, respectively. Once the relative importance of sub-criteria is determined, the process moves to constructing a pairwise comparison matrix for the main criteria themselves, such as evaluating the importance of Efficiency relative to Durability, or Environmental Impact relative to Scalability (Table 4).

This table reveals that C1 and C5 are the most prioritized criteria, reflecting Morocco’s focus on maximizing production performance and scaling renewable technologies to meet industrial and export demands. C2 and C3 hold moderate importance, balancing sustainability and reliability, while C4 is ranked lower, indicating a willingness to prioritize long-term innovation over short-term costs in driving Morocco’s green energy transition.

The calculation of Fuzzy Geometric Means $(\widetilde{G M})$ is a critical step in the Fuzzy AHP methodology (Table 5). It allows to synthesize pairwise comparisons provided by experts into a single representative value for each criterion or sub-criterion, encapsulating their relative importance across all comparisons [63]. It is calculated as:

$\widetilde{G M}_l=\left(\prod_{i=1}^n \widetilde{a_{\imath \jmath}}\right)^{1 / n}$         (1)

where, $\widetilde{a_{\imath \jmath}}$ is the TFN representing the comparison of criterion $i$ to criterion $j$.

Table 5. Fuzzy Geometric means for criteria

C5 and C1 rank highest, emphasizing Morocco's focus on optimizing production and expanding hydrogen and ammonia technologies. C2 and C3 hold moderate significance, ensuring long-term operational reliability and sustainability. C4 is ranked lowest, indicating that financial constraints are secondary to achieving technological advancement and large-scale deployment. These results align with Morocco’s renewable energy strategy, prioritizing efficiency and innovation to strengthen its position in the hydrogen economy.

Normalization of fuzzy weights ensures that the relative importance of each criterion or sub-criterion is scaled proportionately, where the sum of normalized weights equals 1 upon defuzzification [64] (Table 6). This process uses $(\widetilde{G M_J})$ calculated previously and scales them using the following Eq. (2):

$\widetilde{W_J}=\frac{\widetilde{G M_J}}{\sum_{j=1}^n \widetilde{G M_J}}$         (2)

C5 has the highest weight, emphasizing its critical role in ensuring the adaptability and expansion of technologies for large-scale implementation. C1 ranks second with normalized weights, highlighting its vital contribution to optimizing production processes and maintaining overall system performance. C2 follows closely with weights, stressing the necessity of stable and long-term material performance under diverse operational conditions. C4 and C3 hold lower weights, marking their supportive but essential roles in aligning with sustainability objectives, financial feasibility, and eco-friendly practices. These normalized fuzzy weights serve as a foundation for the defuzzification step, which will generate crisp values to finalize the prioritization of criteria.

Table 6. Normalized fuzzy weights for criteria

Defuzzification is the process of converting fuzzy weights represented as TFNs into crisp values that reflect the precise importance of each criterion or sub-criterion (Eq. (3)). This step is vital for ranking priorities in a clear and actionable manner, particularly when moving from fuzzy logic to real-world decision-making applications [65, 66].

$C_j=\frac{\omega_l \cdot l_j+\omega_m \cdot m_j+\omega_u \cdot u_j}{\omega_l+\omega_m+\omega_u}$              (3)

where, $\omega_l, \omega_m, \omega_u$ are weights associated with the lower, middle, and upper bounds to emphasize uncertainty in expert opinions (commonly taken as $\omega_l=1, \omega_m=2, \omega_u=1$, giving priority to the middle value) (Table 7).

Table 7. Final defuzzified weights

C5 holds the highest defuzzified weight (0.26), signifying its essential role in ensuring the adaptability and large-scale implementation of green hydrogen and ammonia technologies. C1 follows with a weight of 0.23, highlighting its significance in optimizing energy output, reaction performance, and overall system functionality. C2, with a weight of 0.19, underscores the necessity of materials that maintain stability under operational stresses. C3 at 0.17 emphasizes the financial feasibility required for widespread adoption, ensuring economic viability. C4, with a weight of 0.14, reflects alignment with Morocco’s sustainability objectives, promoting eco-friendly practices.

The normalized fuzzy weights $\widetilde{W}_J$ act as key inputs in the second part, where Fuzzy TOPSIS evaluates the material alternatives (Material A: Nickel-based alloy, Material B: Cobalt-doped perovskite oxide, and Material C: Innovative nanostructured platinum-free catalyst) against these criteria. The decision matrix constructed in Fuzzy TOPSIS incorporates the criteria weights from Fuzzy AHP [67], ensuring that the influence of each criterion is appropriately reflected in the evaluation of materials. The decision matrix is populated by soliciting qualitative assessments from experts, which are then mapped to TFNs using a predefined linguistic scale [68] (Table 8).

Table 8. Decision matrix for material alternatives and criteria

Material A performs exceptionally well in C1 and C2, making it a strong candidate for long-term stable operations. However, it has slightly lower scores in C4, which may pose sustainability concerns. Material B offers a balanced profile, with solid efficiency and environmental benefits, making it a promising contender for eco-conscious applications. Its C3 rating is moderate, suggesting potential trade-offs between financial feasibility and long-term performance. Material C exhibits competitive scores in C3 and C4, making it an attractive option for economically viable and sustainable solutions. However, its C2 is slightly lower, indicating possible limitations under extreme operational conditions.

To calculate the weighted decision matrix, each element of the decision matrix $\widetilde{X_{l \jmath}}$ is multiplied by the corresponding criterion $\widetilde{W}_J$ (Table 9).

Table 9. Weighted decision matrix for material alternatives

C5 continues to exert significant influence, with Material A maintaining the highest score. C1 reinforces its role in ensuring optimized performance, with Material A and Material C showing competitive results. C2 positions Material B as a resilient choice, while C3 and C4 highlight Material C’s advantage in affordability and sustainability.

The weighted decision matrix lays the groundwork for calculating the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) [69] (Table 10). These serve as benchmarks to evaluate material alternatives. The FPIS represents the most desirable performance across all criteria, while the FNIS represents the least desirable performance [70]. For benefit criteria (e.g., C1, C2, C5), the FPIS corresponds to the maximum fuzzy values among the alternatives, and the FNIS corresponds to the minimum fuzzy values. For cost criteria (e.g., C4, C3, where lower values are preferable), the FPIS is represented by the minimum fuzzy values and the FNIS by the maximum fuzzy values. Mathematically, the FPIS (A⁺) and FNIS (A⁻) for each criterion are defined as:

$A^{+}(C 1, C 2, C 5)=\left\{\left(u_{i j}^{+}\right) \mid \forall \mathrm{j}, u_{i j}^{+}=\max \left(u_{i j}\right)\right\}$           (4)

$A^{+}(C 3, C 4)=\left\{\left(l_{i j}^{+}\right) \mid \forall \mathrm{j}, l_{i j}^{+}=\min \left(l_{i j}\right)\right\}$           (5)

$A^{-}(C 1, C 2, C 5)=\left\{\left(l_{i j}^{-}\right) \mid \forall \mathrm{j}, l_{i j}^{-}=\min \left(l_{i j}\right)\right\}$             (6)

$A^{-}(C 3, C 4)=\left\{\left(u_{i j}^{-}\right) \mid \forall \mathrm{j}, u_{i j}^{-}=\max \left(u_{i j}\right)\right\}$            (7)

Using the performance data from Table 8 and the above definitions, we calculate FPIS and FNIS for each criterion.

Table 10. FPIS and FNIS for each criterion

The FPIS and FNIS establish reference points for evaluating material alternatives. Material A excels in C1 and C5, achieving the highest FPIS values, while Material C ranks lowest in C5. Material B leads in C2, ensuring stability, whereas Material C has the weakest performance in this area. For C4, Material C shows the best results, while Material A scores lowest. C3 favors Material C, making it the most economical option, while Material A has the least desirable score. These values will now be used to calculate distances from ideal and anti-ideal points, forming the basis for ranking the alternatives in the next steps.

Calculating the fuzzy distances between each material alternative and the FPIS and FNIS is essential to determine the relative proximity of each alternative to the ideal and anti-ideal states [71] (Table 11). These distances quantify how closely each material aligns with the best possible performance and how far it diverges from the least desirable outcomes [72]. The distance metric is calculated using a fuzzy Euclidean distance formula, which considers the triangular fuzzy numbers $\widetilde{X_{l J}}=\left(l_{i j}, m_{i j}, u_{i j}\right)$) representing the performance of each material under each criterion and the corresponding $A^{+}$ and $A^{-}$ [73].

The formula for calculating the distance between an alternative i and FPIS ($A^{+}$) is given as [73]:

$\begin{gathered}d_i^{+}=\sum_{j=1}^n \frac{1}{3}\left\{\left(x_{i j}^l-A_j^{+l}\right)^2+\left(x_{i j}^m-A_j^{+m}\right)^2\right. \left.+\left(x_{i j}^u-A_j^{+u}\right)^2\right\}\end{gathered}$            (8)

Similarly, the distance from FNIS (A−) is computed as [73]:

$\begin{gathered}d_i^{-}=\sum_{j=1}^n \frac{1}{3}\left\{\left(x_{i j}^l-A_j^{-l}\right)^2+\left(x_{i j}^m-A_j^{-m}\right)^2\right. \left.+\left(x_{i j}^u-A_j^{-u}\right)^2\right\}\end{gathered}$             (9)

Table 11. Fuzzy distances to FPIS and FNIS for material alternatives

Material A exhibits the shortest distance to FPIS and the largest distance from FNIS, reinforcing its strong alignment with ideal performance across all criteria. Material B has moderate distances to both FPIS and FNIS, making it a balanced choice. Material C has the largest distance to FPIS and the smallest distance to FNIS, indicating relatively weaker performance compared to Materials A and B.

These distances form the foundation for calculating the closeness coefficient (CC), which measures the relative proximity of each material to the ideal solution [74]. CC quantifies the relative closeness of each alternative to FPIS while considering its distance from FNIS.

$C C_i=\frac{d_i^{-}}{d_i^{+}+d_i^{-}}$            (10)

The closeness coefficient $C C_i$ ranges between 0 and 1, where a value closer to 1 indicates that the alternative is nearer to the FPIS (ideal solution) and farther from the FNIS (anti-ideal solution) [75]. Using Eq. (10), CC for each material alternative is calculated based on their previously determined distances to FPIS and FNIS (Table 12).

Table 12. CC for material alternatives

Material C achieves the highest, indicating it is the most suitable option among the three alternatives. This is followed by Material B, which performs moderately well across the criteria. Material A ranks last, reflecting a relatively lower alignment with the ideal solution. These results provide a structured basis for selecting the most optimal material for green hydrogen and ammonia applications.