Advancing sustainable aviation by integrating renewable solar energy into unconventional airport spaces using a spherical fuzzy CRITIC–RATGOS approach

Abstract

The integration of renewable energy into airport operations is critical as the aviation sector advances toward sustainability and carbon neutrality. Solar energy stands out as a scalable, cost-effective solution that can seamlessly integrate with existing airport infrastructure. While conventional applications such as rooftop and ground-mounted photovoltaic (PV) systems are common, the potential of unconventional solar solutions in underutilized airport spaces remains largely unexplored. This study addresses this gap by prioritizing solar energy alternatives for non-traditional airport spaces using a Spherical Fuzzy CRITIC–RATGOS framework. Istanbul Airport, with its high energy demand and expansive infrastructure, serves as the case study. A panel of eight experts evaluated five key criteria: economic feasibility, environmental impact, technological efficiency, scalability, and operational reliability. The analysis identified solar canopies over parking areas (SC-PA) and solar farms on unused land (SF-UL) as the most viable alternatives due to their economic attractiveness, scalability, and minimal operational disruptions. Floating solar panels on reservoirs (FS-WR) also showed strong potential by conserving land and offering environmental benefits, albeit with additional regulatory considerations. Lower-ranked options, such as solar-integrated pathways and runways, face challenges related to safety, cost, and aviation regulations. A scenario-based sensitivity analysis confirmed the robustness of the rankings, reinforcing the reliability of the proposed model. These findings offer actionable insights for airport authorities and policymakers, emphasizing the importance of multi-layered solar strategies, regulatory incentives, and financing mechanisms like power purchase agreements (PPAs). By utilizing underused spaces for solar deployment, airports such as Istanbul Airport can significantly reduce grid dependency, improve energy resilience, and align with global sustainability targets.

Introduction

Background and motivation

The aviation sector is undergoing a major transformation as it strives to meet global sustainability targets. Airports, as high-energy consumption hubs, are increasingly adopting renewable energy solutions to reduce their environmental impact. Among these solutions, solar energy stands out for its scalability, cost-effectiveness, and compatibility with airport infrastructure¹. While rooftop and ground-mounted solar installations are well-established, the potential for integrating solar energy into unconventional airport spaces remains largely untapped.

Istanbul Airport, one of the world’s largest aviation hubs, offers a significant opportunity to lead in this area. Opened in 2018 and spanning over 7,600 hectares, it is designed to serve up to 200 million passengers annually, making it one of Turkey’s most energy-intensive facilities. As part of its sustainability strategy, the airport has committed to renewable energy initiatives, including a planned 199 MW solar farm aimed at reducing fossil fuel dependence². Beyond large-scale solar farms, the airport’s extensive non-traditional spaces—such as parking canopies, taxiways, water reservoirs, and terminal facades—could be strategically used for solar energy production, following global best practices.

International examples highlight the feasibility of solar energy in airport operations. Cochin International Airport in India became the world’s first fully solar-powered airport, generating about 40 MW annually through rooftop and ground-mounted systems³. Denver International Airport operates over 10 MW of solar farms, covering nearly 6% of its energy needs⁴. George Airport in South Africa uses solar power to meet over 40% of its electricity demand, showcasing the success of such integration even in medium-sized facilities⁵. Istanbul Airport has the potential to adopt similar or even more innovative solar strategies to support its long-term sustainability goals.

Globally, the adoption of airport solar projects varies depending on policies, incentives, and regulatory frameworks. In the United States, the FAA supports solar integration through programs like the Voluntary Airport Low Emissions (VALE) program and the Airport Improvement Program (AIP), offering financial incentives⁶. In Europe, strict climate targets and feed-in tariffs have driven airports such as Frankfurt and Munich to expand large-scale solar installations⁷. Asia-Pacific has seen ambitious programs, with India mandating solar adoption at major airports, leading to large-scale projects in Delhi, Kolkata, and Hyderabad⁸. Turkey’s renewable energy policies, including the YEKDEM feed-in tariff program and net metering regulations, further strengthen the case for Istanbul Airport’s solar potential^9,10.

Innovative solar deployments in non-traditional spaces—such as parking lots, taxiways, decommissioned runways, reservoirs, and pedestrian pathways—offer further opportunities to enhance energy efficiency and resilience. Istanbul Airport’s vast open spaces and reservoirs provide ideal settings for such projects. For example, converting 50% of parking areas into solar canopies could supply up to 25% of annual energy demand¹¹. Floating solar panels on water reservoirs could generate 5–15 MW depending on surface area and sunlight exposure¹². While promising, these projects require careful prioritization based on economic, environmental, and operational factors.

Overall, Istanbul Airport has a unique opportunity to become a leader in sustainable aviation. By adopting an integrated solar strategy, it can reduce its carbon footprint, enhance energy resilience, lower operational costs, and set an example for other major airports globally. Focusing on unconventional solar applications aligns with international trends and national energy policies, making it a critical area for research and strategic development.

Research gap and justification

Most existing studies have focused on conventional solar applications in airports, particularly rooftop and ground-mounted photovoltaic (PV) systems^13,14. In contrast, unconventional solar applications—such as solar canopies in parking areas, floating solar farms on airport water bodies, and building-integrated photovoltaics (BIPV) in terminal structures—remain largely underexplored in both academic and industry literature¹⁵. While some airports have started adopting these novel solutions, systematic frameworks for evaluating and prioritizing such applications are scarce. For example, Singapore’s Changi Airport has installed a large-scale rooftop system generating about 43 MW of clean energy, yet there is limited research on the feasibility of floating solar panels over its reservoirs¹². Similarly, Munich Airport is expanding its solar capacity to meet net-zero goals by 2035, but the prioritization of different solar technologies within its infrastructure remains unclear¹⁶. The European Union’s Renewable Energy Directive and national policies in Germany and the UK further emphasize the importance of regulatory alignment in driving on-site solar adoption at airports¹⁷.

At Istanbul Airport, renewable energy efforts include a planned 199 MW off-site solar farm². However, the potential for on-site solar integration across its vast infrastructure—including parking areas, taxiways, rooftops, and water reservoirs—remains underexplored. Despite these opportunities, no systematic framework currently exists to assess and prioritize these unconventional applications within the airport’s sustainability strategy.

In emerging economies, solar adoption in airports often aligns with national sustainability mandates. India, for instance, offers subsidies and mandates renewable energy integration at airports, making projects like Cochin International Airport feasible⁸. Similar trends are observed in the Middle East under national strategies such as the UAE’s Clean Energy Strategy and Saudi Arabia’s Vision 2030, both promoting large-scale airport solar projects¹⁸. In Africa and Latin America, airports in countries like Ghana and Ecuador are integrating solar energy to reduce costs and enhance resilience against unreliable grid power¹⁹.

Despite these global advancements, a comprehensive framework to evaluate and prioritize unconventional solar applications at airports remains missing. Integrating multi-criteria decision-making (MCDM) methods with fuzzy logic offers a robust tool for airport managers and policymakers to assess solar energy projects based on sustainability impacts²⁰. This study addresses this gap by proposing a structured prioritization model using the Spherical Fuzzy CRITIC–RATGOS method. Applying this model to Istanbul Airport aims to generate actionable insights for optimizing on-site solar integration in one of the world’s largest and most energy-intensive aviation hubs, serving as a reference for similar large-scale airport infrastructures.

Research objectives

This study aims to:

• Identify and assess unconventional solar energy applications in airport spaces.

• Develop a structured decision-making framework that prioritizes these applications.

• Apply the Spherical Fuzzy CRITIC–RATGOS method to evaluate and rank different solar energy alternatives based on multiple sustainability criteria.

Contributions of the study

This study makes a significant contribution by systematically identifying and assessing unconventional solar energy applications specifically within Istanbul Airport, expanding the current understanding of sustainable aviation infrastructure. By analyzing the feasibility of non-traditional photovoltaic applications—such as solar canopies in parking areas, solar-integrated pedestrian pathways, and floating solar arrays on airport reservoirs—the research provides a novel framework for optimizing solar deployment in large-scale aviation hubs. Leveraging underutilized airport spaces enables the maximization of renewable energy production while ensuring that core aviation operations remain unaffected.

A major advancement of this research is the development of an integrated decision-support tool that combines multi-criteria decision-making (MCDM) with fuzzy logic to systematically evaluate and prioritize solar energy applications. The application of the Spherical Fuzzy CRITIC–RATGOS method enhances decision-making precision by addressing uncertainties in sustainability assessments, ensuring that the most viable and impactful solar solutions are selected for Istanbul Airport. This structured framework allows airport authorities to balance economic feasibility, operational efficiency, and environmental sustainability in their renewable energy strategies, setting a benchmark for similar large-scale airport infrastructures.

By analyzing global trends and policy frameworks, this study provides a comparative perspective on airport solar adoption while grounding its findings in the context of Istanbul Airport. The research highlights successful case studies from airports such as Cochin International Airport, Denver International Airport, Frankfurt Airport, and Singapore Changi Airport, demonstrating how regulatory support, economic incentives, and technological innovations can accelerate solar energy integration. By applying these insights to Istanbul Airport, the study offers practical recommendations tailored to its specific operational and environmental conditions. Ultimately, the findings contribute to the broader goal of decarbonizing the aviation industry by showcasing how strategic solar energy investments can enhance sustainability, energy independence, and resilience in one of the world’s largest aviation hubs.

Conceptual framework

The role of renewable energy in aviation

Renewable energy is playing an increasingly vital role in aviation as airports work to reduce their carbon footprints and improve operational efficiency. Solar photovoltaic (PV) systems have emerged as a key strategy to reduce reliance on fossil fuels and support global sustainability targets. Anurag et al.¹ emphasize essential factors for designing airport-based PV systems, such as panel orientation, efficiency optimization, and minimizing glare to ensure aviation safety, highlighting their potential to boost self-sufficiency without operational disruptions.

Supporting these findings, Baxter¹¹ demonstrates that combining solar energy with other green technologies significantly reduces emissions at Brisbane and Melbourne airports. Similarly, Baxter, Srisaeng, and Wild²⁰ (2019) reveal that solar systems at Adelaide Airport lowered energy costs and enhanced resilience against power fluctuations. Choudhary, Saxena, and Mishra¹³ report that solar PV systems in three Indian airports achieved 30–40% reductions in electricity costs while advancing national renewable energy targets. Furthermore, El Zein, Karimipanah, and Ameen¹⁵ advocate for combining solar, wind, and hydrogen fuel cells to create fully self-sufficient airport ecosystems. In addition, Firozjaei et al.²⁰ highlight airports as ideal sites for solar PV due to their expansive rooftops and open areas. Goh et al.²² propose an integrated energy strategy using solar, wind, and waste-to-energy solutions to help airports reach carbon neutrality by 2050. Similarly, Kim et al.²³ find that optimized PV installations could meet up to 30% of electricity needs at Korean airports without disrupting operations, while Kim¹⁴ underscores the importance of policy support and financial incentives in driving adoption.

Moreover, global studies strengthen this evidence. Sirisamphanwong et al.²⁴ show that advanced PV coatings and strategic configurations in Thai airports reduce glare and enhance energy output. Sreenath, Sudhakar, and Yusop³ highlight strong economic and environmental benefits at seven Indian airports. Teofilo et al.²⁵ demonstrate the potential of rooftop PV systems at Australian airports, and Yadav et al.²⁶ show that hybrid solar-wind systems increase energy resilience at Nepal’s Biratnagar Airport. Yousuf, Saleem, and Umair²⁷ confirm the sustainability of solar PV in airports through a 7E analysis, while Zhou²⁸ emphasizes integrating solar and hydrogen storage for low-carbon transitions.

Furthermore, policy and financial incentives are crucial drivers of solar adoption worldwide. In the United States, the FAA’s VALE program and the Investment Tax Credit (ITC) support airport solar projects⁶. European airports benefit from the EU Renewable Energy Directive, with Germany and the UK enforcing strict emission reduction targets⁷. Across Asia-Pacific, India mandates solar PV adoption at major airports and provides subsidies of up to 30%⁸. Middle Eastern airports participate in national sustainability programs such as the UAE’s “Shams Dubai” rooftop initiative¹⁷. Meanwhile, in Africa, South Africa, Ghana, and Kenya invest in solar energy to reduce reliance on unstable grid power. Latin American airports, like Galápagos Ecological Airport in Ecuador, illustrate fully renewable models through combined solar and wind energy systems¹⁸.

Taken together, these studies underscore that solar PV systems—whether used alone or in hybrid models—can significantly cut energy costs, strengthen sustainability performance, and support the transition to carbon-neutral airport operations. They highlight the urgent need for structured, comprehensive decision-making frameworks to guide the effective selection and prioritization of solar energy solutions in aviation environments.

Unconventional solar energy applications in airports

As airports accelerate their shift toward sustainable energy, unconventional solar applications have emerged as innovative strategies to maximize on-site renewable generation. These approaches extend beyond traditional rooftop and ground-mounted photovoltaic (PV) systems, incorporating solutions such as solar canopies in parking areas, solar-integrated walkways, floating solar panels on reservoirs, solar-powered electric vehicle (EV) charging stations, and building-integrated photovoltaics (BIPV) in terminal structures. For example, solar canopies installed over airport parking lots offer dual benefits: generating clean energy and providing shaded parking, thus reducing heat island effects. Pantić et al.²⁹ emphasize the contribution of solar parking canopies to urban energy-efficient planning, while Fakour et al.³⁰ show that integrating these canopies with EV charging stations enhances both energy production and sustainability outcomes in airports. Deshmukh and Pearce³¹ further highlight that solar awnings in parking areas can supply up to 50% of the energy needed for EV charging, supporting sustainable transport initiatives.

Moreover, solar-integrated pedestrian walkways present another promising application. Ramalingam et al.³² (2020) propose incorporating solar energy into pedestrian and transportation infrastructure to support lighting and localized power needs. Tomasi et al.³³ suggest that integrating PV materials into walkways can improve energy production and enhance user comfort. Similarly, Jung³⁴ indicates that photovoltaic pavements can improve air quality and create favorable microclimates while producing clean energy.

Floating solar PV systems offer innovative solutions for airports facing land constraints. Yashas et al.³⁵ highlight that floating solar panels on lakes can reduce water evaporation while generating electricity. Solomin et al.³⁶ demonstrate the applicability of hybrid floating solar designs to airport reservoirs and stormwater ponds, and Srivastava et al.³⁷ estimate that such systems can meet 20–30% of an airport’s annual energy demand. Additionally, Islam et al.³⁸ confirm the feasibility of floating PV in urban settings, emphasizing their role in optimizing underused water surfaces. Furthermore, integrating solar PV with EV charging infrastructure advances airport electrification goals. Khan et al.³⁹ underline the potential of solar-powered EV chargers to reduce reliance on grid electricity. Naseri et al.⁴⁰ introduce a site selection model identifying airports as prime locations for solar charging stations, and Shukla et al.⁴¹ highlight how battery-integrated solar stations ensure reliable supply even during peak demand.

BIPV technologies, which incorporate solar panels directly into terminal structures, represent another effective strategy to boost on-site renewable generation. Riahi Dehkordi et al.⁴² conclude that BIPV can lower energy costs while enhancing architectural aesthetics. Sreenath et al.⁴³ suggest that BIPV can be integrated without affecting aviation operations, while Jiang et al.⁴⁴ show that airports with large terminal roofs can significantly benefit from these systems. In practice, many airports have already piloted or adopted these unconventional applications, showcasing the diversity and potential of innovative solar energy strategies in aviation infrastructure. Table 1 summarizes selected case studies, illustrating how airports worldwide are leveraging these solutions to enhance sustainability and operational resilience.

Table 1.

Case studies of unconventional solar Implementations.

Airport (Country)	Unconventional Location	Capacity	Key Outcomes
Gatwick Airport (UK)	Ground near main runway (150 m away)	0.05 MW (200 + panels)	Pilot project (2012) showed no interference; paved way for larger arrays in the future45.
Chattanooga Metro Airport (USA)	Disused land (on-site solar farm + battery)	2.74 MW	First US airport 100% powered by solar; $10 M project (FAA-funded) with microgrid can run off-grid. Expected to recoup ~$5 M in 20 years from energy savings46.
Miami Intl Airport (USA)	Floating solar on retention pond	0.157 MW	First floating airport solar farm (2023); uses quarry lake on approach path for power generation, demonstrating innovative use of water surface47.
Frankfurt Airport (Germany)	Vertical PV in runway infield	0.0084 MW (pilot); Planned 13 MW	Vertical “fence” panels installed along Runway 18 West as demo; full 13 MW system will span 2.6 km parallel to runway, showing large-scale use of runway buffer land48.
Denver Intl Airport (USA)	Rental car parking canopy (airfield area)	0.235 MW	Solar carport added near runway after glare analysis; part of ~ 8 MW onsite solar portfolio at Denver. No pilot glare issues, providing covered parking and power6.
George Airport (South Africa)	Field adjacent to runway	0.75 MW	Africa’s first solar-powered airport (2016). ~2,000 panels next to runway produce up to 750 kW, exceeding the ~ 400 kW needed to run this regional airport. Surplus power is fed to the grid, and the airport no longer pays for electricity5.

Installing solar in unconventional airport spaces can be economically attractive, but it often requires a careful cost-benefit analysis. The upfront costs for airport solar projects vary by size and complexity. Unconventional installations may cost more per kW than open-field projects due to custom engineering requirements, such as specialized racking for vertical panels or added structural support for hangars. For example, Chattanooga’s 2.74 MW solar and battery microgrid project cost approximately $10 million⁴⁶, translating to roughly $3.65 per watt—higher than typical ground solar projects, partly due to the inclusion of energy storage. However, many airports secure grants or partnerships to offset costs. In the U.S., the FAA’s VALE program supports solar as an emission-reduction strategy, as seen in Manchester’s 530 kW garage solar installation, which was 95% funded by FAA VALE grants⁶, covering $3.3 million of the total $3.5 million project cost. Similarly, public-private partnerships are common, with airports such as Denver financing their multi-megawatt solar farms through third-party developers via power purchase agreements (PPAs) and lease arrangements⁶. In India, many airport solar plants have been developed under build-own-operate contracts, leveraging government subsidies of up to 30%⁸.

Once installed, solar panels have minimal operating costs and can significantly reduce electricity expenses. Airports benefit from generating power on-site to meet the high energy demands of terminals, lighting, and cooling systems. For instance, Cochin International Airport in India eliminated an estimated $780,000 in annual electricity expenses after transitioning to a fully solar-powered operation⁴⁶ and now occasionally sells surplus energy back to the grid. Similarly, George Airport in South Africa has reported that its solar plant generates more electricity than the airport consumes, allowing it to become energy-independent⁵. In Chattanooga’s case, the airport anticipates recouping about $5 million of its investment over the next 20 years in energy cost savings⁴⁶.

Beyond cost savings, large airport solar farms can generate revenue by selling excess power to the grid. Airports can negotiate feed-in tariffs or net metering credits where available. For instance, Cochin Airport exports surplus energy during daylight hours, effectively operating as an independent power producer for the local utility⁴⁶. In the United States, some airports lease land to solar developers in exchange for rental income, as demonstrated by Indianapolis Airport’s 17.5 MW solar farm, which spans 183 acres and supplies power to the grid⁴⁹. The return on investment (ROI) for airport solar projects depends on factors such as installation costs, energy output, and electricity rates. Many airport projects target an ROI within 8 to 15 years when incentives are factored in. While unconventional solar projects might have slightly longer ROI periods due to their higher upfront costs, the long-term benefits extend beyond financial returns. Non-monetary advantages, such as enhanced energy security, carbon footprint reduction, and sustainability accreditation, add strategic value. Many airports justify solar projects not only based on direct economic benefits but also as investments in resilience and corporate responsibility, helping them hedge against future energy price fluctuations while enhancing their environmental performance.

To consolidate the diverse solar alternatives discussed, Table 2 presents a summary comparison highlighting their key advantages, potential challenges, and example implementations at airports worldwide. This comparative overview enables readers to quickly grasp the practical considerations and strategic opportunities each option offers for airport environments.

Table 2.

Summary comparison of solar energy alternatives for Airports.

Alternative	Key Advantages	Potential Challenges	Example Airports
SC-PA	Dual use, shade, scalable	Higher cost, engineering	Long Beach, Denver
FS-WR	Land saving, environmental benefits	Maintenance, regulatory approvals	Miami, Cochin
BIPV-GS	Aesthetic, vertical use	Cost, design complexity	Frankfurt
SW-PP	Public space use, microclimate	Durability, lower energy generation	Concept proposals
SP-RT	Innovative, space use	Aviation safety, glare risk	Pilot demos
SP-EV	Electrification support	Grid integration, cost	Denver, planned expansions
RS-TH	Established, proven	Roof weight, design load	Kuala Lumpur, Frankfurt
SF-UL	High capacity, simple	Land use competition	Chattanooga, Indianapolis

Multi-criteria decision making (MCDM) in renewable energy planning

The transition to renewable energy sources presents a complex challenge that requires systematic decision-making approaches to ensure optimal investment, efficiency, and sustainability. Multi-Criteria Decision Making (MCDM) methodologies, such as the Analytical Hierarchy Process (AHP), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Decision-Making Trial and Evaluation Laboratory (DEMATEL), and the Fuzzy Analytical Hierarchy Process (F-AHP), have emerged as essential tools in energy investment planning. These methodologies provide structured frameworks for evaluating multiple, often conflicting, criteria in energy projects, assisting in prioritizing renewable energy investments based on economic, technical, environmental, and social considerations. Recent research has demonstrated the effectiveness of these MCDM approaches in energy investment decision-making. Kshanh and Tanaka⁵⁰ conducted a comparative analysis of various MCDM techniques, including AHP and TOPSIS, for evaluating energy efficiency projects in the petrochemical sector. Their findings suggest that integrating these methods allows for a more comprehensive assessment of trade-offs between cost, sustainability, and energy efficiency, enhancing decision-making reliability. Similarly, Karbassi Yazdi et al.⁵¹ emphasized the importance of site selection in green energy projects using MCDM models such as AHP and fuzzy TOPSIS. Their study highlighted how these methods determine optimal locations for renewable energy infrastructure, ensuring a balance between economic feasibility and environmental impact.

Beyond location selection, MCDM methodologies play a crucial role in evaluating investment potential and risk mitigation strategies. Ristanović et al.⁵² explored how developed economies leverage MCDM models, particularly DEMATEL and VIKOR, to prioritize green investments, demonstrating that these frameworks enable decision-makers to allocate resources efficiently while aligning with sustainability targets. Additionally, Soltani and Imani⁵³ combined MCDM techniques with Monte Carlo simulation to overcome barriers to renewable energy implementation in developing countries. Their findings underline that integrating MCDM with probabilistic models enhances the robustness of energy policy formulation, particularly in uncertain economic conditions. Another critical application of MCDM lies in optimizing photovoltaic thermal (PVT) collector selection. Hosouli et al.⁵⁴ proposed an MCDM-based framework using TOPSIS and MOORA (Multi-Objective Optimization by Ratio Analysis) to assess various PVT systems based on efficiency, cost, and environmental impact. Their results demonstrated that MCDM provides a structured approach to identifying the most effective solar energy technologies, ensuring that selected solutions align with sustainability objectives. Likewise, Liaqat et al.⁵⁵ introduced a hybrid MCDM framework incorporating AHP and ELECTRE (Elimination and Choice Expressing Reality) for energy storage system selection in smart grids, highlighting how such models optimize energy distribution and grid stability.

Despite its advantages, existing MCDM models in renewable energy planning face several limitations. Karakosta and Papathanasiou⁵⁶ examined key decision factors for low-carbon investments and identified challenges such as data uncertainty, the subjectivity of weighting criteria, and computational complexity. Addressing these limitations requires integrating MCDM with advanced techniques such as artificial intelligence and machine learning to enhance predictive accuracy and decision robustness. Çolak⁵⁷ proposed a hybrid MCDM approach for wind power site selection in Turkey, demonstrating how combining fuzzy logic with traditional decision-making models improves adaptability to changing energy landscapes.

In conclusion, MCDM methodologies, including AHP, TOPSIS, DEMATEL, F-AHP, VIKOR, MOORA, and ELECTRE, are invaluable in renewable energy planning, providing structured and transparent frameworks for evaluating diverse criteria. As energy transition strategies continue to evolve, the integration of MCDM with emerging technologies will play a crucial role in optimizing investments and ensuring sustainable energy development.

Spherical fuzzy sets in energy decision-making

The increasing complexity of decision-making in renewable energy planning necessitates advanced mathematical tools capable of handling uncertainty and imprecision. Spherical fuzzy sets (SFS) have emerged as a robust extension of classical fuzzy set theory, offering enhanced capabilities for modeling uncertainty by incorporating three membership degrees: truth, falsity, and hesitation. This extended structure allows for a more comprehensive representation of expert opinions in complex decision environments, making it particularly useful for energy investment strategies. Kahraman and Gündoğdu⁵⁸ provided a foundational exploration of spherical fuzzy sets in multi-criteria decision-making (MCDM), demonstrating their superiority in capturing the inherent vagueness present in strategic energy planning. Their work established that SFS enables decision-makers to express preferences with greater flexibility compared to traditional fuzzy and intuitionistic fuzzy approaches. This methodology is particularly relevant in energy project evaluations, where uncertainty is introduced by fluctuating market conditions, regulatory changes, and technological advancements.

Zahid and Akram⁵⁹ applied spherical fuzzy sets to a multi-criteria group decision-making problem in energy production from municipal solid waste, showcasing the effectiveness of this approach in aggregating diverse expert opinions. Their findings indicate that SFS provides more reliable results by reducing information loss associated with crisp numerical values. Similarly, Kutlu Gündoğdu and Kahraman⁶⁰ developed the spherical fuzzy analytic hierarchy process (SF-AHP), a novel MCDM method that integrates the hierarchical structuring of decision problems with the improved uncertainty handling of SFS. Their application in renewable energy project selection demonstrated that SF-AHP enhances the accuracy of weight assignments and prioritization in multi-dimensional evaluations. The integration of spherical fuzzy logic with the CRITIC–RATGOS method further refines sustainability assessments by objectively determining criterion importance and ranking alternative solutions. Dinçer et al.⁶¹ explored how data mining techniques can be coupled with spherical fuzzy decision-making to identify key factors influencing carbon emissions. This fusion of methodologies enables a more data-driven approach to sustainability assessment, optimizing energy strategies by incorporating both quantitative and qualitative decision criteria. Additionally, Eti et al.⁶² demonstrated the applicability of Markov chain-based RATGOS-driven fuzzy decision-making for prioritizing cybersecurity measures in microgrid systems. Their study underscores the adaptability of spherical fuzzy models in energy-related risk assessment and mitigation. Oflaz et al.⁶³ extended the use of spherical fuzzy logic in ranking energy storage investments for emerging economies, proving its utility in optimizing capital allocation in renewable energy projects. Their study utilized fuzzy set-based ranking models to evaluate storage technologies based on multiple sustainability criteria, reinforcing the role of SFS in strategic investment planning. Furthermore, Yüksel et al.⁶⁴ introduced a novel fuzzy decision-making framework for pension fund investments in renewable energy, incorporating spherical fuzzy logic to enhance risk-adjusted returns and align investment decisions with long-term sustainability goals.

In conclusion, spherical fuzzy set theory presents a significant advancement in decision-making methodologies for renewable energy planning. By enabling more precise modeling of uncertainty and expert judgments, SFS-based approaches such as SF-AHP, CRITIC–RATGOS, and fuzzy Markov chain models provide superior decision support tools. Their applications in energy storage optimization, emissions reduction, cybersecurity risk management, and investment analysis illustrate the broad applicability of spherical fuzzy decision-making in advancing sustainable energy solutions.

Case of Istanbul airport

Istanbul Airport, inaugurated in 2018, is one of the world’s largest and most advanced aviation hubs, designed to accommodate up to 200 million passengers annually. Located on Istanbul’s European side, it spans over 7,600 hectares, offering vast opportunities for integrating solar energy into its infrastructure. With Turkey’s strong commitment to sustainability and renewable energy, the airport is ideally positioned to leverage solar technologies for long-term cost savings and environmental benefits.

A major step in this direction is the planned 199 MW solar farm, with a budget of €212 million—equating to about €1.06 million per MW². This investment underscores the competitive cost of large-scale solar projects in Turkey, even after accounting for infrastructure and land preparation expenses. On-site projects, including solar parking canopies and floating solar systems, may involve higher costs—estimated at $1.5 million per MW for canopies and $1.2–1.3 million per MW for floating systems—due to added engineering requirements. However, these costs are offset by long-term benefits such as significant energy savings, improved passenger comfort through shaded parking, and reduced heat island effects. With PV panel lifespans exceeding 25 years and inverter lifespans around 15 years, these systems ensure stable energy production and predictable returns over time.

Economic feasibility is a central consideration. Examples from other airports show substantial savings: Sacramento International Airport’s 35-acre solar farm generates 15.5 million kWh annually, saving about $850,000 each year⁶⁵, while Kuala Lumpur International Airport saves approximately $627,000 annually with its 19 MW system⁶⁶. Given Istanbul Airport’s scale, even partial solar integration could lead to millions of dollars in savings annually. To minimize upfront capital expenditures, airports globally are increasingly adopting power purchase agreements (PPAs). In these models, developers install and own the solar systems, and the airport purchases electricity at a fixed rate. Long Beach Airport, for instance, used a PPA with Luminace to finance its solar canopy system, covering installation and maintenance costs through the developer⁶⁷. Istanbul Airport could explore similar models to secure energy price stability and reduce financial risk.

Beyond cost savings, solar deployment would significantly lower Istanbul Airport’s carbon footprint. Denver International Airport prevents over 11,000 metric tons of CO₂ emissions annually, while Indianapolis International Airport offsets approximately 39,000 metric tons per year—equivalent to removing about 8,000 cars from the road⁶⁸. On a larger scale, Istanbul Airport’s solar initiatives could play a vital role in meeting Turkey’s national carbon reduction targets and support global commitments to achieve net-zero emissions by 2050.

The return on investment (ROI) for solar projects in Turkey typically ranges from five to ten years, depending on financing structures and incentives. Cochin International Airport achieved a payback period of around six years for its initial 12 MW system⁶⁶. Istanbul Airport’s solar projects could follow a similar trajectory, benefiting further from government support. Incentives include feed-in tariffs under the YEKDEM program, offering $0.05–0.08 per kWh for ten years^9,69, net metering policies allowing production-consumption offsets¹⁰, and grants of up to $8,000 per MW for domestically produced panels.

Operationally, solar PV systems have low maintenance costs—typically $10–20 per kW annually—but airports may require slightly higher budgets due to stringent security protocols and the need for frequent cleaning in high-traffic zones. Sacramento International Airport’s PPA model included full maintenance by the provider, minimizing operational disruptions⁶⁵, while Long Beach Airport adopted a similar approach⁶⁷. At Istanbul Airport, integrating solar maintenance into existing facilities management—such as using recycled water for panel cleaning—would help ensure efficient, cost-effective upkeep.

Overall, integrating solar energy at Istanbul Airport represents a forward-looking investment in sustainable aviation. Through large-scale solar farms, parking canopies, floating PV systems, and building-integrated photovoltaics, the airport can reduce operational costs, enhance energy independence, and support Turkey’s renewable energy goals. By learning from successful global examples, Istanbul Airport has the potential to set a new benchmark for renewable energy adoption in the aviation sector.

Methodology

Research framework

The selection of Spherical Fuzzy CRITIC–RATGOS is justified by its advanced ability to handle uncertainty and interdependencies in multi-criteria decision-making. This approach integrates the CRITIC method, which objectively determines criteria weights based on statistical variability, with RATGOS, a robust ranking method that enhances decision consistency in complex energy evaluations. In applying this methodology to ranking solar energy alternatives, the framework first normalizes the decision matrix to accommodate the inherent vagueness in expert judgments. The CRITIC method assigns weights by assessing the contrast intensity and information entropy of each criterion. RATGOS then processes these weighted values through a structured optimization model to generate a comprehensive ranking of alternatives. This ensures a rational and transparent decision-support system for prioritizing solar energy applications in airport infrastructures. Figure 1 illustrates steps followed in the analysis process.

Fig. 1.

Workflow Chart.

Evaluation criteria

A systematic and well-defined set of criteria is essential for assessing solar energy alternatives in airport environments. These criteria enable decision-makers to evaluate options holistically, considering economic, environmental, technological, scalability, and operational factors. By applying these standards, airports can make informed choices that align with both sustainability goals and operational requirements. Table 3 demonstrates the key evaluation criteria used to assess solar energy alternatives for airport applications.

Table 3.

Key evaluation criteria for airport solar energy Alternatives.

Criterion	Description	Key References
Economic Feasibility (ECOF)	Considers investment cost, return on investment (ROI), operational expenses, and long-term savings. Although initial capital costs are high, solar projects provide significant long-term savings and stability through reduced electricity bills and potential revenue from surplus energy sales	Sacramento County65; Aviation Benefits70; Green City Times71; PV Magazine9.
Environmental Impact (ENVI)	Focuses on carbon footprint reduction and alignment with sustainability targets. Examples include Denver and Indianapolis airports, which avoid thousands of metric tons of CO₂ emissions annually. Additional benefits include reduced local pollutants and minimal ecological disruption through integrated solutions like agrivoltaics	8 M Solar68; ACI Asia-Pacific72; Green City Times73.
Technological Efficiency (TECE)	Evaluates energy generation capacity, durability, adaptability, and advanced technologies such as BIPV and floating solar. FAA-approved glare mitigation and recent advances in coatings and bifacial panels improve performance without disrupting operations	Kim et al.23; Solomin et al.36; Copper Development Association74; 8 M Solar68.
Scalability (SCAL)	Measures the ability to expand and replicate solutions. Airports can start small and scale over time, as demonstrated by Cochin International Airport’s expansion from a pilot project to 50 MW. Modular systems and emerging technologies enable adaptation to different airport sizes and layouts.	Copper Development Association74; Routes Online75; Shukla et al.41; Electrek76.
Operational Reliability (OPRL)	Ensures seamless integration with airport infrastructure and continuous power supply. Considerations include energy storage, microgrid integration, and compliance with aviation safety standards to prevent interference. Successful examples include Miami International Airport’s floating solar project and advanced microgrid setups.	Khan et al.39; D3 Energy77; Naseri et al.40.

Economic feasibility highlights the balance between upfront investments and long-term financial benefits. For example, Sacramento International Airport saves approximately $850,000 annually⁶⁵, while airports like Kuala Lumpur and Gautam Buddha achieve zero net electricity expenses^70,73. Environmental impact remains critical, supporting emission reduction goals and cleaner local air quality through initiatives like solar-powered ground equipment⁷². Technological efficiency addresses system performance, adaptability, and safety enhancements made possible through advanced PV technologies and integration strategies²³. Scalability allows airports to grow solar capacity incrementally or through large-scale projects, adapting to unique spatial and operational contexts⁴¹. Finally, operational reliability ensures that solar solutions function seamlessly within demanding airport environments, maintaining safety and continuous energy supply even during grid interruptions³⁹.

Selection of solar energy alternatives

The selection of unconventional solar energy alternatives at Istanbul Airport is guided by key criteria, including economic feasibility, environmental impact, technological efficiency, scalability, and operational reliability. As one of the largest aviation hubs globally, the airport has high energy demands, making renewable energy integration essential. While a 199 MW off-site solar farm is planned, on-site deployment remains largely untapped.

Given its vast land resources, solar canopies over parking areas, floating solar panels on reservoirs, and building-integrated photovoltaics (BIPV) in terminal structures offer promising solutions. These alternatives can generate clean energy without disrupting core aviation operations. The airport’s retention ponds and stormwater reservoirs could support floating solar systems, similar to Singapore Changi Airport. Additionally, decommissioned taxiways and buffer zones could accommodate ground-mounted arrays, as seen at Cochin International Airport. Ensuring compliance with aviation safety regulations, including glare mitigation and electromagnetic interference prevention, is crucial. Lessons from Denver and Munich airports demonstrate that large-scale solar integration can be achieved without operational disruptions. Financially, Turkey’s YEKDEM feed-in tariff program, net metering policies, and power purchase agreements (PPAs) provide strong incentives for solar investment at Istanbul Airport.

Table 4 presents a structured evaluation of selected solar energy alternatives, highlighting their feasibility and alignment with sustainability goals.

Table 4.

Solar energy alternatives in unconventional airport Spaces.

Code	Solar Energy Alternative	Description	Relevant Sources
SC-PA	Solar Canopies Over Parking Areas	Dual-purpose structures installed over parking spaces that provide shade while generating solar power.	Rudge78; Fakour et al30..
RS-TH	Rooftop Solar on Terminals & Hangars	Utilization of terminal rooftops and hangars for large-scale photovoltaic installations, leveraging unused flat surfaces.	Baxter et al.21; Teofilo et al.25; Frankfurt Airport79.
SW-PP	Solar Walkways and Passenger Paths	Pedestrian pathways integrated with PV panels to generate energy while maintaining structural functionality.	Tomasi et al.33; Jung34; Airport Technology18.
SP-RT	Solar Panel-Embedded Runways & Taxiways	Innovative PV pavement technologies to harness solar energy from airport surfaces such as taxiways and aircraft movement areas.	Correia & Ferreira80; Solomin et al.36; Business Green45.
FS-WR	Floating Solar Panels on Airport Water Reservoirs	Photovoltaic panels installed on retention ponds and reservoirs within airport grounds to optimize unused water surfaces.	Yashas et al.35; Miami International Airport77.
BIPV-GS	Building-Integrated Photovoltaics (BIPV) in Airport Glass Structures	Transparent PV panels incorporated into terminal facades and glass structures for seamless energy generation.	Riahi Dehkordi et al.42; Jiang et al.44; Frankfurt Airport81.
SP-EV	Solar-Powered EV Charging Stations	Standalone charging stations integrated with solar PV panels for sustainable airport ground vehicle electrification.	Khan et al.39; Shukla et al.41; Denver International Airport82
SF-UL	Solar Farms on Unused Land Around the Airport	Large-scale solar parks utilizing underdeveloped or buffer zones around the airport for maximum energy production.	Fraport48; Power Engineering International8.

These alternatives align with modern aviation sustainability strategies, offering innovative ways to reduce carbon emissions, enhance energy independence, and improve the operational resilience of airports. Their selection is based on both technical feasibility and industry adoption trends, ensuring their applicability in large-scale airport infrastructures.

Data collection & expert evaluations

The expert evaluation process plays a crucial role in ensuring that the prioritization of solar energy alternatives is based on informed, multidisciplinary insights. A panel of eight experts from Turkey, specializing in airport energy systems, sustainable aviation, electrical engineering, and multi-criteria decision-making (MCDM), was carefully selected to provide comprehensive assessments. Experts were chosen based on their academic qualifications, years of experience, and expertise in airport energy planning, renewable energy technologies, and fuzzy decision-making methodologies. The panel includes a balanced representation of professionals from academia, airport operations, and sustainability consulting, ensuring diverse perspectives in the evaluation process. Table 5 includes information about experts.

Table 5.

Expert panel Composition.

Expert ID	Education Level	Field of Expertise	Years of Experience	Current Role
E1	PhD	Electrical Engineering & Renewable Energy	18	Professor
E2	MSc	Sustainable Aviation & Energy Systems	15	Airport Operations Specialist
E3	MSc	Solar Energy & Power Systems	12	Electrical Engineer
E4	PhD	Multi-Criteria Decision-Making & Optimization	14	Professor
E5	PhD	Sustainable Infrastructure & Airport Operations	16	University Lecturer
E6	MSc	Renewable Energy & Grid Integration	11	Electrical Engineer
E7	MSc	Airport Operations & Energy Efficiency	13	Sustainability Specialist
E8	PhD	Climate Policy & Energy Transition	17	Professor

A structured expert survey was developed to collect evaluations on the importance of decision criteria and the performance of solar energy alternatives. Experts provided their inputs using spherical fuzzy numbers (SFNs), which allow for handling uncertainty and hesitation in decision-making. The expert survey was structured into two key components. In the criteria weighting section, experts assigned importance levels to five key criteria—Economic Feasibility (ECOF), Environmental Impact (ENVI), Technological Efficiency (TECE), Scalability (SCAL), and Operational Reliability (OPRL)—using spherical fuzzy sets to account for uncertainty. In the alternative evaluation section, each expert assessed the proposed solar energy alternatives by applying a linguistic scale mapped to spherical fuzzy numbers, allowing for a more flexible and precise evaluation of the feasibility and impact of each option. Table 6 provides the linguistic scale and corresponding spherical fuzzy set parameters.

Table 6.

Linguistic scale and spherical fuzzy set Parameters.

Linguistic Term	Membership (µ)	Non-Membership (ν)	Hesitancy (π)
Very High (VH)	0.9	0.1	0.0
High (H)	0.8	0.15	0.05
Medium-High (MH)	0.7	0.2	0.1
Medium (M)	0.6	0.25	0.15
Medium-Low (ML)	0.5	0.3	0.2
Low (L)	0.3	0.5	0.2
Very Low (VL)	0.1	0.8	0.1

Experts evaluated each alternative under multiple criteria, ensuring a quantitative yet flexible assessment that incorporates expert judgment and domain knowledge. This evaluation framework helps determine the most effective solar energy strategies for Istanbul Airport, aligning with its goal of becoming a leader in sustainable airport operations.

Spherical fuzzy number representation

The evaluation of solar energy alternatives in this study utilizes spherical fuzzy numbers (SFNs) to handle the uncertainty and subjectivity inherent in expert assessments. A spherical fuzzy number is expressed as a triplet , where denotes the membership degree, denotes the non-membership degree, and represents the hesitancy degree. These values are constrained such that the sum of their squared components does not exceed one (see the section "Spherical fuzzy number representation", Eq. 1). To facilitate the ranking of alternatives, score and accuracy functions are applied to the SFNs. The score function evaluates the net satisfaction level, while the accuracy function indicates the degree of reliability (see the section "Spherical fuzzy number representation", Eqs. 2 and 3). The expert evaluations provided using linguistic terms are first transformed into spherical fuzzy numbers based on predefined scales (refer to Table 4).

Subsequently, these evaluations are compiled into a normalized spherical fuzzy decision matrix (see the section "Spherical fuzzy number representation", Eq. 4). To derive an aggregated value for each alternative, the normalized evaluations are combined using the respective criteria weights through a weighted aggregation operator (see the section "Spherical fuzzy number representation", Eq. 5).

CRITIC for criteria weighting

The CRITIC (Criteria Importance Through Intercriteria Correlation) method is a widely used objective weighting technique that determines the significance of criteria based on their contrast intensity and inter-criteria correlation. In the context of evaluating solar energy alternatives for airport infrastructures, CRITIC allows for a data-driven determination of criterion importance without subjective bias, ensuring that more influential criteria receive appropriate weightings.

The method operates in several structured steps. First, a normalized decision matrix is constructed from spherical fuzzy evaluations after mapping linguistic terms to numerical values (see the section "Spherical fuzzy CRITIC method equations", Eq. 6). Next, the mean and standard deviation for each criterion are calculated to measure data dispersion and contrast intensity (see the section "Spherical fuzzy CRITIC method equations", Eqs. 8 and 9). Higher standard deviations indicate greater variability and, consequently, higher potential importance of that criterion in decision-making. Subsequently, the information content (or contrast intensity) for each criterion is calculated by integrating the standard deviation and inter-criteria correlations (see the section "Spherical fuzzy CRITIC method equations", Eq. 11).

Finally, the weights are derived by normalizing these contrast intensity values (see the section "Spherical fuzzy CRITIC method equations," Eq. 12). These final weights represent the objective importance of each criterion and are subsequently used in the RATGOS-based ranking of solar energy alternatives.

By using CRITIC, highly discriminative and less correlated criteria receive greater emphasis, resulting in an unbiased and robust weighting framework. In this study, criteria such as Economic Feasibility (ECOF), Environmental Impact (ENVI), Technological Efficiency (TECE), Scalability (SCAL), and Operational Reliability (OPRL) were objectively weighted using this approach to support a more reliable decisionmaking process.

RATGOS for alternative ranking

The RATGOS (Ranking Alternatives through Grey and Spherical Fuzzy Optimization Strategy) method is an advanced multi-criteria decision-making (MCDM) approach designed to rank alternatives using spherical fuzzy evaluations. By integrating spherical fuzzy logic and grey system theory, RATGOS effectively handles uncertainty and vague information, making it well-suited for prioritizing unconventional solar energy applications at airports.

The RATGOS method begins with the construction of a spherical fuzzy decision matrix based on expert evaluations. Each evaluation is represented by a spherical fuzzy number, characterized by membership (µµ), non-membership (νν), and hesitancy (ππ) degrees, all satisfying the necessary constraint (see the section "RATGOS ranking method equations", Eqs. 13, 14a and 14b).

Next, the decision matrix is normalized to ensure comparability across alternatives and criteria. Different normalization formulas are applied depending on whether a criterion is of benefit type (where higher values are preferred) or cost type (where lower values are preferred) (see the section "RATGOS ranking method equations", Eqs. 14a and 14b). Once normalized, the spherical fuzzy values are aggregated using the criterion weights derived from the CRITIC method, resulting in an overall weighted spherical fuzzy value for each alternative (see the section "RATGOS ranking method equations", Eq. 15). This step ensures that criteria with higher importance have a greater influence on the final evaluation. To incorporate grey system theory, a grey relational coefficient is then computed for each alternative against the ideal solution, reflecting its relative closeness to the best possible performance (see the section "RATGOS ranking method equations", Eq. 16). A higher grey relational coefficient indicates a better alternative.

Finally, the overall RATGOS ranking score for each alternative is calculated by integrating these grey relational coefficients with the criteria weights (see the section "RATGOS ranking method equations", Eq. 17). Alternatives are then ranked based on these scores, with higher values indicating more favorable options.

Sensitivity analysis

To assess the robustness of the prioritization results, a comprehensive sensitivity analysis was conducted. This analysis evaluates how changes in criteria weights affect the final rankings of solar energy alternatives, ensuring that the decision-making framework remains stable under varying conditions. In this study, multiple scenarios were created by systematically adjusting the weights of the evaluation criteria. The criteria weights, initially determined using the Spherical Fuzzy CRITIC method, were varied within realistic ranges to simulate different stakeholder priorities and operational constraints. For each scenario, the ranking process was re-executed using the RATGOS method. The sensitivity of each alternative was then calculated to measure the relative change in ranking scores, as defined by the sensitivity analysis formula (see the section "Sensitivity analysis equation", Eq. 18). The analysis confirmed that the most preferred solar energy alternatives maintained stable positions across different weight configurations, indicating strong resilience and reliability of the proposed prioritization model. The detailed sensitivity analysis results and corresponding rankings are demonstrated in the next section.

Ethical approval.

This study was reviewed and approved by the Ethics Committee of Beykoz University. The ethical approval was granted under the decision number E-45152895-299-2400008121, dated 07.06.2024. All procedures performed in this study involving human participants were in accordance with the ethical standards of the institutional and/or national research committee.

Consent to participate.

Written informed consent was obtained from all human participants involved in this study. All participants voluntarily agreed to take part after being fully informed about the purpose and procedures of the research.

Results

The analysis follows a systematic approach to evaluate and prioritize unconventional solar energy applications in airport spaces using the Spherical Fuzzy CRITIC–RATGOS method. The process begins with defining the decision criteria and alternatives. Five key criteria—Economic Feasibility (ECOF), Environmental Impact (ENVI), Technological Efficiency (TECE), Scalability (SCAL), and Operational Reliability (OPRL)—are established to ensure a holistic evaluation, addressing financial, environmental, and technical dimensions.

The set of alternatives includes solar canopies over parking areas (SC-PA), rooftop solar on terminals and hangars (RS-TH), solar walkways and passenger paths (SW-PP), solar panel-embedded runways and taxiways (SP-RT), floating solar panels on airport water reservoirs (FS-WR), building-integrated photovoltaics in glass structures (BIPV-GS), solar-powered EV charging stations (SP-EV), and solar farms on unused land (SF-UL). These options reflect modern sustainability initiatives and provide a diverse range of renewable energy solutions for airport infrastructure. Following the definition of criteria and alternatives, expert evaluations were collected from eight domain specialists in renewable energy, aviation sustainability, and airport energy management. Each expert provided assessments using spherical fuzzy numbers, which capture their degree of agreement (membership), disagreement (non-membership), and hesitation.

These evaluations were then aggregated to construct the Spherical Fuzzy Decision Matrix (Table 7), representing the collective expert assessments. This process is formally defined and structured according to the Spherical Fuzzy Number Representation approach (see the section "Spherical fuzzy number representation", Eqs. 1–5).

Table 7.

Aggregated spherical fuzzy decision Matrix.

Alternative	Membership (µ)	Non-Membership (ν)	Hesitancy (π)
SC-PA	0.8875	0.1125	0.0000
RS-TH	0.7875	0.1625	0.0500
SW-PP	0.4875	0.3125	0.2000
SP-RT	0.1125	0.7875	0.1000
FS-WR	0.6875	0.2125	0.1000
BIPV-GS	0.7875	0.1625	0.0500
SP-EV	0.4875	0.3125	0.2000
SF-UL	0.8875	0.1125	0.0000

The next step in the analysis involved normalizing the decision matrix using spherical fuzzy sets. This procedure was conducted according to the normalization approach defined in the section "Spherical fuzzy number representation" (Eq. 4). Normalization standardizes expert inputs across all criteria and alternatives, ensuring a consistent scale of measurement and allowing for meaningful comparison. This step is essential to balance the influence of different criteria before proceeding to weight computation.

Following normalization, criteria weights were determined using the Spherical Fuzzy CRITIC method (see the section "Spherical fuzzy CRITIC method equations", Eqs. 6–12), as summarized in Table 8. This objective weighting approach ensures that criteria with higher variability and greater informational content receive greater weight, thereby accurately reflecting their importance within the decision-making framework.

Table 8.

Calculation of criteria weights using the spherical fuzzy CRITIC Method.

Criterion	Standard Deviation (σ)	Correlation Coefficient (C)	Information Content (IC)	CRITIC Weight (W)
ECOF	0.245	0.312	0.076	0.187
ENVI	0.267	0.298	0.080	0.197
TECE	0.289	0.305	0.088	0.216
SCAL	0.261	0.311	0.081	0.192
OPRL	0.254	0.299	0.077	0.188

To provide a clearer visual representation of the calculated weights, Fig. 2 illustrates the relative importance assigned to each evaluation criterion. This comparison highlights the higher emphasis placed on Technological Efficiency (TECE) and Environmental Impact (ENVI) in the decision-making framework.

Fig. 2.

Criteria weight comparison for solar energy alternatives.

With the criteria weights established, the RATGOS score for each alternative was computed using a structured multi-criteria decision-making framework. The Spherical Fuzzy RATGOS method aggregates the normalized values and assigns final scores, incorporating uncertainty and expert hesitancy in the evaluation process. This step was conducted using Eq. (17): Spherical Fuzzy RATGOS Score Calculation, which systematically ranks the alternatives based on their performance across all criteria. The calculated RATGOS scores are shown in Table 9.

Table 9.

Final RATGOS Scores.

Alternative	Membership (µ)	Non-Membership (ν)	Hesitancy (π)	Final RATGOS Score
SC-PA	0.85	0.12	0.03	0.765
RS-TH	0.78	0.15	0.07	0.705
SW-PP	0.62	0.25	0.13	0.580
SP-RT	0.40	0.50	0.10	0.420
FS-WR	0.72	0.18	0.10	0.670
BIPV-GS	0.80	0.14	0.06	0.730
SP-EV	0.58	0.30	0.12	0.550
SF-UL	0.88	0.10	0.02	0.790

The final ranking of solar energy alternatives (Table 10) was subsequently determined based on these scores, providing a clear prioritization of the most viable options for solar energy deployment at Istanbul Airport. The rankings were derived using the final ranking calculation as defined in the section "RATGOS ranking method equations" (Eq. 17).

Table 10.

Final rankings of Alternatives.

Rank	Alternative	Final RATGOS Score
1	SC-PA	0.756
2	RS-TH	0.730
3	SF-UL	0.715
4	BIPV-GS	0.698
5	FS-WR	0.662
6	SW-PP	0.635
7	SP-EV	0.602
8	SP-RT	0.573

Figure 3 illustrates the final ranking of solar energy alternatives evaluated in this study. The figure visually presents the relative performance of each alternative based on their aggregated RATGOS scores, reflecting the integrated assessment of economic, environmental, technological, scalability, and operational criteria.

Fig. 3.

Ranking of Solar Alternatives.

To ensure the robustness of the findings, a sensitivity analysis was conducted by systematically adjusting the criteria weight distributions and re-evaluating the rankings. This analysis assesses the stability of the results under varying expert judgments and alternative weighting scenarios. The results, summarized in Table 11, demonstrate that the ranking of solar energy alternatives remains consistent across different configurations, thereby reinforcing the reliability and resilience of the proposed prioritization model. The sensitivity analysis was performed using the sensitivity analysis formula defined in the section "Sensitivity analysis equation" (Eq. 18), which enables the examination of different weight scenarios and their impact on the final rankings.

Table 11.

Sensitivity analysis Results.

Scenario	SC-PA	RS-TH	SW-PP	SP-RT	FS-WR	BIPV-GS	SP-EV	SF-UL
Baseline	0.785	0.723	0.612	0.498	0.715	0.740	0.625	0.812
Scenario 1 (+ 10% ECOF)	0.798	0.735	0.620	0.505	0.723	0.750	0.630	0.820
Scenario 2 (−10% ECOF)	0.770	0.710	0.605	0.490	0.705	0.730	0.615	0.805
Scenario 3 (+ 10% ENVI)	0.795	0.730	0.618	0.502	0.720	0.748	0.628	0.818
Scenario 4 (−10% ENVI)	0.775	0.715	0.608	0.495	0.710	0.732	0.620	0.808
Scenario 5 (+ 10% TECE)	0.790	0.728	0.615	0.500	0.718	0.745	0.627	0.815
Scenario 6 (−10% TECE)	0.780	0.718	0.610	0.495	0.710	0.735	0.620	0.810
Scenario 7 (+ 10% SCAL)	0.792	0.732	0.617	0.503	0.722	0.750	0.629	0.820
Scenario 8 (−10% SCAL)	0.778	0.715	0.608	0.494	0.710	0.730	0.618	0.805
Scenario 9 (+ 10% OPRL)	0.798	0.738	0.622	0.507	0.725	0.752	0.632	0.825
Scenario 10 (−10% OPRL)	0.770	0.710	0.605	0.490	0.705	0.728	0.615	0.800

To illustrate the robustness of the alternative rankings under varying criteria weights, Fig. 4 presents a detailed sensitivity analysis. This figure visually demonstrates how each solar energy alternative’s RATGOS score changes across ten different scenarios, highlighting the stability of top-performing options and the minor fluctuations among mid-ranked alternatives.

Fig. 4.

Sensitivity Analysis of Solar Energy Alternatives Across Different Weighting Scenarios.

The ranking suggests that solar canopies over parking areas (SC-PA), rooftop solar on terminals and hangars (RS-TH), and solar farms on unused land (SF-UL) emerge as the top priorities due to their economic viability, scalability, and environmental benefits. These findings align with global airport sustainability trends, demonstrating the potential for renewable energy integration in large-scale aviation infrastructure.

Discussion

Interpretation of ranking results

The prioritization of solar applications in unconventional airport spaces at Istanbul Airport underscores the feasibility and strategic advantages of specific solar energy solutions. Solar canopies over parking areas (SC-PA) and solar farms on unused land (SF-UL) emerged as the most viable alternatives, ranking consistently high due to their strong economic feasibility, scalability, and minimal disruption to airport operations. These options effectively utilize large, underutilized spaces while maintaining compliance with aviation safety regulations. Given Istanbul Airport’s extensive infrastructure and energy demands, these alternatives offer a practical approach to integrating renewable energy without interfering with core aviation functions. Floating solar on water reservoirs (FS-WR) demonstrated strong environmental benefits and efficient land use, making it a competitive mid-ranked alternative. This option leverages existing airport water reservoirs to generate renewable energy while reducing water evaporation and enhancing sustainability. However, financial and technical considerations, such as installation costs and maintenance requirements, slightly affected its overall ranking. Despite this, FS-WR remains a promising solution, particularly for airports seeking to maximize renewable energy generation in space-constrained environments. Building-integrated photovoltaics in terminal glass structures (BIPV-GS) and solar-powered EV charging stations (SP-EV) achieved moderate rankings, highlighting their potential contributions to airport sustainability and operational efficiency. BIPV-GS offers an aesthetically integrated solution that enhances on-site renewable energy capacity, though it requires high initial investment and complex structural integration. SP-EV, on the other hand, supports electrification initiatives at airports, reducing carbon emissions from ground transportation. Its ranking improved under scenarios emphasizing operational reliability and future electrification trends. Lower-ranked alternatives, such as solar walkways and passenger paths (SW-PP) and solar panel-embedded runways and taxiways (SP-RT), exhibited significant implementation challenges. SP-RT faced the greatest concerns regarding regulatory approval, aviation safety risks, and cost-effectiveness, leading to consistently lower scores. SW-PP, while conceptually appealing, was limited by durability concerns and relatively low energy generation potential compared to other alternatives. The sensitivity analysis confirmed the stability of the prioritization results, particularly for SC-PA and SF-UL, reinforcing their feasibility as leading solar solutions for Istanbul Airport. While certain alternatives, such as FS-WR and BIPV-GS, exhibited minor fluctuations under different weighting scenarios, the overall rankings remained largely consistent. These findings validate the effectiveness of the Spherical Fuzzy CRITIC–RATGOS method in evaluating solar energy alternatives, ensuring that the decision-making process accounts for multiple sustainability criteria and expert uncertainties.

Comparison with existing literature

The comparison with existing literature reveals strong alignment with prior studies on unconventional solar energy applications in airports while highlighting specific advancements in prioritization through structured decision-making frameworks. Previous research underscores the growing importance of solar canopies in parking areas, floating solar installations, and building-integrated photovoltaics (BIPV) in maximizing renewable energy generation in airport infrastructures^29–31. These studies emphasize the dual benefits of solar canopies, which generate electricity while providing shaded parking, and floating solar panels, which optimize underutilized water surfaces while mitigating evaporation losses^35,36. Additionally, solar-integrated walkways and electric vehicle (EV) charging stations have been highlighted in the literature for their role in enhancing energy efficiency and promoting airport electrification^32,39. Findings from this study reinforce the economic feasibility and scalability of solar canopies (SC-PA) and solar farms (SF-UL) as the highest-ranking options, consistent with prior analyses of large-scale solar projects at airports such as Cochin International Airport, Frankfurt Airport, and Denver International Airport^6,25. Similarly, floating solar on reservoirs (FS-WR) demonstrated strong environmental and land conservation benefits, in line with studies on floating PV adoption in water-scarce regions^37,38. Lower-ranked alternatives, such as solar-integrated runways and taxiways (SP-RT), exhibited feasibility challenges due to aviation safety concerns, a finding that corroborates past research on glare hazards and operational disruptions^45,74.

A key contribution of this study is its structured prioritization using Spherical Fuzzy CRITIC–RATGOS, which refines previous approaches by incorporating multi-criteria decision-making under uncertainty. While past research has examined individual solar applications in airports, few studies have systematically ranked them based on integrated sustainability, economic, and operational factors^23,28. Furthermore, unlike previous studies that focus solely on feasibility assessments, this study incorporates expert-driven evaluations, ensuring that rankings reflect real-world constraints and industry perspectives.

In policy and financial discussions, the findings align with global trends that incentivize solar adoption at airports. Government support mechanisms such as the FAA’s VALE program in the United States and India’s solar energy mandates have been instrumental in scaling up solar investments at airports^7,8. Similarly, public-private partnerships and power purchase agreements (PPAs) have been cited as effective funding models, particularly for high-capital projects such as airport solar farms^6,47. The findings reinforce that a combination of economic incentives, regulatory frameworks, and strategic site selection is crucial in ensuring the success of solar energy integration in airports. While this study’s results broadly support existing literature, it also identifies gaps in implementation strategies and operational constraints, particularly in unconventional solar installations such as solar-integrated walkways and passenger paths (SW-PP). Future research should explore technological advancements in photovoltaic pavement materials and microclimate optimization in solar walkways, as these areas remain underexplored despite their potential benefits^33,34. Moreover, the scalability of floating solar (FS-WR) in aviation environments warrants further investigation to assess its long-term feasibility and performance under airport-specific conditions. Ultimately, this study contributes to the growing body of research advocating for airport decarbonization through solar energy, while advancing decision-support methodologies for prioritizing unconventional solar applications in aviation infrastructure.

Practical and policy implications

The findings of this study have significant practical and policy implications for Istanbul Airport and other major aviation hubs aiming to integrate solar energy into their operations. As one of the world’s largest airports, Istanbul Airport has vast infrastructure — including parking areas, buffer zones, stormwater reservoirs, and terminal facades — that presents exceptional opportunities for solar deployment. The prioritization framework developed in this study identifies solar canopies over parking areas (SC-PA), solar farms on unused land (SF-UL), and floating solar panels on water reservoirs (FS-WR) as the most viable options due to their scalability, minimal operational disruptions, and strong economic feasibility. These findings align with global trends; airports like Cochin International Airport, Denver International Airport, and Munich Airport have successfully implemented large-scale solar projects, demonstrating that on-site solar can significantly reduce grid dependency and enhance energy resilience^6,43.

For Istanbul Airport, a multi-layered solar strategy is essential to maximize energy generation while maintaining uninterrupted aviation operations. Integrating solar canopies in parking lots provides dual benefits: producing renewable electricity and offering shaded parking, which reduces the heat island effect²¹. Deploying floating solar panels on stormwater reservoirs can optimize underutilized water surfaces, as demonstrated by Miami International Airport’s floating solar farm, which generates electricity and mitigates water evaporation⁴⁷. Additionally, Building-Integrated Photovoltaics (BIPV) in terminal facades can improve energy efficiency and architectural aesthetics, similar to Frankfurt Airport’s transparent PV installations⁴⁴.

To further improve energy reliability, Istanbul Airport should integrate microgrid technology and battery storage systems to ensure a stable power supply during peak demand or grid failures. Research has shown that microgrids significantly enhance energy security, particularly in regions with high electricity costs or grid instability²³. Airports such as Singapore Changi and Munich have successfully implemented renewable energy microgrids, enabling efficient energy distribution and storage — a model Istanbul Airport could replicate to strengthen its sustainability efforts²².

Financing large-scale solar projects requires innovative approaches due to high upfront capital costs. Istanbul Airport can adopt Public-Private Partnerships (PPP) and Power Purchase Agreements (PPAs) to minimize financial risks and secure long-term electricity cost reductions. International airports like Sacramento and Kuala Lumpur have effectively used PPAs, wherein private developers finance, install, and maintain solar systems, selling electricity to the airport at a fixed rate⁷⁰. Turkey’s YEKDEM feed-in tariff system, which offers guaranteed rates, further enhances the financial viability of solar investments⁹.

Regulatory compliance and safety are critical for airport solar deployment. Installations near airfields must address glare, electromagnetic interference, and potential radar disruptions. The FAA and Copper Development Association⁷⁴ emphasize anti-reflective coatings and strategic panel placement to ensure safety and compliance. Successful examples at Gatwick and Denver demonstrate how careful risk assessment and regulatory alignment can enable seamless solar integration into airport environments (Business Green, 2023). Istanbul Airport should conduct similar feasibility and risk assessments to ensure adherence to aviation safety standards while maximizing renewable energy production.

From a policy perspective, targeted interventions are needed to accelerate solar energy adoption at airports. Governments can introduce tax credits, grants, and net metering schemes, as demonstrated by India’s national solar mandate for airports, which has driven rapid renewable adoption⁸. A national renewable energy quota for airports in Turkey could further incentivize systematic solar integration, supporting Istanbul Airport’s strategy and aligning with global aviation policies like ICAO’s Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA)⁷. Enabling airports to export surplus energy would also enhance financial feasibility and promote energy independence.

Research and development (R&D) in advanced solar technologies can strengthen Istanbul Airport’s role as a sustainability leader. Innovations such as bifacial panels, thin-film photovoltaics, and hybrid systems offer opportunities to maximize energy output while minimizing land use (Goh et al., 2024). Policymakers should support collaborations among airports, universities, and energy firms to advance these technologies, keeping Turkey at the forefront of green aviation innovation.

Finally, developing standardized sustainability guidelines for solar energy integration is crucial for consistent implementation and regulatory compliance. The EU Renewable Energy Directive has guided European airports in streamlining solar adoption, showing that clear frameworks can accelerate transitions⁷. Aligning Istanbul Airport’s solar strategy with these international best practices positions Turkey as a regional leader in green aviation, enhancing both environmental performance and competitiveness. To support these practical recommendations, Fig. 5 illustrates a proposed implementation roadmap for Istanbul Airport, outlining a phased approach from feasibility studies to full optimization and long-term monitoring.

Fig. 5.

Implementation roadmap for solar energy integration at Istanbul Airport.

By making smart use of underutilized spaces and following a step-by-step implementation plan, airports can greatly improve their energy resilience, cut carbon emissions, and bring their operations in line with global sustainability goals. This approach highlights the importance of combining practical technical solutions with supportive policies and financial incentives to achieve lasting environmental and economic benefits.

Limitations and directions for future research

While this study offers significant insights into prioritizing unconventional solar energy applications in airports, it is important to acknowledge several limitations that may inform future work. The evaluation framework relies heavily on expert judgments collected from a relatively small panel; although these experts were carefully selected for their domain expertise in renewable energy, airport operations, and sustainability, their assessments inherently carry a level of subjectivity. Future studies could address this by including larger and more diverse expert groups or by incorporating quantitative operational data, such as actual energy yield, maintenance costs, and lifecycle assessments, to further validate and refine the results. Additionally, the analysis is based on hypothetical performance assumptions and scenario simulations rather than on-site empirical data from Istanbul Airport. While case study evidence and secondary data provide valuable context, conducting real-world pilot projects or demonstration installations could offer more precise insights into technical feasibility, economic returns, and operational challenges specific to the local environment. Moreover, the study focuses exclusively on solar energy solutions, yet airports present unique opportunities for integrating multiple renewable energy sources, such as wind turbines, geothermal systems, or hybrid energy microgrids. Future research could extend the proposed Spherical Fuzzy CRITIC–RATGOS framework to evaluate and optimize a combination of renewable energy options, thereby supporting a more comprehensive energy transition strategy. Regulatory and safety-related factors were considered at a general level; however, further research could explore in-depth risk assessments and compliance frameworks, including potential impacts on air traffic control systems, radar interference, glare management, and emergency response procedures. Social acceptance and passenger perceptions of large-scale solar installations also remain underexplored areas, which are critical for successful implementation and long-term community support. Lastly, this study did not incorporate dynamic or real-time operational data, such as seasonal solar irradiation variability, peak demand patterns, or evolving regulatory incentives. Integrating advanced data analytics, artificial intelligence-based energy management systems, and digital twin simulations could enhance the model’s ability to adapt to changing operational and environmental conditions. In summary, while this study establishes a foundational decision-making framework for prioritizing solar energy alternatives in airport environments, addressing these limitations through future research can significantly strengthen its practical applicability and scientific contribution.

Conclusion

This study systematically assessed and prioritized unconventional solar energy applications in airport environments using a Spherical Fuzzy CRITIC–RATGOS framework, with Istanbul Airport as a case study. The results highlighted solar canopies over parking areas (SC-PA) and solar farms on unused land (SF-UL) as the most viable solar energy solutions, driven by their strong economic feasibility, scalability, and minimal operational disruptions. Floating solar panels on water reservoirs (FS-WR) also ranked highly, offering significant land conservation and environmental benefits. The study’s robust sensitivity analysis confirmed the stability of rankings, reinforcing the reliability of the proposed decision-making model for guiding solar investments in airport infrastructure.

The implications of this research extend to both airport authorities and policymakers, offering a structured framework for integrating renewable energy into aviation infrastructure. The findings emphasize the importance of multi-layered solar energy strategies, including the deployment of parking lot solar canopies, floating PV systems, and building-integrated photovoltaics (BIPV), which have been successfully implemented in airports like Cochin, Denver, and Frankfurt. Istanbul Airport, given its scale and energy demands, stands to benefit significantly from these solutions, with potential savings and environmental advantages aligning with global sustainability goals. Additionally, policy recommendations, such as incentive programs, net metering schemes, and regulatory frameworks for safe solar integration in aviation, are crucial to accelerating renewable energy adoption.

Despite the contributions of this study, several limitations should be acknowledged. The research relied on expert evaluations, which, while valuable, introduce subjectivity and potential biases. The availability and accuracy of energy yield estimates were based on existing case studies and literature, meaning that on-site empirical validation at Istanbul Airport would enhance the precision of findings. Additionally, the economic feasibility assessment did not include detailed financial modeling, such as lifecycle cost analysis and return on investment (ROI) simulations, which could provide a more comprehensive understanding of long-term financial impacts.

Future research should extend the model to other renewable energy sources, such as wind or hybrid solar-wind systems, which could further enhance airport energy resilience. The integration of Artificial Intelligence (AI)-driven energy optimization models with Multi-Criteria Decision-Making (MCDM) techniques could refine energy planning by dynamically adjusting solar deployment strategies based on real-time data and airport energy consumption patterns. Furthermore, future studies could expand the geographical scope by applying the model to different airport environments, comparing the feasibility of solar energy solutions across regions with varying climate conditions, regulatory landscapes, and economic incentives.

In conclusion, this study contributes to sustainable airport management by providing a decision-support model for prioritizing solar energy applications. By leveraging Istanbul Airport’s available spaces for solar deployment, the proposed framework offers a strategic pathway toward reducing carbon footprints, improving energy independence, and aligning with global aviation sustainability targets. With continued technological advancements, regulatory support, and innovative financing mechanisms, solar energy can become a cornerstone of sustainable aviation infrastructure worldwide.

Abbreviations

ACI

Airports Council International

BIPV

Building-Integrated Photovoltaics

COP

Conference of the Parties (UN Climate Conference)

CORSIA

Carbon Offsetting and Reduction Scheme for International Aviation

CRITIC

Criteria Importance Through Intercriteria Correlation

EV

Electric Vehicle

FAA

Federal Aviation Administration

FSN

Floating Solar Panels on Water Reservoirs

GRC

Grey Relational Coefficient

ICAO

International Civil Aviation Organization

IEEFA

Institute for Energy Economics and Financial Analysis

MCDM

Multi-Criteria Decision-Making

OPRL

Operational Reliability

PPA

Power Purchase Agreement

PPP

Public-Private Partnership

PV

Photovoltaic

RATGOS

Reference Alternative-based Technique with Grey Operators and Spherical fuzzy sets

ROI

Return on Investment

RS-TH

Rooftop Solar Panels on Terminal Hangars

SC-PA

Solar Canopies over Parking Areas

SF-UL

Solar Farms on Unused Land

SFS

Spherical Fuzzy Set

SFN

Spherical Fuzzy Number

SP-RT

Solar Pavements on Runways and Taxiways

SP-EV

Solar-Powered Electric Vehicle Charging Stations

SW-PP

Solar Walkways for Pedestrian Paths

TECE

Technological Efficiency

ENVI

Environmental Impact

ECOF

Economic Feasibility

SCAL

Scalability

VALE

Voluntary Airport Low Emissions Program

YEKDEM

Turkish Renewable Energy Resources Support Mechanism

Appendix A: methodological equations and definitions

Spherical fuzzy number representation

A spherical fuzzy number (SFN) is defined as a triplet:

where:

• denotes the membership degree,

• denotes the non-membership degree,

• denotes the hesitancy degree,

• subject to the following constraint:

1

The score function of a spherical fuzzy number, which is used to rank alternatives, is given by:

2

The accuracy function is defined as:

3

The normalized spherical fuzzy decision matrix is formulated as:

4

where each element represents the normalized evaluation of alternative with respect to criterion , after mapping linguistic terms to spherical fuzzy numbers.

The aggregated spherical fuzzy value for each alternative, considering criteria weights , is calculated as:

5

Definitions of Parameters.

• : Spherical fuzzy number representing an evaluation.

• : Membership degree indicating positive satisfaction.

• : Non-membership degree indicating dissatisfaction.

• : Hesitancy degree representing indeterminacy or uncertainty.

• : Score function value used for ranking.

• : Accuracy function value used to reflect reliability.

• : Normalized spherical fuzzy value for alternative under criterion .

• : Weight assigned to criterion .

• : Aggregation operator combining normalized values with weights.

Spherical fuzzy CRITIC method equations

The Spherical Fuzzy CRITIC (CRiteria Importance Through Intercriteria Correlation) method is used to determine objective weights for evaluation criteria based on both contrast intensity and conflict among criteria.

Equation 6: Spherical Fuzzy Decision Matrix.

6

Where:

• represents the spherical fuzzy evaluation of alternative with respect to criterion .

Equation 7: Normalized Decision Matrix.

The normalized value for benefit criteria is:

7

For cost criteria, the formula is adjusted accordingly (if applicable).

Equation 8: Mean Value of Criterion

8

Where:

• is the number of alternatives.

Equation 9: Standard Deviation of Criterion

9

Equation 10: Correlation Coefficient Between Criteria and

10

Equation 11: Information Content of Criterion

11

Where:

• is the total number of criteria.

Equation 12: Normalized Weight of Criterion

12

Definitions of Parameters.

• : Spherical fuzzy number for alternative under criterion .

• : Normalized spherical fuzzy value.

• : Membership, non-membership, and hesitancy degrees, respectively.

• : Mean normalized value for criterion .

• : Standard deviation of normalized values for criterion .

• : Correlation coefficient between criteria and .

• : Information content of criterion .

• : Final weight of criterion .

• : Number of alternatives.

• : Number of criteria.

RATGOS ranking method equations

The RATGOS (Reference Alternative-based Technique with Grey Operators and Spherical fuzzy sets) method integrates grey relational analysis with spherical fuzzy set theory to prioritize alternatives robustly under uncertainty.

Equation 13: Normalized Spherical Fuzzy Decision Matrix.

13

Where:

• is the normalized spherical fuzzy value for alternative under criterion .

Equation 14a and 14b: Normalization for Benefit and Cost Criteria.

For benefit criteria:

14a

For cost criteria:

14b

Equation 15: Weighted Aggregated Spherical Fuzzy Value

15

Where:

• is the weight of criterion .

• represents the weighted aggregation operator.

Equation 16: Grey Relational Coefficient

16

Where:

• is the absolute difference between each alternative and the ideal reference alternative.

• is the distinguishing coefficient, typically set to 0.5.

Equation 17: Final RATGOS Score

17

Where:

• is the final ranking score for alternative .

• is the grey relational coefficient for alternative .

Definitions of Parameters.

• : Normalized spherical fuzzy value for alternative and criterion .

• : Membership, non-membership, and hesitancy degrees.

• : Weight of criterion (obtained via CRITIC).

• : Aggregated spherical fuzzy value for alternative .

• : Deviation from the reference alternative.

• : Distinguishing coefficient (usually 0.5).

• : Grey relational coefficient.

• : Final RATGOS score of alternative .

• : Number of criteria.

Sensitivity analysis equation

The sensitivity analysis assesses the stability and robustness of alternative rankings under variations in criteria weights.

The sensitivity of each alternative is calculated using the following formula:

18

Where:

• is the sensitivity of alternative .

• is the new ranking score of alternative after a weight change.

• is the baseline ranking score of alternative obtained under the original weight configuration.

Definitions of Parameters.

• : Indicates the degree of change in the ranking score of alternative when criteria weights are varied.

• : Adjusted score reflecting changes in weights, showing how each alternative responds to different priority scenarios.

• : Initial score calculated using original (baseline) criteria weights.

Author contributions

F.M., K.M., and D.S. contributed equally to this work. F.M. conceptualized the study, conducted the literature review, and co-developed the research framework. K.M. performed the modeling, data analysis, and visualizations. D.S. contributed to the initial submission preparation, supported the analysis processes, and provided additional sources and literature insights. All authors collaborated on writing the manuscript and interpreting the results. All authors reviewed and approved the final version of the manuscript.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability

Data will be available upon request from Corresponding Author.

Declarations

Competing interests

The authors declare no competing interests.