A Symmetry-Based Spherical Fuzzy MCDM Approach for the Strategic Assessment of Alternative Fuels Toward Sustainable Energy Policies

Abstract

Alternative fuels obtained from renewable sources, providing low greenhouse gas emissions and high energy efficiency, offer significant advantages in terms of sustainability. In addition, the wide applicability of these fuel types in sectors such as housing, transportation, and industry creates significant opportunities in terms of reducing dependence on fossil fuels. Alternative fuels should be evaluated not only according to their environmental contributions but also based on multi-dimensional criteria such as economic cost, technical suitability, sustainability level, fuel properties, infrastructure requirements, and social acceptance. In this context, a comparative analysis of alternative fuel types in terms of various basic parameters is no longer optional, but a necessity. These parameters generally include symmetrical relationships such as balanced trade-offs between economic and environmental dimensions or mutual effects between technical and social criteria. However, they also show variability and uncertainty depending on the fuel type. Therefore, Spherical Fuzzy Multi-Criteria Decision Making (SF-MCDM) methods, which can effectively represent symmetry in membership and hesitation degrees, have been used to achieve more realistic and reliable results in uncertain decision environments. The proposed model provides a systematic and flexible evaluation structure that helps decision makers determine the most appropriate alternative fuel options and contributes to the formation of sustainable energy policies.

1. Introduction

The rapid industrialization of Western countries following the two major world wars in the 20th century, the exponential increase in the world population since the 1950s, and the significant rise in per capita income have paved the way for increased environmental pollution on a global scale [1]. During this period, fossil fuels were used as the primary energy source. While this reliance has made significant contributions to economic growth since the Industrial Revolution, it has also become one of the main causes of environmental degradation [2]. The accumulation of greenhouse gases in the atmosphere—particularly carbon dioxide (CO₂), leads to an increase in global temperatures and the subsequent deterioration of climate systems [3].

Global warming and climate change trigger a variety of devastating disasters, ranging from melting glaciers in both Greenland and Antarctica–which contributes to raising sea levels—to droughts in Africa, increased floods in Asia, and hurricanes in the Americas [4]. These environmental disasters and climate changes have evolved into crises that threaten not only individual countries but also the entire world [5,6]. This situation has led to energy security, environmental health, and sustainable development becoming concepts that can no longer be considered separately.

In this context, the search for alternative fuels is becoming increasingly important for the establishment of sustainable energy policies. Alternative fuels not only reduce dependence on fossil fuels but also offer multifaceted advantages, including low greenhouse gas emissions, efficient utilization of domestic energy resources, enhanced energy security, and high energy efficiency [7,8]. Since the transportation sector in particular accounts for a significant share of global carbon emissions, the development of sustainable fuel solutions in this area has become a necessity. The European Union’s zero-emission target by 2035 encompasses not only newly produced vehicles but also the existing internal combustion engine vehicle (ICE) fleet, further underscoring the need for low-carbon fuel alternatives [9].

The literature reveals that numerous studies have been conducted in this field. For instance, recent contributions include bibliometric analysis of the last 50 years of sustainable green energy [10], green energy and sustainable development [11], recent developments in urban green energy studies [12], green energy, innovation and capital [13], the sustainable development of green energy companies [14], a comparison of alternative fuels in terms of life cycle energy and cost [15], a life cycle comparison of alternative marine fuels [16], the use of hydrogen as an alternative fuel in the shipping sector [17], a fuzzy-MCDM based comparison of alternative fuel vehicles [18], comparison of road transportation vehicles using alternative fuels in the USA with fuzzy MCDM [19], optimization of fuel values for emission reduction [20], MCDM approach in the supply of alternative fuels used in the aviation sector [21], MCDM application in the fuel supply of power plants [22] are some of these studies. Although there are many studies on alternative fuels in the literature and even many publications with comparisons made using MCDM, no study has been found in which a comparative analysis was made according to the properties of alternative fuels, especially using Fuzzy (F)-MCDM.

Although the literature includes many studies on alternative fuels—and several employing multi-criteria decision-making (MCDM) methods—no study has been found that conducts a comparative analysis based specifically on the properties of alternative fuels using Fuzzy Multi-Criteria Decision Making (F-MCDM) methods.

Various studies in the literature focus on alternative fuels, with particular emphasis on themes such as hydrogen, emissions, biomass, performance, and biodiesel. Furthermore, many publications present comparative evaluations using MCDM methods. However, no study has been identified that conducts a comparative analysis based on the specific properties of alternative fuels using F-MCDM methods. In this context, Figure 1 presents a visualization of the results from a literature search conducted in the Web of Science database using the keyword “alternative fuels”, generated with VOSviewer software (version 1.6.20).

In this study, alternative fuel types were evaluated based on environmental, economic, technical, and strategic criteria. To obtain more realistic results in decision environments containing uncertainty, Fuzzy Spherical (FS)-MCDM methods were employed. The primary objective was to contribute to the development of scientifically based strategic roadmaps for sustainable energy policies by proposing a systematic decision support model to assist decision-makers in identifying the optimal alternatives.

This study was structured in five stages. In the first stage, the concepts of global warming, climate change, green transition, and sustainable energy policies were examined. The second stage focused on alternative fuels, including their characteristics and environmental impacts. In the third stage, fuzzy sets, fuzzy logic, and FS-MCDM methods were introduced. These methods are particularly well-suited to modeling symmetrical uncertainty in expert evaluations—capturing balanced degrees of membership, non-membership, and hesitation—thereby reflecting the inherent symmetry present in many decision-making criteria. In the fourth stage, various fuel types were evaluated using FS-MCDM methods. Finally, in the fifth stage, the results were compared, and recommendations were provided. The overall process is illustrated in Figure 2 below.

This study is motivated by the increasing need for robust and transparent decision models in energy policy planning, particularly under uncertainty and conflicting stakeholder preferences. Despite the rich body of literature on alternative fuels and MCDM approaches, there is a noticeable lack of applications integrating Spherical Fuzzy Sets into strategic energy decision frameworks. This paper addresses this gap by providing a structured, adaptable, and explainable model.

From a managerial perspective, the model helps policymakers, energy strategists, and environmental planners evaluate alternatives with nuanced uncertainty representation, supporting more reliable and informed decisions.

The main contributions of this study include the following:

• The integration of FS-MCDM into the context of sustainable energy planning,
• A structured methodological framework applicable to similar multi-criteria decision environments, and
• Insights into how advanced fuzzy modeling can improve the realism and reliability of energy policy decisions.

2. Materials and Methods

Today, in the development of alternative fuels for ICEs, the easy accessibility of raw materials and sustainability of resources have become prominent factors, particularly in efforts to combat global warming and climate change through the reduction of carbon emissions. In this context, research on the development of alternative fuels that are both technically compatible with gasoline and diesel engines and environmentally and economically sustainable has been ongoing for a considerable period.

Among the most studied alternative biofuels (such as ethanol, biodiesel, advanced biofuels), natural gas derivatives (including compressed natural gas, liquefied petroleum gas), electricity, hydrogen, and propane [23]. These fuel types represent innovative solutions designed to reduce greenhouse gas emissions, enhance energy efficiency, and support sustainability, especially in the transportation sector [24]. This ongoing shift toward cleaner and more efficient fuels represents a critical pillar of the green transition, which seeks to restructure energy and economic systems in pursuit of carbon neutrality [25]. In this context, the process highlights the necessity of well-formulated, evidence-based, sustainable energy policies that not only promote long-term energy security but also mitigate environmental degradation [26]. To provide a clearer understanding of the types and subcategories of alternative fuels, a general classification based on their sources and application methods is presented in Figure 3 [27].

Biofuels derived from renewable biomass sources—such as agricultural products, algae, and waste materials-represent one of the most widely recognized types of alternative fuels. Their compatibility with ICEs, requiring only minor modifications, makes them a practical and effective solution to reduce emissions in the short term. The main categories of biofuels are outlined below [28].

Ethanol produced from corn, sugar cane, or biomass is one of the most widely used biofuels. It can be blended with gasoline to form ethanol-gasoline blends such as E85 (85% ethanol, 15% gasoline). Compared to fossil fuels, ethanol reduces greenhouse gas emissions by 54% and benefits from compatibility with existing fuel infrastructures [29,30]. For instance, in the Far East—particularly in densely populated countries such as India and China-ethanol-powered motorcycles have the potential to reduce greenhouse gas emissions by 56% compared to traditional gasoline motorcycles. When compared to electric motorcycles, ethanol-powered motorcycles in China, India, and the region overall were observed to emit 52%, 48% and 37% less, respectively [31].

In hybrid vehicles, increasing the ethanol concentration in fuel blends has been shown to enhance energy efficiency and reduce carbon emissions. Notably, significant improvements have been observed with blends containing 70% bioethanol [32]. Ethanol (C₂H₅OH) has also been found to positively influence key performance parameters in internal combustion engines (ICEs), particularly thermal efficiency and brake power. Optimal performance was reported with the E15 blend, which contains 15% ethanol [33].

Furthermore, the use of methanol–butanol–ethanol mixtures in spark ignition engines has been shown to improve fuel economy by reducing specific fuel consumption by 21.05% [34]. Ethanol’s high octane number and oxygen content not only increase engine efficiency but also ensure technical compatibility with conventional gasoline engines. These properties facilitate the transition to ethanol-gasoline blends and have contributed to their widespread adoption [33]. In addition, hybrid vehicles powered by biofuels demonstrate significantly improved performance and overall energy efficiency due to the integration of stored electric power [32].

Methanol Since the 1970 oil crisis—and particularly during periods of rising crude oil prices—methanol has attracted considerable global interest from researchers in the field of engine technologies. Following ethanol, methanol is one of the most prominent alcohol-based alternative fuels for automotive applications, offering significant potential to reduce dependence on fossil fuels. Studies have demonstrated that methanol can serve as a viable substitute for gasoline and other petroleum-derived fuels in terms of engine performance, particularly in the automotive sector [35].

Methanol (CH₃OH), a lower alcohol, exhibits promising potential for use in unmodified internal combustion engines (ICEs). However, its high heat of vaporization poses a significant challenge for cold-start performance, as it hinders fuel evaporation and thus reduces combustion efficiency, especially in low-temperature environments [36]. Among all primary alcohols, methanol has the highest oxygen content—approximately 50%—which contributes to cleaner exhaust emissions during combustion. Furthermore, its ability to be synthesized from a wide range of abundant feedstocks—including coal, natural gas, biomass, municipal solid waste, and carbon dioxide (CO₂)—positions methanol as a sustainable alternative fuel [37].

Despite these advantages, methanol also presents several limitations. Its low cetane number impedes direct application in compression ignition (CI) engines by increasing ignition delay, thereby diminishing engine performance [36]. Additionally, methanol–diesel blends may lead to safety concerns due to vapor-phase flammability. To suppress this risk, excessive methanol concentrations are required, which can result in overly rich mixtures that are difficult to ignite [38].

Taken together, these factors indicate that increasing methanol content in fuel blends elevates both the autoignition temperature and the latent heat of vaporization. As a result, the direct and safe use of methanol in engines is limited and necessitates the development of appropriate engine modifications and additive technologies.

Biodiesel is a type of biofuel derived from vegetable oils or animal fats and holds a prominent position among renewable energy sources. It can be used directly in place of conventional diesel, particularly in CI engines, and contributes significantly to emission reduction. Studies indicate that biodiesel use can lead to a 41% decrease in overall emissions [30,39]. Furthermore, biodiesel is considered an environmentally friendly option due to its biodegradable and non-toxic characteristics.

Blends containing biodiesel have been shown to significantly reduce carbon monoxide (CO) emissions. For instance, compared to conventional diesel, CO emissions from biodiesel blends have been reported to decrease by up to 48.63% [40]. However, increasing the biodiesel content in blends tends to elevate the emissions of CO₂ and NO_x, indicating that careful attention must be paid to blend ratios during practical application [41].

From the perspective of engine performance, high-ratio biodiesel blends often result in increased fuel consumption, which can present limitations regarding fuel efficiency [41,42]. Nonetheless, performance outcomes vary significantly depending on the biodiesel blend ratio. Notably, lower-ratio blends (e.g., B5 to B25) demonstrate engine performance that closely aligns with conventional standards [43].

In addition, biodiesel produced from alternative feedstocks such as waste cooking oil and palm oil has shown promising performance in full-load diesel engine operations. These results suggest that the use of diverse raw materials provides biodiesel with flexibility and adaptability as an alternative fuel [40,43,44]. While blending biodiesel with conventional diesel offers a way to optimize engine performance, determining the ideal blend ratio remains a key technical challenge due to the differing physical and chemical properties of the two fuel types [42,45].

Advanced biofuels, including cellulosic ethanol and biohydrogen, are derived from non-food biomass sources such as agricultural residues, algae, and lignocellulosic materials. These next-generation fuels offer substantial environmental benefits, with the potential to reduce greenhouse gas emissions by up to 70% compared to conventional fossil fuels [30]. Despite their promising environmental profile, the development and widespread adoption of advanced biofuels are significantly constrained by the high costs and technical complexities associated with their production processes.

Natural gas, primarily composed of methane, is considered a cleaner-burning fuel relative to conventional fossil fuels. When used in ICEs, it generates significantly lower levels of greenhouse gas and air pollutant emissions [46]. Due to these characteristics, natural gas and its derivatives have emerged as viable alternatives in the transition toward more sustainable transportation systems.

Compressed Natural Gas (CNG) is one of the most widely adopted alternative fuels for both light- and heavy-duty vehicles. It offers up to a 63% reduction in emissions compared to conventional fuels and is economically advantageous, making it a practical solution for short- and medium-term applications [30,47].

Liquefied Petroleum Gas (LPG), a by-product of the natural gas refining process, represents another alternative fuel option. Due to its relatively low operating costs and satisfactory performance characteristics, LPG is regarded as a suitable transitional fuel for the short-term replacement of traditional fossil fuels [39,48].

Hydrogen-powered ICEs play a strategic role in the fight against global warming and climate change, primarily due to their significantly lower CO₂ emissions compared to conventional fossil fuel engines [49,50]. As a carbon-free energy carrier, hydrogen holds the potential to dramatically reduce CO₂ emissions by replacing carbon-intensive fuels. Nevertheless, the use of hydrogen in ICEs is still associated with NO_x emissions, which remain a considerable environmental concern. These emissions, however, can be mitigated through ultra-lean burn combustion strategies, thereby contributing to improved environmental sustainability [50].

One of the primary technical challenges in the use of hydrogen is its safe and efficient storage, alongside the development of robust fuel delivery systems. Although substantial progress has been made in recent years, issues such as pre-ignition and backfiring still persist and require further technological refinement [49]. The advancement of hydrogen injection technologies and hybrid engine architectures has enhanced the feasibility of mass-producing hydrogen-powered ICEs [50].

Despite their environmental advantages, the widespread adoption of hydrogen-powered engines is hindered by a number of structural and technical barriers. The establishment of comprehensive infrastructure for the production, storage, transportation, and distribution of hydrogen necessitates significant investment and long-term planning. Moreover, the ability of hydrogen ICEs to maintain stable and efficient operation under variable load conditions remains critical to their viability in practical applications [49].

In addition to ICEs, hydrogen can be effectively utilized in fuel cell electric vehicles (FCEVs). In these systems, hydrogen is stored as chemical energy and converted into electricity through fuel cells to drive the vehicle. FCEVs are particularly suitable for high-demand applications, such as long-haul and heavy-duty transport, due to their long driving range and short refueling times. Nevertheless, high hydrogen production costs and infrastructure limitations continue to pose substantial challenges to their widespread commercialization [47,48,51]. Therefore, for hydrogen technologies to become a viable component of sustainable transportation systems, comprehensive advancements are required across both technical and economic dimensions.

Propane (C₃H₈), a hydrocarbon fuel obtained as a byproduct of natural gas processing and crude oil refining, represents a cost-effective alternative to conventional fuels. Its relatively lower emission levels and economic advantages make it particularly suitable for short- to medium-term applications in transportation [52]. Despite being a carbon-based compound, propane still releases carbon dioxide (CO₂) during combustion; therefore, it does not offer a fully carbon-neutral solution [53].

However, propane exhibits favorable thermophysical properties, such as density, viscosity, and specific heat capacity that are comparable to those of ammonia. This compatibility has led to an increasing number of studies exploring dual-fuel applications involving propane and ammonia [54]. These hybrid systems aim to leverage the advantages of both fuels—propane’s combustion stability and ammonia’s carbon-free nature—thereby reducing net emissions while maintaining performance. Due to these attributes, propane is considered a viable alternative fuel for vehicle fleets used in logistics and other commercial transport sectors where fuel cost, availability, and infrastructure readiness are critical factors.

Emerging alternative fuels such as Dimethyl Ether (DME) and synthetic fuels are gaining increasing attention due to their potential to reduce emissions while remaining compatible with existing energy infrastructure. Although these fuels are still in the early stages of development, they present promising prospects for future transportation and energy applications [55].

Among these, Dimethyl Ether (DME)—with the chemical formula C₂H₆O—has attracted particular interest as a viable alternative to conventional diesel. DME stands out for its relatively high energy density, ease of on-vehicle storage, and the potential for production from various renewable resources. Its high cetane number also makes it well-suited for use in CI engines, enabling efficient and durable engine operation. Furthermore, because the DME molecule lacks carbon–carbon bonds and contains oxygen atoms, it facilitates low-soot combustion, offering a significant advantage in reducing particulate emissions [56]. These characteristics highlight DME’s potential as a next-generation fuel capable of supporting both environmental sustainability and technological compatibility in internal combustion engine systems.

Electricity plays a central role in the transition toward sustainable transportation systems. Electric vehicles (EVs), which operate without producing tailpipe emissions, significantly contribute to reducing greenhouse gas emissions and mitigating air pollution, particularly in densely populated urban areas [57].

BEVs are fully electric vehicles powered exclusively by energy stored in rechargeable battery systems. They are characterized by higher energy efficiency and lower maintenance costs compared to ICE vehicles. Despite these advantages, limited charging infrastructure and the ongoing development of battery technologies remain major challenges to their widespread adoption [47,48].

HEVs combine an internal combustion engine with an electric motor, allowing for improved fuel efficiency and reduced emissions. HEVs are generally regarded as a transitional technology facilitating the gradual shift from conventional vehicles to fully electric alternatives [58].

However, despite their promising characteristics and increasing attention in recent literature, both emerging fuels, such as DME and electricity-based technologies, are excluded from the scope of this study. Instead, attention is directed toward other types of alternative fuels, with a particular emphasis on fuel blends, which represent an area of growing academic interest.

According to a literature review conducted via the Web of Science database, a substantial number of studies have been published in this field. Research on alternative fuels has attracted global attention, and the geographical distribution of related publications—along with the countries where this research is concentrated—is visualized using VOSviewer (version 1.6.20) in Figure 4. These findings indicate that alternative fuel technologies are not solely discussed within the context of environmental concerns but are also evaluated through broader lenses, such as energy security and economic sustainability.

Each alternative fuel presents distinct advantages and limitations, making the identification of the most appropriate option for a sustainable energy transition a complex task. In order to enable a meaningful comparison among these fuels, it is first necessary to establish a set of evaluation parameters. These criteria will be detailed in the following section of this study.

2.1. Evaluation Criteria of Alternative Fuels

The main elements used in comprehensively evaluating the basic physical and chemical properties of a fuel include the source of the raw material used (renewable or non-renewable), its stability under environmental conditions, and safety properties related to flammability. Understanding the structural properties of a fuel is of great importance in determining its potential for integration into existing energy infrastructure, its safety in storage and transportation processes, and its compatibility with engine design [59]. For example, fuels obtained from renewable sources are more compatible with sustainability goals, while parameters such as flash point and auto-ignition temperature have a direct impact on usage and process safety [60]. These properties [61,62,63];

The parameters to be used to comprehensively evaluate and compare alternative fuels are explained under the following headings.

• Fuel Material (Raw Materials): The source of the fuel—renewable (e.g., algae, waste oils) or non-renewable (e.g., natural gas)—has a direct impact on sustainability, carbon footprint, and lifecycle emissions. Renewable raw materials stand out as a more sustainable and environmentally friendly option in terms of reducing environmental impacts and supporting long-term energy policies.
• Physical State: Fuels can be gaseous, liquid, or solid in environmental conditions. This directly affects operational factors such as storage, transportation, infrastructure integration, and energy density. Liquid fuels generally offer easier solutions for transportation and processing, while gaseous fuels often require special pressurization systems.
• Flash Point: Flash point is defined as the lowest temperature at which a fuel can form a flammable vapor-air mixture and is a safety-critical parameter. Fuels with higher flash points are considered safer, especially in storage, transportation, and processing.
• Auto-Ignition Temperature: This is the lowest temperature at which a fuel will spontaneously ignite without an external ignition source. Fuels with lower auto-ignition temperatures may increase safety risks, while higher temperatures may require specific engine conditions and ignition systems.
• Lower Heating Value (LHV): LHV measures the energy content of a fuel, excluding the energy obtained from the condensation of water vapor. This value is a more meaningful measure for fuel efficiency and real-world performance evaluations because it reflects the net amount of energy that can be practically used in engines.
• Higher Heating Value (HHV): HHV includes the latent heat recovered from the condensation of water vapor and represents the total energy potential of the fuel. It is especially critical for complete combustion conditions and system efficiency comparisons.
• Cetane Number: It is an indicator that determines the ignition quality of fuels used in diesel engines. A high cetane number means shorter ignition delay, smoother combustion, and therefore better engine performance and lower emission values. In addition, a high cetane number increases the operating stability of the engine.
• Octane Number: Octane number, which is valid for gasoline fuels, allows higher compression ratios and better efficiency by preventing engine knocking with a higher octane number. It is an important factor in terms of vehicle compatibility and combustion quality.
• Gasoline or Diesel Gallon Equivalent (GGE/DGE): Fuels with higher energy content and better equivalence to gasoline/diesel allow for smoother integration into existing systems and offer better performance with fewer modifications. This criterion standardizes the energy content of alternative fuels by comparing them to conventional fuels. It helps evaluate how much of an alternative fuel is needed to perform equivalent to gasoline or diesel, facilitating infrastructure and cost comparisons [64].
• Maintenance Requirements and Technological Barriers: Maintenance requirements and technological barriers significantly impact the cost-effectiveness and user acceptance of a fuel. Maintenance Issues: Fuels that cause injector clogging, deposit build-up, or require special filters and lubricants can increase maintenance costs. This subcriterion evaluates ease of integration into existing engine platforms and user experience [65].
• Energy Security Impacts: It aims to assess the broader strategic impacts of a fuel’s adoption at national and global scales, and is particularly important in the context of energy security. The main aim is to reduce dependence on imported fossil fuels and increase resilience in energy supply. One of the most important drivers of the shift towards alternative fuels is the desire to strengthen energy security. Fuels obtained from domestic and renewable sources minimize geopolitical risks by reducing external dependence and contribute to long-term energy independence. This is directly aligned with sustainable development strategies at the national level [66].
• Emissions: Internal combustion engines are significant contributors to air pollution, releasing various harmful emissions such as carbon monoxide (CO), carbon dioxide (CO₂), nitrogen oxides (NO_x), unburned hydrocarbons (UHC), polycyclic aromatic hydrocarbons (PAH), etc. [67,68]. Among these, CO₂ is the primary gaseous byproduct and a major greenhouse gas. Its atmospheric concentration continues to rise due to the combustion of fossil fuels such as coal and petroleum. Approximately 60% of the CO₂ emitted remains in the atmosphere, while the rest is absorbed by natural processes like photosynthesis and ocean diffusion [67]. NO_x, produced during high-temperature combustion through reactions between nitrogen and oxygen, contributes to the formation of acid rain and ground-level ozone—both of which pose serious health risks and cause environmental degradation [67]. Additionally, PAHs, which are found naturally in fossil fuels and also formed during the incomplete combustion of organic materials, can adhere to fine particulates in the air and are recognized for their potential carcinogenic properties [68].

A fuel’s contribution to energy security is measured by the extent to which it reduces imported fuel use, how effectively it uses local resources, and the country’s capacity to diversify its energy portfolio [69]. Fuel types that have positive impacts in this area play a key role in achieving long-term energy independence. Research conducted in this context not only increases energy security but also supports environmental sustainability by reducing greenhouse gas emissions. Ultimately, the goal of this research is to provide scientific guidance to society on alternative fuels and to encourage individuals to make conscious decisions that will leave a more livable and sustainable planet for future generations. Alternative fuels are evaluated under the headings specified in

Table 1. Alternative fuels and fuel criteria.

Fuel Criterion	Symbol	Alternative Fuels	Symbol
Fuel Material (feedstocks)	FM	Gasoline	G
Energy Comparison	EC	Diesel	D
Energy Content (lower heating value)	LHV	Biodiesel	B100
Energy Content (higher heating value)	HHV	Propane	LPG
Physical State	PS	Compressed Natural Gas	CNG
Flash Point	FP	Liquefied Natural Gas	LNG
Autoignition Temperature	AT	Ethanol	E100
Maintenance Issues	MI	Methanol	M
Energy Security Impacts	ESI	Hydrogen	H
Sustainability	S
CO2 emission	CO2
NOX emission	NOX
PAH	PAH

below, within the framework of these characteristics.

2.2. Fuzzy Multi-Criteria Decision-Making (FMCDM) Methods

Multi-Criteria Decision Making (MCDM) techniques were developed in the 1960s to address the need to consider multiple views and complex datasets in the decision process [70]. These techniques provide a systematic evaluation of numerous and often conflicting criteria when choosing between alternatives. Since the decision process becomes more complex with the increase in the number of criteria and options, the use of MCDM methods becomes inevitable at this point [71].

Classical Multi-Criteria Decision Making (MCDM) methods may be inadequate in representing the uncertainties and ambiguities encountered in decision-making processes. In order to eliminate these deficiencies, various improvements have been made in the methods, and different fuzzy set approaches have been developed to model uncertainty more effectively [72]. In this direction, the classical fuzzy set theory was put forward by Zadeh in 1965 [73] and has evolved over time [74]. It has been expanded with various extensions such as Atanassov’s Intuitive Fuzzy Sets (IFS) [75], Torra’s Hesitant Fuzzy Sets [76], and Smarandache’s Neutrosophic Fuzzy Sets (NFS) [77]. The first important step in enriching fuzzy sets with multi-dimensional structures was taken with the IFS model developed by Atanassov. This approach represents the decision maker’s positive and negative judgments about alternatives and the uncertainty between them through membership (μ), non-membership (v), and indecision (π) degrees. In this way, uncertainty can be addressed in a much more comprehensive way compared to classical models.

The three-dimensional structure offered by IFSs has been made even more flexible by the Type-2 Intuitive Fuzzy Sets (IFS2) model, also developed by Atanassov. In this model, while the sum of membership and non-membership degrees can exceed 1, the sum of the squares of these values still remains in the [0, 1] range. Thus, a wider range of expression is offered to decision makers [78].

The NFS developed by Smarandache has three components: accuracy (t), inaccuracy (f), and uncertainty (i). The main feature that distinguishes NFSs is that these values are not limited to the [0, 1] range only, but can go below 0 or above 1. This allows a clearer distinction to be made between absolute and relative memberships, and the sum of membership degrees can be defined in the range of [0, 3] [77].

Recently, in response to the need to generalize between different fuzzy set structures, Pythagorean fuzzy sets [79] and neutrosophic fuzzy set theory have been synthesized, and the concept of Spherical Fuzzy Sets (SFS) has been introduced to the literature. In SFSs, membership, non-membership, and uncertainty components are defined on a spherical surface; the difference between two alternatives is measured by the spherical arc distance [78].

As a result, the integration of MCDM methods with fuzzy logic has made the decision-making process more realistic and holistic by providing decision makers with the opportunity to evaluate uncertainty with multidimensional and flexible structures.

2.2.1. Spherical Fuzzy Sets (SFS)

SFS, one of the three-dimensional extensions of fuzzy set theory, was developed in 2018 [78]. This structure is called “spherical” because the degrees of membership, non-membership, and hesitation can be defined on a spherical surface. An important difference of SFSs is the method of measuring the distance between clusters; while this distance is calculated with the Euclidean distance in the classical IFS, the spherical arc distance is taken as the basis in SFSs. This feature allows decision makers to evaluate uncertainty in a more comprehensive and geometrically meaningful way [80]. Figure 5 visualizes the measurement differences between SFS with the same membership degrees and IFS, IFS2 and NFS structures. According to Kutlu Gündoğdu and Kahraman [78], the main purpose of the SFS approach is to provide decision makers with the opportunity to generalize other fuzzy set extensions through a membership function that can be defined on a spherical surface and to define the parameters of this function independently in a wider domain. The distinguishing feature of the SFS model is that it restructures the wide definition range in NFS by allowing the sum of μ, v and π to be defined as less than 1, and it eliminates the criticisms directed at the Fuzzy Image Cluster Theory by basing the degree of instability on an independent formula. Thanks to this structure, when the values of μ (membership) and v (non-membership) are known, the degree of π (instability) can be calculated directly using the spherical arc distance. Thus, decision makers have access to a more flexible and comprehensive evaluation area. In SFSs, all membership degrees continue to be defined in the range [0, 1].

Below, an A SFS and operations defined in the U universe are defined [78].

$${\tilde{A}}_S=\left\{x,\left({\mu }_{\tilde{A}s}\left(x\right),v_{\tilde{A}s}\left(x\right),{\pi }_{\tilde{A}s}\left(X\right)\right)\left|x\in U_1\right.\right\}$$

where;

${\mu }_{\tilde{A}s}\left(x\right):U_1\to \left[\mathrm{0,1}\right]$,

$v_{\tilde{A}s}\left(x\right):U_1\to \left[\mathrm{0,1}\right]$,

${\pi }_{\tilde{A}s}\left(x\right):U_1\to \left[\mathrm{0,1}\right]$,

$0\le {\mu }_{\tilde{A}s}^2\left(x\right)+v_{\tilde{A}s}^2\left(x\right)+{\pi }_{\tilde{A}s}^2\left(x\right)\le 1\forall x\in U_1$. Some calculations to be made between two spherical fuzzy sets ${\check{A}}_s$ and ${\tilde{B}}_s$ are expressed by the equations shown below. Equality (1) shows the distance between two SFSs.

$$dis\left({\check{A}}_s,{\tilde{B}}_s\right)={\displaystyle \frac{2}{\pi }}{\sum }_{i=1}^{n}arccos=\left(\begin{array}{c}{\displaystyle \genfrac{}{}{0pt}{}{{\mu }_{{\tilde{A}}_s\left(u_i\right),{\mu }_{{\tilde{B}}_s}\left(u_i\right)+}}{v_{{\tilde{A}}_s\left(u_i\right),v_{{\tilde{B}}_s}\left(u_i\right)+}}}\\ {\pi }_{{\tilde{A}}_s\left(u_i\right),{\pi }_{{\tilde{B}}_s}\left(u_i\right)}\end{array}\right)$$

(1)

The normalized distance between two SFSs is shown in Equation (2).

$${dis}_n\left({\check{A}}_s,{\tilde{B}}_s\right)={\displaystyle \frac{2}{n\pi }}{\sum }_{i=1}^{n}arccos=\left(\begin{array}{c}{\displaystyle \genfrac{}{}{0pt}{}{{\mu }_{{\tilde{A}}_s\left(u_i\right),{\mu }_{{\tilde{B}}_s}\left(u_i\right)+}}{v_{{\tilde{A}}_s\left(u_i\right),v_{{\tilde{B}}_s}\left(u_i\right)+}}}\\ {\pi }_{{\tilde{A}}_s\left(u_i\right),{\pi }_{{\tilde{B}}_s}\left(u_i\right)}\end{array}\right)$$

(2)

The sum of two SFS is expressed by Equation (3).

$${\tilde{A}}_s⨁{\tilde{B}}_s=\left({\displaystyle \genfrac{}{}{0pt}{}{{({\mu }^2{\tilde{A}}_s+{\mu }^2{\tilde{B}}_s-{\mu }^2{\tilde{A}}_s{\mu }^2{\tilde{B}}_s)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},v_{{\tilde{A}}_s}{v}_{{\tilde{B}}_s},}{{\left[\left(1-{\mu }_{{\tilde{B}}_s}^2\right){\pi }_{{\tilde{A}}_s}^2+\left(1-{\mu }_{{\tilde{A}}_s}^2\right){\pi }_{{\tilde{B}}_s}^2-{\pi }_{{\tilde{A}}_s}^2{\pi }_{{\tilde{B}}_s}^2\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\right)$$

(3)

The product of two SFS is expressed by the Equation (4).

$${\tilde{A}}_s⨂{\tilde{B}}_s=\left({\displaystyle \genfrac{}{}{0pt}{}{{\mu }_{{\tilde{A}}_s}{\mu }_{{\tilde{B}}_s},{(v^2{\tilde{A}}_s+v^2{\tilde{B}}_s-v^2{\tilde{A}}_s{v}^2{\tilde{B}}_s)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},,}{{\left[\left(1-v_{{\tilde{B}}_s}^2\right){\pi }_{{\tilde{A}}_s}^2+\left(1-v_{{\tilde{A}}_s}^2\right){\pi }_{{\tilde{B}}_s}^2-{\pi }_{{\tilde{A}}_s}^2{\pi }_{{\tilde{B}}_s}^2\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\right)$$

(4)

The multiplication of a SFS by a number λ > 0 is expressed by the Equation (5).

$$\lambda .{\tilde{A}}_s=\left({\displaystyle \genfrac{}{}{0pt}{}{{\left(1-{(1-{\mu }_{{\tilde{A}}_s}^2)}^{\lambda }\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},v_{{\tilde{A}}_s}^{\lambda },}{{\left[{{\left(1-{\mu }_{{\tilde{A}}_s}^2\right)}^{\lambda }-\left(1-{\mu }_{{\tilde{A}}_s}^2-{\pi }_{{\tilde{A}}_s}^2\right)}^{\lambda }\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}\right)$$

(5)

Taking a SFS to the power of a number λ > 0 is shown by Equation (6).

$${\tilde{A}}_s^{\lambda }=\left(\begin{array}{c}{\mu }_{{\tilde{A}}_s}^{\lambda },{\left(1-{\left(1-{\nu }_{{\tilde{A}}_s}^2\right)}^{\lambda }\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},\\ {\left[{\left(1-{\nu }_{{\tilde{A}}_s}^2\right)}^{\lambda }-{\left(1-{\nu }_{{\tilde{A}}_s}^2-{\pi }_{{\tilde{A}}_s}^2\right)}^{\lambda }\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\end{array}\right)$$

(6)

The Spherical Weighted Arithmetic Mean (SWAM) in SFSs is defined below and is calculated using Equation (7)

$$w=\left(w_1,w_2\dots ,w_a\right)w_a);w_i\in \left[\mathrm{0,1}\right];ve{\displaystyle \sum _{i=1}^n}{w}_i=1ise$$

$${SWAM}_w({\tilde{A}}_{s1},{\tilde{A}}_{s2},\dots ,{\tilde{A}}_{sn}{)=w}_1{\tilde{A}}_{s1}+w_2{\tilde{A}}_{s2}+\dots +w_a{\tilde{A}}_{sn}$$

$$\widetilde{{\omega }_i}=\tilde{S}\left(\begin{array}{c}{\left(1-{\displaystyle \prod _{İ=1}^n}{\left(1-{\displaystyle {\mu }_{{\tilde{A}}_{s^i}}^2}\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},{\displaystyle \prod _{i=1}^n}\left(v_{{\tilde{A}}_{s^i}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right),\\ {\left[{\displaystyle \prod _{i=1}^n}{(1-{\mu }_{{\tilde{A}}_{s^i}}^2)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}-{\displaystyle \prod _{i=1}^n}{(1-{\mu }_{{\tilde{A}}_{s^i}}^2-{\pi }_{{\tilde{A}}_{s^i}}^2)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\end{array}\right)$$

(7)

In Spherical Fuzzy Sets (SFSs), the spherical weighted geometric mean (SWGM) is defined as follows and is computed according to Equation (8).

$$w=\left(w_1,w_2\dots ,w_a\right)w_a;w_i\in \left[\mathrm{0,1}\right];and{\displaystyle \sum _{i=1}^n}{w}_i=1then$$

$${SWGM}_w\left({\tilde{A}}_{s1},{\tilde{A}}_{s2},\dots ,{\tilde{A}}_{sn}\right)={{\tilde{A}}_{s1}}^{w1}+{{\tilde{A}}_{s2}}^{w2}+\dots +{{\tilde{A}}_{sn}}^{wn}$$

$$\widetilde{{\omega }_i}=\tilde{S}\left(\begin{array}{c}{\displaystyle \prod _{i=1}^n}\left({\mu }_{{\tilde{A}}_{s^i}}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right),{\left(1-{\displaystyle \prod _{İ=1}^n}{\left(1-v_{{\tilde{A}}_{s^i}}^2\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},\\ {\left[{\displaystyle \prod _{i=1}^n}{(1-v_{{\tilde{A}}_{s^i}}^2)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}-{\displaystyle \prod _{i=1}^n}{(1-v_{{\tilde{A}}_{s^i}}^2-{\pi }_{{\tilde{A}}_{s^i}}^2)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}}\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\end{array}\right)$$

(8)

In the computations, the score function is applied as given in Equation (9), and the accuracy function is used as defined in Equation (10).

$$Score\left({\tilde{A}}_s\right)={({\mu }_{{\tilde{A}}_s}-{\pi }_{{\tilde{A}}_s})}^2-{(v_{{\tilde{A}}_s}-{\mu }_{{\tilde{A}}_s})}^2$$

(9)

$$Accuracy\left({\tilde{A}}_s\right)={\mu }_{{\tilde{A}}_s}^2+v_{{\tilde{A}}_s}^2+{\pi }_{{\tilde{A}}_s}^2$$

(10)

In case ${\tilde{A}}_s<{\tilde{B}}_s$

• $Score\left({\tilde{A}}_s\right)<Score\left({\tilde{B}}_s\right)$ or
• $Score\left({\tilde{A}}_s\right)=Score\left({\tilde{B}}_s\right)$ and $Accuracy\left({\tilde{A}}_s\right)<Accuracy\left({\tilde{B}}_s\right)$.

2.2.2. Spherical Fuzzy Technique for Order Preference by Similarity to Ideal Solution (SF-TOPSIS)

The TOPSIS method was developed by Hwang et al. [81] to rank the available alternatives in decision problems according to the determined criteria. It is one of the MCDM (Multi-Criteria Decision-Making) techniques that helps decision-makers in evaluating alternatives based on the specified parameters in various real-life problems. This technique is based on determining the option that is closest to the ideal solution, which has the best values. At the same time, it also considers the option that is farthest from the undesirable negative solution or outcomes [81,82]. Since TOPSIS facilitates decision-making in real-world problems, it is frequently used in academic studies. The steps of the TOPSIS method are shown in Figure 6 [83,84].

However, in decision-making problems involving uncertainty, the traditional TOPSIS method may be inadequate. Therefore, fuzzy methods are employed to model uncertainty more effectively. The Fuzzy TOPSIS (FTOPSIS) method incorporates differences arising from certain fuzzy set operations, as it is often difficult for decision-makers to assign precise performance ratings to alternatives based on criteria. Particularly in cases where the weights of the criteria are expressed using linguistic variables instead of numerical values, the FTOPSIS method enables group decision-making in fuzzy environments [85]. The method works with fuzzy numbers by allowing the representation of linguistic variables through various metrics [73,86].

In classical TOPSIS applications, the objectivity of the available data contributes to obtaining more reliable, robust, accurate, precise, original, and realistic results. However, fuzzy logic becomes relevant in subjective decision-making processes where uncertainty and ambiguity are present. While classical fuzzy TOPSIS offers a simpler and faster, yet limited, model for handling uncertainty [87], spherical fuzzy TOPSIS provides a more effective approach for modeling uncertainty, albeit with increased computational complexity.

The reason behind this is that classical fuzzy sets operate solely on membership functions and are thus limited in expressing the indecision or conflicting judgments of decision-makers. In contrast, spherical fuzzy sets are better suited to model situations in which decision-makers are unsure, indecisive, or express contradictory evaluations [78].

Another method, known as Neutrosophic fuzzy TOPSIS, is considered one of the most flexible and powerful models, particularly when there are conflicting, indecisive, or neutral statements among decision-makers. In neutrosophic sets, the degrees of membership, non-membership, and indeterminacy are independent, and their sum must be less than 3 [88]. In spherical fuzzy sets, however, these values are interrelated, and the sum of their squares must not exceed 1 [78]. Since the components in spherical fuzzy sets are treated as interconnected, the SF-TOPSIS method was employed in this study.

In this study, the Spherical Fuzzy TOPSIS (SF-TOPSIS) method was employed, and the linguistic variables used were defined using positive spherical fuzzy numbers. The linguistic scale used for evaluating the criteria is presented in

Table 2. The linguistic scale used to weight the criteria [78].

Linguistic Terms	Symbol	Spherical Fuzzy Numbers
Absolutely more importance	AMI	(0.9, 0.1, 0.1)
Very high importance	VHI	(0.8, 0.2, 0.1)
High importance	HI	(0.7, 0.3, 0.2)
Slightly more importance	SMI	(0.6, 0.4, 0.3)
Equally importance	EI	(0.5, 0.4, 0.4)
Slightly low importance	SLI	(0.4, 0.6, 0.3)
Low importance	LI	(0.3, 0.7, 0.2)
Very low importance	VLI	(0.1, 0.8, 0.1)
Absolutely low importance	ALI	(0.1, 0.9, 0)

, and the scale used for ranking the alternatives is given in

Table 3. The linguistic scale used to compare alternatives [87].

Linguistic Terms	Symbol	Spherical Fuzzy Numbers
Extremely good	EG	(0.9, 0.1, 0.1)
Very good	VG	(0.8, 0.2, 0.2)
Good	G	(0.7, 0.3, 0.3)
Fair	F	(0.5, 0.5, 0.5)
Poor	P	(0.3, 0.7, 0.3)
Very poor	VP	(0.2, 0.8, 0.2)
Extremely poor	EP	(0.1, 0.9, 0.1)

.

The TOPSIS method, which is one of the most frequently used techniques in fuzzy MCDM problems, is also preferred in three-dimensional fuzzy set environments. This preference is due to the fact that the TOPSIS method evaluates the distances to both the ideal and negative-ideal solutions in an integrated manner.

$$X=\left\{x_1,x_2,\dots ,x_m\right\}m\ge 2\mathrm{Alternatives},$$

$$C=\left\{c_1,c_2,\dots ,x_n\right\}\mathrm{Criterion},$$

$$w=\left\{w_1,w_2,\dots ,w_m\right\}0\le w_j\le 1and{\displaystyle {\sum }_{i=1}^n}{w}_j=1\mathrm{They}\mathrm{represent}\mathrm{the}\mathrm{weights}.$$

The steps of an SF-TOPSIS application are explained below [80,89,90,91].

Step 1. Construction of the decision matrix:

The decision matrix is constructed using the linguistic variables presented in Table 3.

Step 2. Aggregation of matrices:

The matrices are aggregated using the SWAM and SWGM operators, as defined by Equations (7) and (8), respectively, and the weights are calculated. The sum of the weights must be equal to 1.

Step 3. Construction of the aggregated spherical fuzzy matrix:

Let the alternatives be $X_i\left(i=\mathrm{1,2},\dots ,m\right)$ and the criteria be $C_j(j=\mathrm{1,2},\dots ,n)$ and $\left(C_j\left(X_{İ}\right)\right)=({\mu }_{ij},v_{ij},{\pi }_{ij})$. Here, ${\mu }_{ij}$, $v_{ij}$ and ${\pi }_{ij}$ denote the membership, non-membership, and hesitation degrees of alternative i with respect to criterion j in the spherical fuzzy environment.

The aggregated spherical fuzzy decision matrix is represented as $D={\left(C_j\left(X_i\right)\right)}_{m*n}$. The matrix D constructed in this manner is expressed by Equation (11).

$$D={\left(C_j\left(X_i\right)\right)}_{m*n}=\left(\begin{array}{ccc}({\mu }_{11},v_{11},{\pi }_{11}& \dots & ({\mu }_{1n},v_{1n},{\pi }_{1n})\\ \dots & \dots & \dots \\ \left({\mu }_{m1},v_{m1},{\pi }_{m1}\right)& \dots & ({\mu }_{mn},v_{mn},{\pi }_{mn})\end{array}\right)$$

(11)

Step 4. Construction of the weighted spherical fuzzy matrix:

Using the linguistic variables shown in Table 2 and the SWAM operator, the spherical fuzzy weights of the criteria affecting the problem are calculated as expressed in Equation (12).

$$D={\left(C_j\right(X_{iw}\left)\right)}_{m*n}=\left(\begin{array}{ccc}({\mu }_{11w},v_{11w},{\pi }_{11w}& \dots & ({\mu }_{1nw},v_{1nw},{\pi }_{1nw})\\ \dots & \dots & \dots \\ \left({\mu }_{m1w},v_{m1w},{\pi }_{m1w}\right)& \dots & ({\mu }_{mnw},v_{mnw},{\pi }_{mnw})\end{array}\right)$$

(12)

where, ${\mu }_{ijw}$, $v_{ijw}$ and ${\pi }_{ijw}$ denote the weighted membership, non-membership and hesitation degrees of alternative i with respect to criterion j in the weighted spherical fuzzy matrix.

Step 5. Fuzzification:

The weighted spherical fuzzy matrix D is fuzzified using Equation (9).

$$Score\left({\tilde{A}}_s\right)={({\mu }_{{\tilde{A}}_s}-{\pi }_{{\tilde{A}}_s})}^2-{(v_{{\tilde{A}}_s}-{\mu }_{{\tilde{A}}_s})}^2$$

Step 6. Calculation of spherical fuzzy positive ideal solution (SF-PIS) and spherical fuzzy negative ideal solution (SF-NIS) sets:

The SF-PIS is calculated using Equation (13), while the SF-NIS is calculated using Equation (14).

$$A^{+}=\left\{C_j,{max}_i<Score\left(C_j\left(X_{iw}\right)\right)>\left|j=\mathrm{1,2},3,\dots ,n\right.\right\}$$

(13)

$$A^{+}=\left\{〈C_1({\mu }_1,v_1,{\pi }_1)〉,〈C_2({\mu }_2,v_2,{\pi }_2)〉,\dots ,〈C_n({\mu }_n,v_n,{\pi }_n)〉\right\}$$

$$A^{-}=\left\{C_j,{min}_i<Score\left(C_j\left(X_{iw}\right)\right)>\left|j=\mathrm{1,2},3,\dots ,n\right.\right\}$$

(14)

$$A^{-}=\left\{〈C_1({{\mu }_1}^{-},{v_1}^{-},{{\pi }_1}^{-})〉,〈C_2({{\mu }_2}^{-},{v_2}^{-},{{\pi }_2}^{-})〉,\dots ,〈C_n({{\mu }_n}^{-},{v_n}^{-},{{\pi }_n}^{-})〉\right\}$$

Step 7. Calculation of distances to the spherical fuzzy positive ideal solution and spherical fuzzy negative ideal solution:

Using the normalized Euclidean distance, the SF-PIS value for each alternative is calculated by Equation (15), and the SF-NIS value is calculated by Equation (16).

$$=\sqrt[D(X_i,A^{+}]{{\displaystyle \frac{1}{2n}}{\displaystyle \sum _{i=1}^n}({({\mu }_{x_i}-{\mu }_{A^{+}})}^2+{(v_{x_{İ}}-v_{A^{+}})}^2+{({\pi }_{x_i}-{\pi }_{A^{+}})}^2)}$$

(15)

$$=\sqrt[D(X_i,A^{-}]{{\displaystyle \frac{1}{2n}}{\displaystyle \sum _{i=1}^n}({({\mu }_{x_i}-{\mu }_{A^{-}})}^2+{(v_{x_{İ}}-v_{A^{-}})}^2+{({\pi }_{x_i}-{\pi }_{A^{-}})}^2)}$$

(16)

Step 8. Calculation of the minimum distance to SF-PIS and maximum distance to SF-NIS:

For this purpose, the operations shown in Equations (17) and (18) are performed.

$$D_{min}\left(X_i,A^{+}\right)=\underset{1\le i\le m}{\mathit{min}}D\left(X_i,A^{+}\right)$$

(17)

$$D_{max}\left(X_i,A^{-}\right)=\underset{1\le i\le m}{\mathit{max}}D\left(X_i,A^{-}\right)$$

(18)

Step 9. Calculation of the relative closeness of alternatives:

For this purpose, the revised calculation proposed by Kutlu Gündoğdu and Kahraman [78] is performed using Equation (19).

$$\xi \left(X_i\right)={\displaystyle \frac{D(X_i,A^{+})}{D_{min}(X_i,A^{+})}}-{\displaystyle \frac{D(X_i,A^{-})}{D_{max}(X_i,A^{-})}}$$

(19)

Step 10. Ranking of alternatives:

The obtained $\xi \left(X_i\right)$ values are ranked in descending order.

3. Results and Discussion

The fuel characteristics presented in Table 1 were evaluated by three experts using the linguistic scale shown in Table 2. The evaluation results are presented in

Table 4. Evaluation of Fuel Characteristics.

Expert	Fuel Properties
	FM	EC	LHV	HHV	PS	FP	AT	MI	ESI	S	CO2	NOX	PAH
KV1	SMI	HI	VHI	VHI	SMI	EI	SMI	HI	VHI	AMI	HI	AMI	VHI
KV2	VHI	HI	HI	HI	VLI	VLI	LI	SLI	LI	HI	VLI	SMI	LI
KV3	VHI	AMI	VHI	HI	HI	HI	HI	HI	AMI	AMI	AMI	VHI	HI
KV4	HI	AMI	AMI	SLI	HI	SMI	VHI	HI	SLI	HI	HI	VLI	ALI

below.

The expert evaluations presented in Table 4 were converted into the corresponding spherical fuzzy numbers indicated in the table, and the weights of the fuel characteristics were obtained using the SWAM operator defined in Equation (7). The results are presented in

Table 5. Spherical Fuzzy Weights of the Criteria.

Criteria	FM	EC	LHV	HHV	PS
$\widetilde{{\mathit{w}}_{\mathit{j}}}$	(0.74, 0.26, 0.18)	(0.83, 0.17, 0.11)	(0.82, 0.19, 0.11)	(0.69, 0.32, 0.20)	(0.61, 0.41, 0.22)
Criteria	FP	AT	MI	ESI
$\widetilde{{\mathit{w}}_{\mathit{j}}}$	(0.55, 0.44, 0.28)	(0.65,0.36, 0.21)	(0.65, 0.36, 0.22)	(0.72, 0.30, 0.15)
Criteria	S	CO2	NOX	PAH
$\widetilde{{\mathit{w}}_{\mathit{j}}}$	(0.83, 0.17, 0.11)	(0.73, 0.29, 0.14)	(0.74, 0.28, 0.14)	(0.60, 0.44, 0.16)

below.

In MCDM applications, the sum of the weights equals 1. The SF values in Table 5 were defuzzified using Equation (9) to obtain the score values. These values were then normalized using the formula provided below to determine the actual criterion weights. According to the calculated weights of the fuel characteristics, the three most important criteria were identified as C13 (PAH emissions), C11 (CO₂ emissions), and C9 (Energy Security Impacts), respectively.

In multi-criteria decision-making (MCDM) methods, the sum of the weights is required to be equal to one as a fundamental principle. During the defuzzification of spherical fuzzy weights, it was observed that the sum of the defuzzified weights did not satisfy this condition. Therefore, a normalization procedure was applied to ensure that the sum of the defuzzified criterion weights equals one.

Since the resulting normalized weights could not be re-fuzzified directly, a multiplication of spherical fuzzy sets by a constant scalar (as described in Equation (5)) was employed to maintain consistency within the fuzzy algebra framework.

The score values and the final criterion weights are presented in

Table 6. Score Values and Final Weights of the Criteria.

Criterion	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	Sum
$\mathit{S}\mathit{c}\mathit{o}\mathit{r}\mathit{e}\left({\tilde{\mathit{A}}}_{\mathit{s}}\right)$	0.088	0.085	0.107	0.107	0.110	0.061	0.115	0.097	0.154	0.085	0.155	0.145	0.173	1.481
${\mathit{w}}_{\mathit{j}}$	0.060	0.057	0.072	0.072	0.074	0.041	0.078	0.065	0.104	0.057	0.104	0.098	0.117

C1 to C13 represent the considered criteria: C1: FM; C2: EC; C3: LHV; C4: HHV; C5: PS; C6: FP; C7: AT; C8: MI; C9: ESI; C10: S; C11: CO₂; C12: NO_X; C13: PAH.

below.

$$w_j={\displaystyle \frac{w_{ij}}{{\displaystyle {\sum }_{j=1}^n}{w}_{ij}}}$$

(20)

After calculating the spherical fuzzy weights of the fuel characteristics, the aggregated decision matrix expressed by Equation (11) was constructed.

Table 7. Spherical Fuzzy Evaluation Matrix.

Fuel	FM	EC	LHV	HHV	PS	FP	AT	MI	ESI	S	CO2	NOX	PAH
G	EP	VG	VG	VG	VG	P	G	EG	VP	VP	VG	VG	VG
D	EP	EG	EG	EG	VG	VG	F	VG	VP	VP	VG	EG	VG
B100	EG	VG	VG	VG	VG	EG	F	F	EG	EG	F	EG	VP
LPG	VP	G	G	G	P	VP	G	VP	VP	VP	VP	VP	VP
CNG	VP	F	VP	VP	VP	EP	VG	VP	EP	P	VP	VP	VP
LNG	VP	F	VP	VP	F	EP	VG	EP	EP	P	VP	VP	VP
E100	EG	F	F	F	VG	G	G	P	EG	EG	VP	F	VP
M	VP	P	P	P	VG	G	G	VP	G	F	VP	VP	VP
H	VP	VG	P	P	VP	EP	VG	VP	VP	P	EP	VP	EP

was developed based on the alternative fuels and evaluation criteria presented in Table 1, utilizing the linguistic scale outlined in Table 2. The relevant data were derived from the fuel comparison chart published by the U.S. Department of Energy [92].

The defuzzified weights shown in Table 6 are multiplied by the SF evaluation matrix expressed with linguistic variables in Table 7 using the SF multiplication operation defined in Equation (7). The weighted spherical fuzzy matrix, expressed by Equation (12), is presented below in

Table 8. Weighted Spherical Fuzzy Matrix.

Fuel	FM			EC			LHV			HHV			PS
G	0.030	0.991	0.030	0.288	0.873	0.095	0.321	0.842	0.106	0.321	0.842	0.106	0.326	0.838	0.107
D	0.030	0.991	0.030	0.362	0.823	0.063	0.403	0.783	0.069	0.403	0.782	0.069	0.326	0.838	0.107
B100	0.370	0.816	0.064	0.288	0.873	0.095	0.321	0.842	0.106	0.321	0.842	0.106	0.326	0.838	0.107
LPG	0.060	0.980	0.061	0.235	0.903	0.124	0.263	0.880	0.138	0.263	0.879	0.138	0.101	0.962	0.106
CNG	0.060	0.980	0.061	0.155	0.943	0.182	0.066	0.977	0.067	0.066	0.976	0.067	0.067	0.976	0.068
LNG	0.060	0.980	0.061	0.155	0.943	0.182	0.066	0.977	0.067	0.066	0.976	0.067	0.176	0.927	0.205
E100	0.370	0.816	0.064	0.155	0.943	0.182	0.174	0.929	0.202	0.174	0.929	0.203	0.326	0.838	0.107
M	0.060	0.980	0.061	0.089	0.970	0.093	0.100	0.963	0.104	0.100	0.963	0.105	0.326	0.838	0.107
H	0.060	0.980	0.061	0.288	0.873	0.095	0.100	0.963	0.104	0.100	0.963	0.105	0.067	0.976	0.068
Fuel	FP			AT			MI			ESI
G	0.076	0.979	0.079	0.273	0.871	0.143	0.385	0.800	0.067	0.079	0.966	0.081
D	0.246	0.907	0.082	0.180	0.923	0.210	0.307	0.856	0.101	0.079	0.966	0.081
B100	0.310	0.869	0.055	0.180	0.923	0.019	0.166	0.935	0.193	0.475	0.701	0.080
LPG	0.050	0.987	0.051	0.273	0.871	0.143	0.063	0.979	0.064	0.079	0.966	0.081
CNG	0.025	0.994	0.025	0.333	0.831	0.109	0.063	0.979	0.064	0.039	0.984	0.040
LNG	0.025	0.994	0.025	0.333	0.831	0.109	0.031	0.990	0.031	0.039	0.984	0.040
E100	0.200	0.929	0.106	0.273	0.871	0.143	0.095	0.966	0.100	0.475	0.701	0.080
M	0.200	0.929	0.106	0.273	0.871	0.143	0.063	0.979	0.064	0.314	0.830	0.163
H	0.025	0.994	0.025	0.333	0.831	0.109	0.063	0.979	0.064	0.079	0.966	0.081
Fuel	S			CO2			NOX			PAH
G	0.288	0.873	0.095	0.382	0.780	0.124	0.371	0.792	0.121	0.403	0.757	0.130
D	0.288	0.873	0.095	0.382	0.780	0.124	0.463	0.716	0.078	0.403	0.757	0.130
B100	0.362	0.823	0.063	0.209	0.898	0.241	0.463	0.716	0.078	0.084	0.962	0.085
LPG	0.059	0.981	0.060	0.079	0.966	0.081	0.077	0.968	0.078	0.084	0.962	0.085
CNG	0.059	0.981	0.006	0.079	0.966	0.081	0.077	0.968	0.078	0.084	0.962	0.085
LNG	0.059	0.981	0.060	0.079	0.966	0.081	0.077	0.968	0.078	0.084	0.962	0.085
E100	0.362	0.823	0.063	0.079	0.966	0.081	0.202	0.904	0.234	0.084	0.962	0.085
M	0.155	0.943	0.182	0.079	0.966	0.081	0.077	0.968	0.078	0.084	0.962	0.085
H	0.089	0.970	0.093	0.039	0.984	0.040	0.077	0.968	0.078	0.042	0.982	0.042

.

The weighted spherical fuzzy matrix values are defuzzified using Equation (9). Subsequently, the SF-PIS and SF-NIS values are determined. The defuzzified matrix is presented in

Table 9. Defuzzified Matrix in the FS-TOPSIS Method.

	FM	EC	LHV	HHV	PS	FP	AT	MI	ESI	S	CO2	NOX	PAH
Fuel	max	max	max	max	max	max	max	max	max	max	min	min	min
G	−0.923	−0.305	−0.225	−0.225	−0.215	−0.815	−0.340	−0.071	−0.787	−0.305	−0.091	−0.115	−0.051
D	−0.923	−0.123	−0.033	−0.032	−0.215	−0.410	−0.551	−0.259	−0.787	−0.305	−0.091	0.083	−0.051
B100	−0.106	−0.305	−0.225	−0.225	−0.215	−0.247	−0.526	−0.591	0.105	−0.123	−0.475	0.083	−0.771
LPG	−0.847	−0.433	−0.365	−0.364	−0.740	−0.877	−0.340	−0.839	−0.787	−0.851	−0.786	−0.795	−0.771
CNG	−0.847	−0.620	−0.829	−0.829	−0.826	−0.939	−0.198	−0.839	−0.892	−0.848	−0.786	−0.795	−0.771
LNG	−0.847	−0.620	−0.829	−0.829	−0.562	−0.939	−0.198	−0.919	−0.892	−0.851	−0.786	−0.795	−0.771
E100	−0.106	−0.620	−0.569	−0.569	−0.215	−0.522	−0.340	−0.758	0.105	−0.123	−0.786	−0.492	−0.771
M	−0.847	−0.776	−0.744	−0.744	−0.215	−0.522	−0.340	−0.839	−0.244	−0.620	−0.786	−0.795	−0.771
H	−0.847	−0.305	−0.744	−0.744	−0.826	−0.939	−0.198	−0.839	−0.787	−0.776	−0.892	−0.795	−0.884

below.

In Table 9, the green cells represent the positive ideal solution (PIS) points for each criterion, while the red cells indicate the negative ideal solution (NIS) points. The points corresponding to PIS and NIS in the weighted aggregated tables were calculated using the SF-PIS Equation (13) and SF-NIS Equation (14), respectively, and the results are presented in

Table 10. SF-PIS and SF-NIS Values.

	FM			EC			LHV			HHV			PS
SF-PIS	0.370	0.816	0.064	0.362	0.823	0.063	0.403	0.783	0.069	0.403	0.782	0.069	0.326	0.838	0.107
SF-NIS	0.030	0.991	0.030	0.089	0.970	0.093	0.066	0.977	0.067	0.066	0.976	0.067	0.067	0.976	0.068
	FP			AT			MI			ESI
SF-PIS	0.310	0.869	0.055	0.333	0.831	0.109	0.385	0.800	0.067	0.079	0.966	0.081
SF-NIS	0.025	0.994	0.025	0.180	0.923	0.210	0.031	0.990	0.031	0.039	0.984	0.040
	S			CO2			NOX			PAH
SF-PIS	0.288	0.873	0.095	0.039	0.984	0.040	0.077	0.968	0.078	0.042	0.982	0.256	0.288
SF-NIS	0.059	0.981	0.006	0.382	0.780	0.124	0.463	0.716	0.078	0.403	0.757	0.573	0.059

.

Subsequently, the values of $\xi \left(X_i\right)$ obtained by applying Equations (13)–(19) are ranked in descending order to determine the final result. The ranking of the alternatives based on the values of $D_{min}\left(X_i,A^{+}\right)$, $D_{max}\left(X_i,A^{-}\right)$ ve $\xi \left(X_i\right)$ is presented in

Table 11. Evaluation Results of Fuel Types.

Alternative Fuels	Kod	${\mathit{D}}_{\mathit{m}\mathit{i}\mathit{n}}\left({\mathit{X}}_{\mathit{i}}.{\mathit{A}}^{+}\right)$	${\mathit{D}}_{\mathit{m}\mathit{a}\mathit{x}}\left({\mathit{X}}_{\mathit{i}}.{\mathit{A}}^{-}\right)$	$\mathit{\xi }\left({\mathit{X}}_{\mathit{i}}\right)$	Ranking
Gasoline	G	0.165	0.257	0.354	2
Diesel	D	0.17	0.266	0.362	1
Biodiesel	B100	0.163	0.301	0.199	6
Propane	LPG	0.138	0.3	0.016	9
Compressed Natural Gas	CNG	0.177	0.312	0.265	3
Liquefied Natural Gas	LNG	0.174	0.306	0.263	4
Ethanol	E100	0.163	0.295	0.218	5
Methanol	M	0.16	0.305	0.16	7
Hydrogen	H	0.159	0.317	0.117	8

below.

The evaluation results indicate that despite the adverse environmental impacts of conventional fossil fuels such as gasoline and diesel, they remain the most reliable fuels. This suggests that conventional fuels will continue to be used or preferred for an extended period due to their perceived reliability. Although certain alternative fuels, such as ethanol and biodiesel, have been adopted intensively in specific countries—often supported by national blending mandates and renewable energy targets—their global uptake remains uneven and limited. This disparity reflects differences in policy support, infrastructure readiness, and market conditions across regions [93]. Consequently, electric vehicles (EVs), which utilize electricity as a prominent emerging alternative fuel, have experienced rapid growth. Despite challenges related to infrastructure availability and safety concerns, EVs have increasingly positioned themselves as the leading alternative to conventional internal combustion engine vehicles.

In the context of evaluating alternative fuels, multi-criteria decision-making (MCDM) methods play a crucial role in systematically assessing complex and often conflicting criteria. According to the literature, approximately 200 MCDM methods currently exist, with new methods continuously being developed and introduced, such as RADAR [94,95,96].

4. Conclusions

MCDM methods have been successfully applied to many real-world problems, providing decision support to decision-makers. However, each study has specific limitations. It is important to consider certain constraints in the decision support system developed to solve the problem.

One of the main challenges in practical applications is the difficulty decision-makers face when making judgments under uncertainty. They often struggle to effectively use flexible tools such as fuzzy numbers and may require training to apply them properly.

The main limitations of the Spherical Fuzzy Multi-Criteria Decision-Making (SF-MCDM) methodology proposed in this study are summarized as follows:

In this study, the evaluation criteria and fuel types were limited to 13 criteria and 9 alternatives. The selected fuel types are commonly used, and the criteria are those for which data is readily available.

This study has certain limitations, as follows:

• A comprehensive evaluation of alternative and conventional fuels under real-world conditions requires the involvement of a larger number of decision-makers. However, this study is based on the opinions of only four experts.
• Due to structural limitations of traditional fuzzy sets, they may be inadequate for decision-making problems characterized by high uncertainty. Therefore, this study employs Spherical Fuzzy Sets (SF), one of the most recent and comprehensive approaches, to ensure methodological robustness.

Within these limitations, the SF-TOPSIS method was applied. Conventional fossil fuels and several commonly known alternative fuels were compared accordingly.

Furthermore, this study indirectly contributes to answering the question: “Alternative fuels or conventional fossil fuels?” The answer depends on various environmental, economic, and technological factors. Current trends and scientific data indicate that in the short term, fossil fuels are more economical and accessible. However, in the long term, harmful emissions such as CO₂, NO_x, and SO₂ significantly contribute to air pollution, global warming, and climate change, posing serious environmental risks.

At this point, alternative fuels offer promising options. Vehicles powered by energy derived from renewable sources such as solar, wind, biomass, and hydrogen represent a pathway toward a more sustainable and livable future. Although these alternatives may appear costly in the short term, it is expected that the environmental benefits will offset these costs in the long run, making them more economically advantageous. Moreover, the ability of countries to produce and utilize alternative fuels tailored to their local conditions helps reduce foreign dependency and carries strategic importance for energy security.

Therefore, this study could be extended by incorporating the opinions of more experts in the automotive field. Additionally, an AI-assisted model could be developed to create a decision support system with broader expert participation, more criteria, and a wider set of fuel alternatives for comparative analysis.

On the other hand, one of the major obstacles to the widespread adoption of alternative fuels is the lack of suitable technological infrastructure. The reliance of most current vehicles on conventional technologies hampers the transition to next-generation vehicles. While developed countries are in a favorable position during this transition, developing countries with high technological dependence face significant challenges. In these countries, developing infrastructure such as electric vehicle charging stations and hydrogen refueling facilities is not only necessary but imperative for environmental sustainability. In this context, for a more sustainable future, the following are necessary:

• Minimizing the use of fossil fuels, which are rapidly depleting and accelerating climate change, has become imperative.
• Vehicles powered by alternative fuels, particularly hydrogen and renewable sources, as well as electric vehicles (EVs) using electricity generated from clean energy sources, are increasingly central to the energy strategies of many countries.
• Major economies such as the European Union, China, and the United States are expected to implement plans to ban fossil fuel-powered vehicles in the near future, even if not immediately.

Future research can address the current limitations of this study. For example, this study may be replicated using different MCDM methods such as MARCOS, OCRA, or MAIRCA within the framework of spherical fuzzy logic. Alternatively, the TOPSIS method employed here can be implemented with other types of fuzzy sets. A comparison between the results of the SF-TOPSIS method and the classical TOPSIS method could also be conducted. Such comparative sensitivity analyses would thoroughly evaluate the effectiveness of the applied methods.

Finally, the model presented in this study is not limited to alternative fuel selection alone. It can be adapted to a wide range of decision-making problems characterized by uncertainty, such as sustainable plastic recycling processes, site selection for electric vehicle charging stations, battery selection, and emergency facility placement.