A Computational Case Study on Sustainable Energy Transition in the Kingdom of Saudi Arabia

Abstract

With the increasing urgency for sustainable development and energy transition, decision-makers face complex challenges in evaluating and prioritizing viable alternatives. Traditional decision-making techniques often struggle to capture the inherent uncertainty and imprecision associated with the latest sustainable energy transition issues. This paper presents a research framework based on fuzzy set theory and the technique for order of preference by similarity to ideal solution (TOPSIS) method to address these complexities and uncertainties. Our proposed approach offers a comprehensive evaluation and ranking of alternatives for sustainable energy transition. To demonstrate the effectiveness and applicability of this system, we employ a case study in the Kingdom of Saudi Arabia (KSA). As a global leader in fossil fuel production and export, particularly oil, the KSA has recognized the need to address climate change and diversify its energy sector. By leveraging the fuzzy TOPSIS-based framework, we provide decision-makers with a powerful tool to navigate the challenges and uncertainties involved in the energy transition process. This research yields promising results, demonstrating the superior capabilities of the proposed fuzzy TOPSIS-based framework compared to traditional decision-making techniques. The case study in the KSA highlights how our approach effectively captures and addresses the uncertainties and complexities involved in sustainable energy transition decision making. Through comprehensive evaluations and rankings, decision-makers gain valuable insights into alternative solutions, facilitating informed and strategic decision-making processes. Our research contributes to sustainable energy transitions by introducing a robust decision-making framework that integrates fuzzy set theory and the TOPSIS method. Based on the fuzzy TOPSIS-based evaluation, the research findings indicate that solar energy (EA1) ranked as the most favourable alternative among the evaluated options for the sustainable energy transition in the KSA. Using our framework, stakeholders in the KSA and similar contexts can make informed decisions to accelerate their energy transition efforts and achieve sustainable development goals.

1. Introduction

The urgent need for a sustainable energy transition has become increasingly apparent as the world grapples with the challenges of climate change, environmental degradation, and the limited availability of fossil fuels. Governments, organizations, and individuals are seeking alternative energy sources and technologies to mitigate the adverse effects of traditional energy systems. However, evaluating and ranking these alternatives present complex decision-making processes that require the careful consideration of various factors. Sustainable energy in Saudi Arabia has gained significant progress and is essential for several reasons [1,2,3,4].

Firstly, the country has recognized the need to reduce its dependence on fossil fuels, primarily oil, for energy generation. As a result, Saudi Arabia has embarked on an ambitious renewable energy program, setting targets to achieve a substantial share of renewable energy in its overall energy mix. This commitment to sustainable energy reflects the country’s efforts to mitigate greenhouse gas emissions, combat climate change, and align with global sustainability goals.

Secondly, Saudi Arabia possesses abundant renewable energy resources, particularly solar and wind. The country’s geographical location makes it one of the world’s prime locations for solar power generation. By harnessing these resources, Saudi Arabia can tap into its renewable energy potential, reduce carbon emissions, and diversify its energy sources. Additionally, the declining costs of renewable technologies have made them increasingly competitive and economically viable options for the country.

Furthermore, sustainable energy development in Saudi Arabia presents significant economic opportunities. Investing in renewable energy projects stimulates job creation, attracts foreign direct investment, and fosters the growth of a domestic renewable energy industry. This transition can also enhance energy security by decreasing dependence on fossil energy imports and volatility in global oil markets. It allows Saudi Arabia to use its vast oil reserves for other valuable purposes, such as petrochemical industries and exports. The country’s commitment to diversify its economy further emphasises the importance of sustainable energy in Saudi Arabia. As part of its Vision 2030 plan, Saudi Arabia aims to reduce its dependency on oil revenue and create a more sustainable and diversified economy. The development of sustainable energy contributes to this goal by fostering innovation, technological advancement, and the growth of new industries. Moreover, sustainable energy solutions can address the increasing energy demand driven by population growth and urbanization in Saudi Arabia. By integrating energy-efficient practices and renewable energy sources, the country can meet its energy needs while reducing its strain on natural resources and minimizing environmental impact.

As part of the Saudi Arabia Vision 2030 plan, the country has set ambitious targets for renewable energy capacity. The revised targets aim to achieve 27.3 GW of renewable power capability by 2023 and 58.7 GW by 2030. The present rate of renewables progress in Saudi Arabia falls significantly short of these targets; the country’s average annual renewable capacity additions between 2010 and 2021 stand at only 0.1 GW, which indicates a considerable shortfall of 25.8 GW (Gigawatt) in reaching the 2023 target. Even the 2030 targets appear challenging to achieve based on the country’s current trajectory of renewable energy development [5]. The comparison between the current forecast and the target for renewable power capacity in Saudi Arabia for 2023 and 2030 is illustrated below in Figure 1.

Evaluating and ranking alternatives for sustainable energy transition is crucial for identifying the most viable and effective options. Decision-makers must consider multiple criteria, such as environmental impact, cost-effectiveness, scalability, reliability, and social acceptance. The selection of appropriate criteria and the systematic analysis of alternatives are critical for ensuring a successful and efficient transition to sustainable energy systems. Traditional decision-making methods often fall short when it comes to evaluating and ranking options for sustainable energy transition. These methods often overlook the inherent uncertainties, complexities, and interdependencies involved in such evaluations. Moreover, the evaluation process usually involves conflicting objectives and trade-offs among different criteria, making it challenging to arrive at a comprehensive and objective decision [6,7,8].

Researchers and practitioners have turned to advanced decision-making techniques that account for uncertainty, fuzziness, and multiple criteria to address these challenges. These techniques aim to provide a robust and systematic method to assess and rank alternatives in the context of sustainable energy transition. One such approach is the application of multi-criteria decision analysis (MCDA) procedures, which enable the consideration of various criteria and their relative significance. MCDA methods help decision-makers structure the evaluation process, identify trade-offs, and quantify the performance of alternatives based on selected criteria. These methods facilitate a more comprehensive and transparent decision-making process, allowing stakeholders to understand the strengths and weaknesses of each option [9,10,11,12].

Furthermore, the integration of MCDA methods with sustainability assessment frameworks, life cycle analysis, and economic models enhances the evaluation and ranking of alternatives for sustainable energy transition [13,14,15]. By considering environmental, economic, and social factors, decision-makers can account for the alternatives’ long-term sustainability and feasibility. This research aims to contribute to a sustainable energy transition by exploring and implementing advanced evaluation and ranking methods for alternatives. By incorporating MCDA techniques and integrating various sustainability criteria, this research seeks to give decision-makers a comprehensive and objective framework to assess the feasibility and potential impacts of different alternatives.

Through case studies, data analysis, and expert consultations, this research will evaluate and rank a range of alternative energy sources and technologies. The findings will inform policymakers, organizations, and individuals about the most promising alternatives for sustainable energy transition. Additionally, this research will highlight the strengths and limitations of the evaluation and ranking methods employed, enabling further improvements in decision-making processes. Ultimately, evaluating and ranking alternatives for sustainable energy transition play a vital role in shaping the future energy landscape. By adopting a systematic and comprehensive approach, decision-makers can select the most suitable alternatives that align with environmental goals, social values, and economic viability. This research strives to contribute to the advancement of sustainable energy transition and pave the way for a cleaner, more resilient, and sustainable energy future.

The paper follows a structured format to present the research findings on sustainable energy transitions in the Kingdom of Saudi Arabia. Section 1 provides an introduction to the topic, highlighting the significance of the study. Section 2 reviews the existing literature and research conducted in the field of sustainable energy transition in Saudi Arabia. Section 3 describes the methodology employed, explicitly focusing on the fuzzy TOPSIS approach used for the evaluation. Section 4 presents the findings, including the comparative analysis between the results obtained from the fuzzy TOPSIS and analytic hierarchy process (AHP) analyses. In Section 5, the results are further explored and interpreted in the context of the broader sustainable energy transition discourse in Saudi Arabia. Section 6 concludes the paper by summarizing the key findings, highlighting the study’s limitations, and suggesting avenues for future research. The paper’s structure ensures a coherent presentation of the research process, findings, and implications, providing valuable insights into the sustainable energy transition in the Kingdom of Saudi Arabia.

2. Related Works

In their study, Neofytou et al. [16] presented a comprehensive multi-criteria investigation framework for evaluating a nation’s readiness for a sustainable energy switch. The framework encompasses the following four key pillars: social, political/regulatory, economic, and technological, and incorporates eight evaluation criteria. By utilizing the PROMETHEE II and AHP methods, the authors developed a decision analysis framework to assess and rank 14 countries with varying profiles and progress levels in sustainable development. Their objective in this analysis was to identify areas requiring improvement and provide policymakers with insights to design effective pathways towards a greener economy. This research aims to support informed decision making and facilitate the transition to sustainable energy systems at the national level.

Ainou et al. [17] used the 4-As framework to undertake an examination of Morocco’s energy security from 2000 to 2016. The 4-As technique sought to quantify and visually express improvements in Morocco’s energy security by investigating the following four significant dimensions: energy resource availability, technology applicability, acceptability by the environment and society, and energy resource affordability. The statistical evaluation found that Morocco’s energy security performance peaked throughout the study’s starting period (2000–2004). It then fell for the rest of the research period because of higher energy imports, higher costs, as well as poor performance concerning technology relevance, especially low-energy effectiveness. The researchers proposed including more renewable energy sources into the energy mix to improve Morocco’s energy security while encouraging its switch to green energy systems. They also advocated for implementing environmentally friendly innovations through large-scale green finance and green investment programmes. Such efforts can help Morocco improve its energy security, guaranteeing a more resilient and environmentally friendly energy future.

In another study, Meschede et al. [18], from the perspective of a distribution system operator, analysed various key concepts relevant to achieving 100% renewable energy on a subtropical island. Their approach allowed for a comprehensive assessment of all system costs associated with transitioning from a centralized energy system to a fully renewable one, as well as considering the macroeconomic costs of such a transition. The research specifically focused on the case of La Gomera, where the economic competitiveness of renewable energy bases, such as solar photovoltaic (PV) and wind power, was demonstrated. The study evaluated multiple sustainable scenarios, all of which exhibited lower annual costs and reduced primary energy demands contrasted to the business-as-usual (BAU) setting. The cost assumptions utilized in the study provided evidence for the economic viability of renewable energy options in La Gomera. The findings highlight the potential for renewable energy to offer a financially favourable and environmentally sustainable alternative compared to traditional energy sources.

Walker et al. [19] proposed a novel decision support strategy centred on life cycle efficiency modelling to assist in the development of plans for creating energy-neutral neighbourhoods. The assessment method was created by scenario analysis utilising computational simulations, which was then followed by a deterministic computation. The evaluation results enabled decision-makers to determine an optimal clean energy growth strategy. A probabilistic sensitivity evaluation was performed on the chosen scenario using Monte Carlo simulations to prepare for unpredictability. The researchers applied this methodology to a practical case study, demonstrating its feasibility in real-world applications. The study also outlined recommendations and limitations regarding the realization of energy-neutral neighbourhoods. Overall, the proposed methodology provides valuable insights and tools to support decision-making in the planning and implementation of sustainable energy solutions for communities.

Brodny and Tutak [20] conducted an assessment of sustainable energy security, considering energy, climate, economic, and social aspects over an 11-year period from 2008 to 2018. Their analysis involved a designated set of 14 indicators that characterized these dimensions. To provide accurate evaluations for the specific years and dimensions, the researchers employed the entropy-weight and TOPSIS methods. The comprehensive analyses revealed significant differentiation among the Visegrad Group (V4) countries across various areas that were examined. The results indicated that the Czech Republic achieved the highest level of sustainable energy security during the studied period, while Poland exhibited the lowest level. These findings serve as valuable insights into the energy security status of the countries under scrutiny and should be utilized as an essential source of information for future endeavours to ensure their energy security in an ecologically neutral way. Their research contributes to a better understanding of sustainable energy security and provides a foundation for informed decision making and policy development in the studied countries.

Narayanamoorthy et al. [21] conducted an evaluation of five storage alternatives based on multiple criteria, including technology, cost, environmental impact, performance, and social impact. Using the developed framework, they found that battery energy storage systems (BESSs) outperformed the other considered energy storage systems (ESSs). The researchers assessed the flexibility of their proposed model through a comparison and sensitivity analysis. The sensitivity analysis revealed that the weights assigned to each criterion influenced the model’s outcomes. Additionally, the comparison study demonstrated that the linear Diophantine-hesitant fuzzy sets (LDHFSs)-based methodology could effectively handle complex scenarios, incorporating a diverse range of criteria. These findings highlight the suitability and adaptability of the model for addressing storage alternatives in various contexts. Their research provides valuable insights into the performance of different storage alternatives and demonstrates the usefulness of the proposed framework. The study contributes to the field of storage technology selection by considering multiple dimensions and provides a foundation for informed decision making in the deployment of energy storage systems.

A model based on probabilities for decision making in the transition to sustainable energy in emerging nations of SE Europe was created by Hribar et al. [22]. The model will be created following the unique characteristics of the SE European nations for which it is designed. The transition to renewable energy is slower and more challenging in these nations for a variety of reasons, including a high degree of uncertainty, a lack of openness, corruption, issues with investments, a lack of reliable data, a low level of economic growth, a high level of fraud, and a lack of educated personnel. Forming decisions has become more challenging and demanding due to all these reasons.

Höfer and Madlener [23] evaluated four energy transition possibilities while considering various stakeholders’ views. They created a multi-criteria group decision approach that employs multi-attribute utility theory to assess the energy transition possibilities with value-focused thinking to create a holistic objective framework. They could recognise three primary strands of opinion amongst the stakeholders they were considering, despite the fact that the individual scenario assessments revealed that the stakeholders’ views on a transition to sustainable energy vary significantly. They produced comprehensive policy suggestions for a sustainable energy transition by grouping the stakeholder interests using the k-means clustering approach. The approaches for the various phases of multi-criteria decision making for sustainable energy, including criterion selection, criteria weighting, assessment, as well as final aggregation, were examined by Wang et al. [24]. Technical, economic, environmental, and social considerations were used to summarise the criteria for energy supply systems. Subjective weighting, objective weighting, and combination weighting procedures comprise the three types of criteria weighting techniques. To determine energy decisions, several techniques, including weighted sum, priority setting, outranking, fuzzy set technique, and their integrations, were used.

These recent research works contribute to the understanding of sustainable energy transition, addressing various aspects such as renewable energy potential, social acceptance, employment implications, techno-economic analysis, and the role of financial institutions. They provide valuable insights for policymakers, researchers, and stakeholders involved in the ongoing energy transition efforts in Saudi Arabia.

3. Materials and Methods

3.1. Criteria for Evaluation of Sustainable Energy Transition

Multi-criteria decision analysis (MCDA) is a decision-making approach that aims to support complex decision problems involving multiple criteria or objectives. It provides a structured framework for evaluating and comparing alternatives based on performance across multiple criteria. MCDA techniques help decision-makers systematically analyse and prioritize alternatives, taking into account various factors that are often conflicting and difficult to evaluate using a single criterion. MCDA approaches have gained significant attention and applicability in numerous fields, including economics, engineering, environmental management, public policy, and strategic planning. These techniques are particularly useful when decision-making involves diverse stakeholders with different perspectives, preferences, and objectives. By considering multiple criteria, MCDA enables a more comprehensive and balanced evaluation of alternatives, facilitating informed and transparent decision-making processes. The key advantage of MCDA lies in its ability to handle complex decision problems where there is a need to assess and integrate multiple, often conflicting, objectives. Traditional decision-making approaches, such as cost–benefit analysis or simple ranking methods, may overlook important dimensions or fail to capture the complexity and trade-offs involved in real-world decision contexts [22,23,24].

MCDA techniques provide decision-makers with a structured process to identify and define criteria, assign weights to reflect their relative importance, evaluate alternatives against these criteria, and aggregate the results into an overall ranking or preference order. Various MCDA methods have been developed over the years, each employing different mathematical models and algorithms to handle different types of data, uncertainty, and decision contexts. Some commonly used MCDA methods include the analytic hierarchy process (AHP), technique for order of preference by similarity to ideal solution (TOPSIS), preference ranking organization method for enrichment evaluations (PROMETHEEs), and weighted sum model (WSM). These methods offer different approaches for criteria weighting, preference modelling, and aggregation of criteria performance. In the context of sustainable energy transition, MCDA techniques have become increasingly relevant. As decision-makers grapple with the need to shift towards sustainable and low-carbon energy sources, they face complex challenges in evaluating and prioritizing different alternatives. MCDA provides a valuable framework for systematically considering environmental, economic, social, and technological criteria, thereby facilitating the selection and implementation of sustainable energy transition strategies. In our study, we employ MCDA specifically to address the complexities and uncertainties involved in decision making for a sustainable energy transition. By integrating fuzzy set theory and the technique for order of preference by similarity to ideal solution (TOPSIS) method, we extend the capabilities of MCDA to capture and handle imprecision and uncertainty associated with sustainable energy transition decision problems. This allows for a more robust and comprehensive evaluation and ranking of alternatives, supporting decision-makers in navigating the challenges of the energy transition. By leveraging MCDA techniques, decision-makers can make informed choices, considering a wide range of criteria and stakeholder perspectives. This promotes transparency, inclusivity, and sustainability in decision-making processes, ultimately contributing to effective and successful sustainable energy transition efforts [25,26,27].

MCDA enables decision-makers to consider complex decision problems, weigh trade-offs, and make informed choices. In the context of a sustainable energy transition, MCDA techniques play a vital role in supporting the evaluation and selection of sustainable energy strategies. The integration of MCDA with fuzzy set theory and the TOPSIS method in our study enhances its applicability in addressing the complexities and uncertainties of sustainable energy transition decision making. The MCDA approach requires the careful selection and identification of criteria that capture the key dimensions and factors relevant to the evaluation process. The process of identifying criteria involves a systematic analysis of the decision problem, expert consultations, and a literature review. Experts in the field provide valuable insights and domain-specific knowledge to identify criteria that reflect the objectives and priorities of the decision context. Additionally, a thorough review of existing literature helps to identify commonly used criteria and indicators employed in similar decision-making contexts. The identified criteria should be measurable, relevant, non-redundant, and capable of providing valuable information for comparing and evaluating alternative options. Through a rigorous process of expert consultation and literature review, a comprehensive and well-defined set of criteria can be established, enabling an effective MCDA that aids decision-makers in selecting the most suitable alternatives [26,27].

The evaluation of a sustainable energy transition requires the identification of relevant criteria that encompass the multidimensional aspects of such transitions. To ensure a comprehensive and robust set of criteria, a combined approach of expert consultation and literature review is adopted. In our research, we engaged a panel of 75 experts who possess extensive practical experience and expertise in the field of sustainable energy transition. These experts were carefully selected based on their backgrounds, qualifications, and contributions to the subject matter. Their expertise covers a wide range of disciplines related to energy transition, including renewable energy technologies, policy development, environmental impact assessment, economic analysis, and sustainable development strategies. Experts contribute their valuable insights based on their practical experience and expertise. Their input helps capture real-world challenges and considerations in the evaluation process. Additionally, a thorough literature review is conducted, analysing existing research, academic papers, reports, and case studies to identify commonly used criteria and indicators. This comprehensive approach enables the validation and refinement of the identified criteria, ensuring their relevance, applicability, and measurability in different contexts. By combining expert opinions and the findings from the literature review, an effective evaluation framework can be developed, enabling a holistic assessment of sustainable energy transition initiatives.

Environmental impact (C1): This criterion assesses the potential environmental consequences of alternative energy sources and technologies, including greenhouse gas emissions, air pollution, water usage, land use, and ecological impacts. It considers the extent to which an alternative reduces or minimizes environmental harm compared to traditional energy sources.

Cost-effectiveness (C2): This criterion evaluates the economic viability and long-term cost-effectiveness of alternative energy options. It takes into account factors such as initial investment costs, operational expenses, maintenance costs, and the potential for cost reductions over time. The goal is to identify alternatives that provide a favourable balance between upfront costs and long-term financial benefits.

Energy efficiency (C3): This criterion examines the efficiency of energy conversion and utilization in alternative energy systems. It considers the ratio of energy output to energy input, efficiency losses during transmission and distribution, and the potential for optimizing energy use. High energy efficiency alternatives are favoured as they maximize energy production while minimizing waste.

Scalability and reliability (C4): This criterion assesses the scalability and reliability of alternative energy sources and technologies. It considers their ability to meet growing energy demands, their capacity for integration into existing energy infrastructure, and their ability to provide a consistent and reliable energy supply. The reliability of an alternative is evaluated in terms of its ability to generate power continuously, even under varying conditions.

Social acceptance and equity (C5): This criterion takes into account the social acceptance and equity implications of alternative energy options. It considers factors such as public perception, community engagement, stakeholder involvement, and the potential for addressing energy access disparities. Alternatives that promote social acceptance, inclusivity, and equitable distribution of benefits are prioritized.

Technological maturity and innovation potential (C6): This criterion evaluates the technological readiness and innovation potential of alternative energy sources and technologies. It considers the level of development, deployment, and commercialization of the alternative, as well as its potential for further advancements, breakthroughs, and integration with other emerging technologies.

3.2. Alternatives for Evaluation of Sustainable Energy Transition

In the context of a sustainable energy transition, the identification of alternative energy options is crucial for diversifying the energy mix and reducing reliance on fossil fuels. Here are some commonly recognized alternatives that contribute to sustainable energy transition:

• Solar energy (EA1): photovoltaic (PV) panels and concentrated solar power (CSP) systems that convert sunlight into electricity or heat.
• Ocean energy (EA2): extraction of energy from tides, waves, and ocean currents through technologies such as tidal turbines, wave energy converters, and ocean thermal energy conversion.
• Geothermal energy (EA3): utilizing heat from the Earth’s crust to generate electricity or provide heating and cooling through geothermal power plants or geothermal heat pumps.
• Hydropower (EA4): harnessing the energy of flowing or falling water to generate electricity through dams, turbines, and water turbines.
• Biomass energy (EA5): conversion of organic materials, such as agricultural residues, forestry waste, and dedicated energy crops, into heat or electricity through combustion, anaerobic digestion, or gasification.
• Wind energy (EA6): utilization of wind turbines to harness wind power and generate electricity.
• Energy storage technologies (EA7): innovative solutions for storing excess energy generated from renewable sources, including battery storage, pumped hydro storage, and thermal energy storage.

These criteria and alternatives provide a broad framework for evaluating and selecting sustainable energy options. However, the specific weightings and importance assigned to each criterion may vary depending on the context, goals, and priorities of the evaluation process. Decision-makers must carefully assess and customize the criteria based on the unique circumstances and specific objectives of the sustainable energy transition they aim to achieve.

3.3. Fuzzy TOPSIS Method

Decision-making is a complex process that involves considering multiple criteria and evaluating alternatives against these criteria. Traditional decision-making methods often struggle to handle the inherent uncertainties and vagueness in real-world decision problems. To address these challenges, the fuzzy TOPSIS (technique for order of preference by similarity to ideal solution) method was developed. Fuzzy TOPSIS is a powerful decision-making technique that combines fuzzy set theory and the TOPSIS approach to facilitate decision making under uncertainty and imprecision [27,28,29,30,31,32].

The fuzzy TOPSIS method can be effectively applied to evaluate and prioritize alternative energy options in the context of the sustainable energy transition. Sustainable energy transition involves the shift from conventional, fossil fuel-based energy systems to cleaner and more sustainable alternatives. The evaluation and selection of appropriate energy options play a crucial role in achieving the goals of sustainability, environmental protection, and reduced reliance on non-renewable resources. The fuzzy TOPSIS method provides a structured framework for assessing and ranking alternative energy options based on multiple criteria that are relevant to the sustainable energy transition. These criteria may include environmental impact, cost-effectiveness, energy efficiency, scalability, social acceptance, and technological feasibility.

By employing fuzzy set theory, the fuzzy TOPSIS method allows decision-makers to capture the inherent uncertainties and imprecisions associated with sustainable energy transition. The linguistic terms or fuzzy membership functions can be used to represent the subjective judgments and fuzzy nature of criteria evaluations. This ensures that the evaluation process reflects the complexity and ambiguity inherent in decision making related to sustainable energy transition [33,34,35,36].

The fuzzy TOPSIS method enables decision-makers to quantify the degree of membership or preference of each alternative in relation to the ideal solution and negative ideal solution. The ideal solution represents the maximum positive performance for each criterion, while the negative ideal solution represents the minimum negative performance. Based on the calculated distances to the ideal and negative ideal solutions, the alternatives can be ranked according to their overall performance. This approach allows decision-makers to consider the trade-offs among different criteria and select alternatives that strike a balance between various objectives of sustainable energy transition. It helps in identifying energy options that offer high environmental benefits, cost-effectiveness, energy efficiency, and social acceptance.

Additionally, the fuzzy TOPSIS method provides a comprehensive evaluation framework by considering multiple criteria simultaneously. This facilitates a holistic assessment of alternative energy options and aids in identifying the most suitable options for sustainable energy transition. Furthermore, the flexibility of the fuzzy TOPSIS method enables decision-makers to adapt the evaluation process to the specific context and requirements of the sustainable energy transition. The inclusion of relevant stakeholders in the decision-making process and the consideration of their preferences and priorities can enhance the accuracy and acceptance of the evaluation outcomes. The fuzzy TOPSIS method is a valuable tool for evaluating and ranking alternative energy options in the domain of sustainable energy transition. By considering the uncertainties, trade-offs, and multiple criteria associated with this complex decision-making process, fuzzy TOPSIS helps decision-makers in selecting the most appropriate energy alternatives that align with the goals of sustainability, environmental protection, and reduced reliance on non-renewable resources [37,38,39,40,41,42].

The following Figure 2 shows the steps of the fuzzy TOPSIS method.

4. Findings

This computational case study applies the fuzzy TOPSIS method to evaluate and rank alternative options for the sustainable energy transition in the Kingdom of Saudi Arabia. By considering multiple criteria, including technical feasibility, economic viability, and environmental sustainability, the study aims to provide valuable insights into the most favourable alternative among various renewable energy options. The findings of this fuzzy TOPSIS-based computational analysis shed light on the potential of different alternatives and offer guidance for policymakers and stakeholders involved in shaping the sustainable energy landscape of Saudi Arabia.

Step 1: Create a decision matrix

The present study employs the fuzzy TOPSIS method to rank seven alternatives based on six criteria.

Table 1. Different types of criteria with their corresponding weights.

	Name	Type	Weight
1	C1	+	(0.167, 0.167, 0.167)
2	C2	+	(0.167, 0.167, 0.167)
3	C3	+	(0.167, 0.167, 0.167)
4	C4	+	(0.167, 0.167, 0.167)
5	C5	+	(0.167, 0.167, 0.167)
6	C6	+	(0.167, 0.167, 0.167)

illustrates the different types of criteria considered in the analysis, along with their corresponding weights assigned in the evaluation process.

Table 2. Fuzzy Scale.

Code	Linguistic Terms	L	M	U
1	Very weak	0	1	3
2	Weak	1	3	5
3	Average	3	5	7
4	Good	5	7	9
5	Very good	7	9	10

displays the fuzzy scale employed within the model.

The evaluation of alternatives based on various criteria has been conducted, and the results of the decision matrix are presented below in

Table 3. Decision Matrix.

	C1	C2	C3	C4	C5	C6
EA1	(5.800, 7.800, 9.400)	(4.800, 6.800, 8.400)	(3.800, 5.800, 7.600)	(3.500, 5.400, 7.300)	(3.300, 5.200, 7.200)	(5.000, 7.000, 8.800)
EA2	(4.400, 6.400, 8.300)	(3.400, 5.400, 7.200)	(3.200, 5.200, 7.100)	(2.800, 4.800, 6.700)	(3.400, 5.400, 7.400)	(5.800, 7.800, 9.400)
EA3	(5.400, 7.400, 9.100)	(3.800, 5.800, 7.400)	(4.400, 6.400, 8.100)	(3.400, 5.400, 7.300)	(2.500, 4.400, 6.300)	(4.600, 6.600, 8.300)
EA4	(5.400, 7.400, 9.000)	(3.600, 5.600, 7.500)	(3.800, 5.800, 7.600)	(3.400, 5.400, 7.400)	(3.800, 5.800, 7.700)	(5.400, 7.400, 9.000)
EA5	(6.200, 8.200, 9.500)	(3.400, 5.400, 7.400)	(3.600, 5.600, 7.500)	(3.600, 5.600, 7.500)	(3.000, 5.000, 7.000)	(5.800, 7.800, 9.400)
EA6	(5.400, 7.400, 9.100)	(4.400, 6.400, 8.000)	(4.100, 6.000, 7.800)	(4.100, 6.000, 7.900)	(3.400, 5.400, 7.400)	(4.600, 6.600, 8.400)
EA7	(5.400, 7.400, 9.100)	(4.200, 6.200, 8.100)	(4.000, 6.000, 8.000)	(3.300, 5.200, 7.200)	(2.900, 4.800, 6.700)	(6.000, 8.000, 9.400)

. It is important to note that in cases where multiple experts participated in the evaluation, the matrix displayed represents the arithmetic mean of all the experts’ assessments.

Step 2: Generate the normalized decision matrix

The normalized decision matrix can be calculated using the following relation, considering the positive and negative ideal solutions as reference points.

$${\tilde{r}}_{ij}=\left(\frac{a_{ij}}{c_j^{\ast }},\frac{b_{ij}}{c_j^{\ast }},\frac{c_{ij}}{c_j^{\ast }}\right)\hspace{1em}\hspace{1em};\hspace{1em}\hspace{1em}{c}_j^{\ast }={max}_i{ c}_{ij} ; \mathit{Positive\; ideal\; solution}$$

$${\tilde{r}}_{ij}=(\frac{a_j^{-}}{c_{ij}},\frac{a_j^{-}}{b_{ij}},\frac{a_j^{-}}{a_{ij}})\hspace{1em}\hspace{1em};\hspace{1em}\hspace{1em}{a}_j^{-}={min}_i{ a}_{ij} ; \mathit{Negative\; ideal\; solution}$$

The normalized decision matrix is shown in

Table 4. A normalized decision matrix.

	C1	C2	C3	C4	C5	C6
EA1	(0.611, 0.821, 0.989)	(0.571, 0.810, 1.000)	(0.469, 0.716, 0.938)	(0.443, 0.684, 0.924)	(0.429, 0.675, 0.935)	(0.532, 0.745, 0.936)
EA2	(0.463, 0.674, 0.874)	(0.405, 0.643, 0.857)	(0.395, 0.642, 0.877)	(0.354, 0.608, 0.848)	(0.442, 0.701, 0.961)	(0.617, 0.830, 1.000)
EA3	(0.568, 0.779, 0.958)	(0.452, 0.690, 0.881)	(0.543, 0.790, 1.000)	(0.430, 0.684, 0.924)	(0.325, 0.571, 0.818)	(0.489, 0.702, 0.883)
EA4	(0.568, 0.779, 0.947)	(0.429, 0.667, 0.893)	(0.469, 0.716, 0.938)	(0.430, 0.684, 0.937)	(0.494, 0.753, 1.000)	(0.574, 0.787, 0.957)
EA5	(0.653, 0.863, 1.000)	(0.405, 0.643, 0.881)	(0.444, 0.691, 0.926)	(0.456, 0.709, 0.949)	(0.390, 0.649, 0.909)	(0.617, 0.830, 1.000)
EA6	(0.568, 0.779, 0.958)	(0.524, 0.762, 0.952)	(0.506, 0.741, 0.963)	(0.519, 0.759, 1.000)	(0.442, 0.701, 0.961)	(0.489, 0.702, 0.894)
EA7	(0.568, 0.779, 0.958)	(0.500, 0.738, 0.964)	(0.494, 0.741, 0.988)	(0.418, 0.658, 0.911)	(0.377, 0.623, 0.870)	(0.638, 0.851, 1.000)

below.

Step 3: Create the weighted normalized decision matrix

To account for the varying weights assigned to each criterion, we can calculate the weighted normalized decision matrix by multiplying the weight of each criterion with its corresponding value in the normalized fuzzy decision matrix. This calculation can be performed using the following formula.

$${\tilde{v}}_{ij}={\tilde{r}}_{ij}.{\tilde{w}}_{ij}$$

where ${\tilde{w}}_{ij}$ represents the weight of criterion $c_j$ .

The weighted normalized decision matrix is presented in the following

Table 5. The weighted normalized decision matrix.

	C1	C2	C3	C4	C5	C6
EA1	(0.102, 0.137, 0.165)	(0.095, 0.135, 0.167)	(0.078, 0.120, 0.157)	(0.074, 0.114, 0.154)	(0.072, 0.113, 0.156)	(0.089, 0.124, 0.156)
EA2	(0.077, 0.113, 0.146)	(0.068, 0.107, 0.143)	(0.066, 0.107, 0.146)	(0.059, 0.101, 0.142)	(0.074, 0.117, 0.160)	(0.103, 0.139, 0.167)
EA3	(0.095, 0.130, 0.160)	(0.076, 0.115, 0.147)	(0.091, 0.132, 0.167)	(0.072, 0.114, 0.154)	(0.054, 0.095, 0.137)	(0.082, 0.117, 0.147)
EA4	(0.095, 0.130, 0.158)	(0.072, 0.111, 0.149)	(0.078, 0.120, 0.157)	(0.072, 0.114, 0.156)	(0.082, 0.126, 0.167)	(0.096, 0.131, 0.160)
EA5	(0.109, 0.144, 0.167)	(0.068, 0.107, 0.147)	(0.074, 0.115, 0.155)	(0.076, 0.118, 0.159)	(0.065, 0.108, 0.152)	(0.103, 0.139, 0.167)
EA6	(0.095, 0.130, 0.160)	(0.087, 0.127, 0.159)	(0.085, 0.124, 0.161)	(0.087, 0.127, 0.167)	(0.074, 0.117, 0.160)	(0.082, 0.117, 0.149)
EA7	(0.095, 0.130, 0.160)	(0.084, 0.123, 0.161)	(0.082, 0.124, 0.165)	(0.070, 0.110, 0.152)	(0.063, 0.104, 0.145)	(0.107, 0.142, 0.167)

.

Step 4: Determine the fuzzy positive ideal solution (FPIS, A*) and the fuzzy negative ideal solution ($\mathit{F}\mathit{N}\mathit{I}\mathit{S},{\mathit{A}}^{-}$)

The FPIS and FNIS of the alternatives can be defined as follows:

$$A^{\ast }=\left\{{\tilde{v}}_1^{\ast },{\tilde{v}}_2^{\ast },\dots ,{\tilde{v}}_n^{\ast }\right\}=\left\{\left(\underset{j}{\max }{v}_{\mathit{ij}}|i\in B\right),\left(\underset{j}{\min }{v}_{\mathit{ij}}|i\in C\right)\right\}$$

$$A^{-}=\left\{{\tilde{v}}_1^{-},{\tilde{v}}_2^{-},\dots ,{\tilde{v}}_n^{-}\right\}=\left\{\left(\underset{j}{\min }{v}_{\mathit{ij}}|i\in B\right),\left(\underset{j}{\max }{v}_{\mathit{ij}}|i\in C\right)\right\}$$

where ${\tilde{v}}_i^{\ast }$ is the max value of i for all the alternatives and ${\tilde{v}}_1^{-}$ is the min value of i for all the alternatives. B and C represent the positive and negative ideal solutions, respectively.

The positive and negative ideal solutions are shown in the

Table 6. The positive and negative ideal solutions.

	Positive Ideal	Negative Ideal
C1	(0.109, 0.144, 0.167)	(0.077, 0.113, 0.146)
C2	(0.095, 0.135, 0.167)	(0.068, 0.107, 0.143)
C3	(0.091, 0.132, 0.167)	(0.066, 0.107, 0.146)
C4	(0.087, 0.127, 0.167)	(0.059, 0.101, 0.142)
C5	(0.082, 0.126, 0.167)	(0.054, 0.095, 0.137)
C6	(0.107, 0.142, 0.167)	(0.082, 0.117, 0.147)

below.

Step 5: Determine the distance among each alternative as well as the fuzzy positive ideal solution  ${\mathit{A}}^{\mathit{\ast }}$ and the distance among each alternative and the fuzzy negative ideal solution  ${\mathit{A}}^{-}$

The distance between each alternative and FPIS and the distance between each alternative and FNIS are, respectively, calculated as follows:

$$S_i^{\ast }={\sum }_{j=1}^{n}d({\tilde{v}}_{ij},{\tilde{v}}_j^{\ast }) i=1, 2,\dots , m$$

$${\displaystyle S_i^{-}}={\sum }_{j=1}^{n}d({\tilde{v}}_{ij},{\tilde{v}}_j^{-}) i=1, 2,\dots , m$$

d is the distance between two fuzzy numbers, when given two triangular fuzzy numbers ( $a_1, b_1, c_1$ ) and ($a_2, b_2, c_2$), e distance between the two can be calculated as follows:

$$d_v\left({\tilde{M}}_1,{\tilde{M}}_2\right)=\sqrt{\frac{1}{3}[{\left(a_1-a_2\right)}^2+{\left(b_1-b_2\right)}^2+{\left(c_1-c_2\right)}^2]}$$

Note that $d({\tilde{v}}_{ij},{\tilde{v}}_j^{\ast })$ and $d({\tilde{v}}_{ij},{\tilde{v}}_j^{-})$ are crisp numbers.

Table 7. Distance from positive and negative ideal solutions.

	Distance From Positive Ideal	Distance from Negative Ideal
EA1	0.058	0.101
EA2	0.116	0.043
EA3	0.098	0.06
EA4	0.069	0.089
EA5	0.069	0.09
EA6	0.058	0.101
EA7	0.067	0.092

below shows the distance from positive and negative ideal solutions

Step 6: Calculate the closeness coefficient and rank the alternatives

The closeness coefficient for each alternative can be calculated using the following formula:

$${CC}_i=\frac{S_i^{-}}{S_i^{+}+S_i^{-}}$$

The ideal solution (FPIS) is used to determine the closest alternative, while the non-ideal solution (FNIS) identifies the farthest alternative.

Table 8. Closeness coefficient.

	Ci	Rank
EA1	0.636	1
EA2	0.269	7
EA3	0.377	6
EA4	0.565	4
EA5	0.564	5
EA6	0.635	2
EA7	0.58	3

and Figure 3 below display the closeness coefficient and ranking order of each alternative.

The following graph shows the closeness coefficient of each alternative.

Based on the fuzzy TOPSIS-based evaluation, the findings suggest the following ranking for the evaluated alternatives: EA1 > EA6 > EA7 > EA4 > EA5 > EA3 > EA2. The ranking indicates that EA1 is the most favourable alternative, followed by EA6, EA7, EA4, EA5, EA3, and EA2. These findings are based on the criteria and weights used in the evaluation, indicating the relative performance and suitability of each alternative in the decision-making process.

Comparative Findings of the Fuzzy TOPSIS and AHP Analysis

Comparative findings of fuzzy TOPSIS and AHP analysis are conducted to compare and evaluate the outcomes obtained from two different MCDA methods. Fuzzy TOPSIS and analytic hierarchy process (AHP) are widely used MCDA techniques that offer different approaches to decision making and ranking alternatives. The purpose of conducting a comparative analysis is to assess the consistency and reliability of the results obtained from both methods [40,41,42,43,44,45]. By comparing the rankings and outcomes generated by fuzzy TOPSIS and AHP, decision-makers can gain insights into the degree of agreement or divergence between the two approaches. The comparative findings help in validating the decision-making process and provide a comprehensive understanding of the alternatives being evaluated. It allows decision-makers to evaluate the robustness and reliability of the results by examining whether the rankings and conclusions align or differ between the two methods. Furthermore, comparative findings can also highlight the strengths and weaknesses of each method in the specific context of the decision problem. It enables decision-makers to make more informed decisions by considering multiple perspectives and gaining a broader understanding of the alternatives. Conducting a comparative analysis of fuzzy TOPSIS and AHP helps in assessing the consistency, reliability, and suitability of the two methods for a particular decision problem, ultimately enhancing the decision-making process.

Table 9. Comparative Analysis.

Ranking Order	1	2	3	4	5	6	7
AHP	EA1	EA6	EA7	EA5	EA4	EA3	EA2
Fuzzy TOPSIS	EA1	EA6	EA7	EA4	EA5	EA3	EA2

shows the comparative analysis result of AHP and fuzzy TOPSIS.

The rankings obtained from both the fuzzy TOPSIS and AHP analyses show a consistent order of the alternatives. EA1 is ranked the highest, followed by EA6, EA7, EA4, EA5, EA3, and EA2, which remain the same in both methods. These comparative findings indicate that both the fuzzy TOPSIS and AHP analyses lead to similar rankings, providing confidence in the evaluation results. The agreement between the two methods strengthens the validity of the evaluations and supports the robustness of the findings. Including a comparison with additional methods such as stable preference ordering towards ideal solution (SPOTIS), ranking comparison (RANCOM), inter-criteria analysis (ICRA), and others would further enrich the evaluation of the proposed approach. These comparisons could provide additional insights into the strengths, weaknesses, and nuances of various MCDA methods in the context of sustainable energy transition decision making.

5. Discussion

The evaluation and ranking of alternatives for sustainable energy transition are complex tasks that involve multiple criteria and inherent uncertainties. Traditional decision-making methods often struggle to capture the fuzzy and uncertain nature of the evaluation process. However, the application of fuzzy TOPSIS provides a robust and effective approach to address these challenges and facilitate informed decision making in sustainable energy transition. Fuzzy TOPSIS is a decision-making method that combines fuzzy set theory with the TOPSIS technique, allowing decision-makers to handle imprecise and uncertain information when evaluating alternatives. This method considers the ambiguity and vagueness inherent in decision making by representing the criteria and performance evaluations in linguistic terms or fuzzy membership functions.

One of the key advantages of the fuzzy TOPSIS-based evaluation in the sustainable energy transition is its ability to account for the inherent uncertainties associated with various criteria. Criteria such as environmental impact, cost-effectiveness, energy efficiency, scalability, and social acceptance often involve subjective judgments and fuzzy information. Fuzzy TOPSIS allows decision-makers to incorporate these uncertainties and quantify the degree of membership or preference for each alternative. Furthermore, fuzzy TOPSIS facilitates a comprehensive evaluation and ranking of alternatives by considering multiple criteria simultaneously. Decision-makers can assign weights to different criteria based on their relative importance and assess the performance of alternatives against these criteria. The method calculates the similarity of each alternative to the ideal solution and the negative ideal solution, enabling the ranking of alternatives based on their overall performance.

Another advantage of the fuzzy TOPSIS-based evaluation is its ability to handle interdependencies and trade-offs among different criteria. Sustainable energy transition involves complex interactions between various factors, and there may be trade-offs between different objectives. Fuzzy TOPSIS provides a systematic approach to analyse these trade-offs and identify alternatives that strike the best balance among competing criteria.

Moreover, the fuzzy TOPSIS-based evaluation can accommodate a wide range of data types and sources, including expert opinions, qualitative assessments, and quantitative measurements. This flexibility allows decision-makers to integrate different types of data and knowledge into the evaluation process, enhancing the reliability and comprehensiveness of the results. However, it is important to note that the fuzzy TOPSIS-based evaluation is dependent on the selection and formulation of criteria, the assignment of weights, and the accuracy of input data. The subjective nature of these decisions and the potential biases in data collection can impact the outcomes. Therefore, careful consideration and transparency in the selection and weighting of criteria, as well as the validation of data sources, are crucial for the reliability and robustness of the evaluation.

Based on the fuzzy TOPSIS-based evaluation, the findings reveal that solar energy (EA1) ranks first and is considered the most favourable alternative among the evaluated options. This indicates that solar energy performs the best in terms of the criteria and weights used in the evaluation process. Solar energy demonstrates strong performance and suitability, making it an attractive choice for sustainable energy solutions. Saudi Arabia is blessed with abundant sunlight throughout the year, making solar energy a top priority. Solar power has immense potential for electricity generation, especially through photovoltaic (PV) systems and concentrated solar power (CSP) plants. The country’s vast desert areas provide ample space for solar installations, and the government has made significant investments in solar projects. While not as abundant as solar energy, wind power has been gaining attention in Saudi Arabia. The country possesses regions with favourable wind resources, particularly along its western coast and in certain inland areas. Expanding wind energy capacity can diversify the renewable energy mix and contribute to the country’s sustainability goals.

As renewable energy sources such as solar and wind fluctuate in their availability, energy storage technologies play a crucial role in maintaining a stable and reliable power supply. Developing and implementing advanced energy storage systems, such as batteries and pumped hydro storage, can help store excess renewable energy for later use and enhance grid stability. Saudi Arabia’s geographical characteristics do not provide significant opportunities for conventional hydropower due to limited water resources. However, the country has been exploring the potential of small-scale hydropower projects, such as run-of-river and micro-hydropower installations, which can harness water flow in certain regions.

Biomass energy, derived from organic waste and agricultural residues, has some potential in Saudi Arabia. The country has significant agricultural and food processing activities, generating substantial biomass feedstock. By implementing efficient biomass conversions technologies, such as anaerobic digestion and biomass gasification, Saudi Arabia can tap into this resource to produce bioenergy. Although Saudi Arabia has limited geothermal resources compared to other countries, exploration studies have been conducted to assess its potential. Geothermal energy remains a relatively less-developed and less-prioritized renewable energy source in the country. Given Saudi Arabia’s geographical location, ocean energy, including wave and tidal energy, has limited practical application. The country’s focus has primarily been on land-based renewable energy sources due to their higher feasibility and potential.

It is important to note that the arrangement of these renewable energy sources and technologies may vary depending on specific factors, such as technological advancements, resource availability, government policies, and economic considerations. Nonetheless, the ranking provided above reflects their general importance and potential in Saudi Arabia’s renewable energy landscape. The fuzzy TOPSIS-based evaluation provides a powerful methodology for assessing and ranking alternatives in the sustainable energy transition. By considering fuzzy and uncertain information, handling interdependencies, and accommodating multiple criteria, this approach enables decision-makers to make informed and comprehensive decisions that align with the goals of the sustainable energy transition. However, it is essential to exercise caution and ensure the soundness of the evaluation process by involving relevant stakeholders, verifying data quality, and validating the results to ensure the effectiveness and reliability of the fuzzy TOPSIS-based evaluation in the context of the sustainable energy transition.

6. Conclusions

The progress and importance of sustainable energy in Saudi Arabia are evident through its commitment to renewable energy targets, the country’s abundant renewable resources, economic opportunities, diversification goals, and the need to meet the growing energy demand sustainably. Embracing sustainable energy sources and technologies not only contributes to environmental sustainability but also supports economic development and enhances energy security for Saudi Arabia. The research on fuzzy TOPSIS-based evaluation of sustainable energy transition highlights the effectiveness of this methodology in addressing the complexities and uncertainties associated with evaluating alternative energy options. By incorporating fuzzy set theory and considering multiple criteria simultaneously, fuzzy TOPSIS provides decision-makers with a robust framework for selecting the most suitable alternatives for the sustainable energy transition. The methodology enables the quantification of fuzzy and uncertain information, handles trade-offs among criteria, and promotes informed decision making. The research emphasizes the need for careful consideration and validation of criteria, weights, and data sources to ensure the reliability and effectiveness of the fuzzy TOPSIS-based evaluation.

This research contributes to the advancement of sustainable energy transition by providing decision-makers with a comprehensive and objective approach to evaluating and ranking alternative energy options. Based on the fuzzy TOPSIS-based evaluation, the research findings indicate that solar energy (EA1) is ranked as the most favourable alternative among the evaluated options for the sustainable energy transition in the Kingdom of Saudi Arabia. This suggests that solar energy holds significant potential and advantages in terms of its technical feasibility, economic viability, and environmental sustainability compared to other renewable energy sources considered in the evaluation. The research’s findings are limited by the availability and quality of data used for the evaluation. Incomplete or unreliable data may impact the accuracy of the results. The fuzzy TOPSIS method relies on subjective judgments and input from experts, which may introduce bias or inconsistencies in the evaluation process. To further enhance the understanding of sustainable energy transition in the Kingdom of Saudi Arabia, future research could consider conducting a comprehensive multi-criteria analysis that incorporates a broader range of factors, including social acceptance, policy support, technological maturity, and infrastructure requirements.