A Novel Combined Hybrid Group Multi-Criteria Decision-Making Model for the Selection of Power Generation Technologies

Abstract

This study assessed ten alternatives, comprising nine power generation technologies and Battery Energy Storage Systems (BESS), using a combined hybrid approach based on group Multi-Criteria Decision-Making (MCDM) methods. Specifically, AHP was employed for determining criteria weights, while fuzzy VIKOR was utilised for ranking the alternatives. Six electricity sector experts evaluated each technology, organised within a hierarchical decision model that included four main criteria: economic, environmental, technical, and social, along with 13 subcriteria. To mitigate subjectivity in criteria weights stemming from diverse expert backgrounds, a consensus technique was implemented post-AHP. Fuzzy VIKOR was employed to address uncertainty in expert ratings. The findings revealed a significant preference towards renewable technologies, with Photovoltaic (PV) and Wind at the forefront, whereas Coal occupied the lowest position. A validation process was conducted using BWM for criteria weights and fuzzy TOPSIS for ranking alternatives. This hybrid soft computing method’s key contributions include its modular design, allowing for the sequential determination of criteria weights, followed by the calculation of alternative rankings, fostering interactive and collaborative evaluations of various energy mixes by expert groups. Additionally, the study evaluated three emerging energy technologies: BESS, Small Modular Nuclear Reactors (SMRs), and Hydrogen, highlighting their potential in the evolving energy landscape.

1. Introduction and Background

Historically, energy sources and their applications have experienced numerous modifications, profoundly affecting society. The first Industrial Revolution transitioned the economy from agriculture to industry, mostly driven by the steam engine, which facilitated the rail transport of produced goods. The second Industrial Revolution introduced electricity as a widespread consumer commodity, utilised in electric engines and extensive public illumination. This resulted in a partially electrified economy reliant on hydropower, coal, oil, and methane for energy generation. In the 1980s, a third industrial Revolution introduced new energy sources, including nuclear power and nascent renewables such as wind, solar, and biomass [1].

Since that time, heightened efforts have been dedicated to mitigating CO₂ emissions from the global energy industry, which is acknowledged as a significant contributor to escalating CO₂ levels [2].

Figure 1 illustrates the evolution of worldwide CO₂ emissions originating from different sectors, where the share of CO₂ emissions from electricity and heat production can be seen.

If we focus on electricity production, selecting the most suitable technologies for national energy mixes is a complex multicriteria problem that policy and decision-makers face worldwide. This paper addresses the energy dilemma [3], trilemma [4], and quadrilemma [5] when considering the different and often conflicting characteristics of the energy technologies, like investment costs, impact on the environment, security of supply and social factors like job opportunities or providing energy in a just way (Figure 2).

Because of the worries about the environmental and social impact of economic growth on the planet, the United Nations established 17 Sustainable Development Goals (SDGs) [6] in 2015, which are aimed at promoting global economic prosperity while protecting the environment by 2030. Economic, environmental, technical, and social criteria of the energy challenges associated to economic growth are linked to the UN’s SDGs 7 and 13, and are closely tied to decarbonising economies through bigger shares of renewable energy [7] and non-GHG-emitting power generation technologies, or to clean technology demand-side investments like electric vehicles, further electrification [8,9,10] in heating, transportation, and in the rest of CO₂-emitting sectors depicted in Figure 1, so as to achieve SDG 7 (Energy) [11] by 2030 and reach SDG 13 net-zero emissions (Climate Change) [12] by 2050.

Due to these initiatives fostering sustainability, the world energy sector is undergoing significant transformations on both the generation and demand sides. Some of the environmental legislation affecting energy, passed in recent years includes the Paris Agreement [13], adopted in December 2015. It is aimed to keep the world temperature rise below +2 °C, preferably +1.5 °C, by 2100.

In Europe, the European Climate Law [14], enacted in July 2021, legally binds the EU to achieve climate neutrality by 2050 and reduce net greenhouse gas emissions by at least 55% by 2030, compared to 1990 levels. To meet these goals, the EU adopted the “Fit for 55” [15] legislative package and mandated the European Commission to propose a climate target of a 90% reduction by 2040 [16]. The European Commission also proposed the Net-Zero Industry Act (NZIA) [17] in March 2023 as part of the Green Deal Industrial Plan [18], aiming to boost EU manufacturing of net-zero technologies and address production scaling barriers. These measures underscore Europe’s leadership in the net-zero transition and support Fit-for-55 and Repower EU [19] objectives. In the USA, the Inflation Reduction Act (IRA) has far-reaching impacts on energy technologies and climate policy. It anticipates historic investments in clean energy and climate change mitigation and intends to cut GHG emissions by 2030 by −40% below 2005, focusing on clean electricity technologies, energy storage [20], electric vehicles [21], hydrogen [22], and carbon capture. China has also launched normative development regarding energy technologies and climate change measures, enacting China’s First Energy Law [23], which introduces emissions neutrality goals and a dual control system for carbon emissions, recognises hydrogen as an energy source, and supports the development of green energy certificates, energy storage, and smart microgrids.

Anyhow, great pressure at a global level is being put on decision-makers to select the best power generation technologies throughout the world, although the pace is being different depending on continents and countries. Renewable energy generation, characterised by multiple small-scale installations, in contrast with the traditional approach of expanding power capacity through a few large-scale generation units, has extended worldwide and will likely keep doing it.

Critical challenges remain in selecting power generation technologies: (1) existing studies often overlook emerging technologies like Hydrogen, BESS or SMRs under uncertain viability; (2) most methods rely on individual expert judgements rather than structured group consensus, risking biases; and (3) few frameworks combine hierarchical weighting with fuzzy ranking to balance qualitative and quantitative criteria. To address these gaps, this study proposes a hybrid AHP-FVIKOR model. The AHP method was selected for its ability to harmonize diverse expert perspectives through pairwise comparisons and consensus techniques—critical for policy-relevant decisions. While BWM offers streamlined comparisons, AHP’s hierarchical structure better accommodates group inputs and aligns with our validation phase. FVIKOR complements this by handling uncertainties in technology assessments through fuzzy compromise solutions. This combination provides a robust yet adaptable tool for policymakers navigating trade-offs between renewables, security of supply, and emerging technologies.

That is the reason why this work presents a novel combined and hybrid soft computing methodology, which not only studies the most usual power generation alternatives but also the three above-mentioned emergent generation or battery-storage technologies. It also considers the opinions of experts in the energy sector, reaches a consensus between them and uses fuzzy assessments so that possible inconsistencies or subjectivities due to experts’ backgrounds do not bias the results.

The paper’s main contributions can be summarised as follows:

(1) Development of a novel methodology for selecting power generation or battery storage technologies, providing a robust evaluation framework valid for further research in this field.

(2) The methodology incorporates economic, environmental, technological, and social criteria, using separated and specialised MCDM techniques (AHP for weights and VIKOR for ranking). In the weights calculation, a consensus approach is used to reduce subjectivity from the experts, while fuzzy values are used to address uncertainty in the ranking assessments. Cross-validation was made for both processes, enhancing the consistency of the results obtained. Moreover, a sensitivity analysis of the VIKOR results was conducted.

(3) The study evaluates both renewable and conventional energy sources, including emerging technologies like SMRs, Hydrogen, and BESS, applicable across various electricity exchange structures (physical or financial power exchanges, bilateral contracts or any other sort of settlement).

(4) The modular approach allows for easy adaptation to different scenarios and countries, serving as a mid- and long-term tool for policymakers in technology selection.

The research questions address whether and to what extent renewable energy trends are alive, if the studied emerging power generation technologies are yet commercially feasible, and if a balance can be found between environmental factors and technical reasons regarding security of supply in national power generation mixes with high shares of renewable energies. So far, the three new technologies mentioned above have not yet appeared consistently in the literature on energy problems to be solved through MCDM. This paper aims to contribute to their study, thus filling the existing research gap. Our combined hybrid method exploits the criteria weights obtained through Group AHP+Consensus in the other used MCDM methods, thus avoiding further expert consultations.

The remainder of the article is organised as follows: Section 2 contains a review of the literature regarding methodologies and criteria in this field. Section 3 presents an illustration of the model, the selected criteria, and potential alternatives. Section 4 outlines the methodologies of AHP combined with Consensus and fuzzy VIKOR, and the validation methods of BWM and fuzzy TOPSIS. Section 5 presents the results, along with comparison and discussion. Finally, Section 6 presents the conclusions.

2. Literature Review

The literature research focused on two key aspects: the most frequently used methods to achieve the objectives of the work, and the criteria commonly considered in evaluations of power production systems or BESS.

2.1. Methodologies

Selecting optimal power generation technologies for a national energy mix is a complex policy challenge involving multiple competing factors. While various decision-making approaches exist in the literature, Multi-Criteria Decision Making (MCDM) methods appear as particularly effective for addressing this multidimensional problem, offering robust solutions that have led to their widespread adoption [24]. Depending on the characteristics and objectives of the multi-criteria analysis, MCDM methods can be classified -in their discrete version MADM- into the following categories: direct scoring, distance-based, pairwise comparison, outranking, or utility-function-based methods [25].

The “Analytic Hierarchy Process” (AHP), either alone or combined with another MCDM method, in its crisp or fuzzy version, is the most prevalent MCDM method applied in the energy sector [26,27,28,29], together with ANP. AHP is simple, adaptable, and makes it possible to obtain both the weights of the qualitative and quantitative criteria used in the evaluation model and a comparative ranking of alternatives for the proposed problem. Solangi et al. [30] utilized factor analysis (FA) and a hybrid of AHP and Fuzzy TOPSIS to prioritize suitable sites for wind project development in Pakistan. A research in Saudi Arabia was presented in [31], wherein the authors combined Extended Fuzzy AHP, Fuzzy VIKOR, and TOPSIS approaches to evaluate eight alternative energy systems against nine criteria to determine the most suitable energy technologies for investment. Another study conducted on Turkish territory through fuzzy AHP and fuzzy TOPSIS was published to prioritise the use of renewable power generation alternatives, along with expert evaluation, to indicate the feasibility of the proposed model [32]. This type of methodological combinations can be also observed in several other research articles [33,34,35,36,37,38,39], covering different application areas: selection of renewable energy resources, decision of energy security factors, or identification of location sites to mention some.

Methodological alternatives to AHP include other techniques like TOPSIS, VIKOR, PROMETHEE, ELECTRE, COPRAS, BWM, etc. Sakthivel et al. [40] use fuzzy versions of TOPSIS and VIKOR to evaluate the optimal fuel mix for energy efficiency improvement in an internal combustion engine. A novel approach is proposed by Gribiss et al. [41] focusing their study on renewable energy communities (RECs). In their research, they employ four multi-criteria decision-making methods—weighted sum (WS), weighted product (WP), technique for order of preference by similarity to ideal solution (TOPSIS), and evaluation based on distance from average solution (EDAS)—to select the best configurations among the 16 proposed, considering economic, environmental, technical, and social criteria. Ecer [42] used the best-worst method (BWM) to assess the sustainability performance of 42 wind plants in Turkey.

In order to mitigate the inherent subjectivity of expert judgments and address issues arising from uncertainty or incomplete information, some works incorporate other methodologies such as Grey numbers [43,44], Monte Carlo simulations [45], ELECTRE-based methods [46], D-BWM (an integration of BWM and D numbers) [47], or fuzzy cognitive mapping (FCM) with weighted aggregated sum product assessment (WASPAS) [48]. Fuzzy Inference Systems (FIS) [49,50] or PROMETHEE [51] can also be useful resources in energy related decisions where evaluations are highly subjective.

Table 1. Commonly used methodologies according to the literature review.

Methodologies (*)	Reference Number	Consensus	RES (**), Fossil or Both	Country
AHP	[35]		RES	Saudi Arabia
AHP	[37]		RES	Pakistan
AHP, Fuzzy-GRA	[44]		RES	China
AHP, TOPSIS	[33]			Global
AHP, VIKOR	[36]		RES	Spain
AHP, ELECTRE, VIKOR, TOPSIS	[26]		RES	Turkey, global
AHP and grey-based methods	[43]		RES	Global
BWM	[42]		RES	Turkey
D-BWM	[47]		RES	Iran
Delphi, FAHP, FVIKOR, TOPSIS	[31]	X	RES	Saudi Arabia
ELECTRE	[46]		Both	Global
Life-cycle assessment, DEA	[52]		Both	Spain
FA, AHP, FTOPSIS	[30]		RES	Pakistan
FAHP	[38]		RES	Korea
FAHP	[39]	X	Both	Europe
FAHP	[29]		Both	China
FAHP, Axiomatic Design	[53]		RES	Turkey
FAHP, FTOPSIS	[32]		RES	Turkey
FIS	[49]		RES	Global
FIS	[50]		Both	Spain
GAMS (Other)	[45]		Both	Europe
PROMETHEE, Sim	[51]		Both	Europe
WASPAS	[48]		RES	Global
WS, WP, TOPSIS, EDAS	[41]		RES	Europe

(*) Methodology acronyms: AHP: Analytic Hierarchic Process, BWM: Best-Worst Method, D-BWM: D numbers combined with BWM, DEA: Data Envelopment Analysis, EDAS: Evaluation based on Distance from Average Solution, ELECTRE: ELimination Et Choice Translating REality, FAHP: Fuzzy AHP, FIS: Fuzzy Inference System; Fuzzy TOPSIS: Fuzzy Technic for Order of Preference by Similarity with Ideal Solution, Fuzzy VIKOR: Fuzzy VIsekriterijumsko KOmpromisno Rangiranje, GAMS: General Algebraic Modelling System, GRA: Grey Relational Analysis, MOO: MultiMOORA (Multi-Objective Optimization on the basis of Ratio Analysis); PROMETHEE: Preference Ranking Organization METhod for Enriching Evaluation, Sim: Simos Procedure, WASPAS: Weighted Aggregated Sum Product Assessment, WP: weighted product, WS: Weighted Sum Method. (**) RES: Renewable Energy Source.

shows an excerpt of the methodologies found in the literature review.

2.2. Criteria

The utilization of MCDM methods is fundamentally supported by the initial identification of criteria and sub-criteria, a challenging task which is the foundation for subsequent analysis. By clearly defining these criteria and sub-criteria at the outset, decision-makers can ensure a comprehensive and structured approach to evaluating the various alternatives. This initial step is crucial, as it provides a clear framework and the set of benchmarks so that all alternatives can be consistently assessed, ultimately leading to more informed and balanced decision-making outcomes.

Usually, these criteria and sub-criteria are organized into a hierarchical structure, so that decision-makers can systematically decompose complex decisions into more manageable parts. This hierarchy allows for a clear visualization of the relationships and relative importance of each element, facilitating a more thorough and nuanced analysis.

Table 2. Most usual criteria in the literature review.

Main Criteria	#	Sub-Criteria	#	Related References
Economic	16	Investment (Capital) cost	12	[29,31,34,35,36,42,44,50,51,53,54,55]
		Operation and maintenance cost	7	[34,35,36,42,44,51,53]
		National economic development	5	[30,31,34,50,51]
		Technology cost	2	[34,45]
		Electric cost	1	[36]
		Fuel costs	1	[42]
		Grid connection costs	1	[29]
		R&D Cost	1	[36]
		Levelized cost of energy (LCOE)	3	[31,45,51]
		Operational life	3	[31,35,37]
		Payback Period	1	[31]
		Net present cost	4	[30,36,54,55]
		Electricity price	1	[50]
		Net import of energy	1	[50]
		Road availability	1	[29]
		Availability of funds	4	[31,37,54,55]
		Power grid company revenue reduction	1	[43]
		Power generation company cost increase	1	[43]
		Electric power consumer expenditure increase	1	[43]
		Economic growth promoting degree	2	[43,53]
		Supply capability	1	[38]
Technical/Technological	14	Ease of decentralization	2	[34,51]
		Efficiency	7	[30,31,34,36,42,51,53]
		Exergy (rational efficiency)	1	[42]
		Maturity	6	[31,34,36,37,42,51]
		Implementation Period	4	[31,35,54,55]
		Lead time	4	[31,36,54,55]
		Risk	5	[31,44,53,54,55]
		Safety	2	[30,34]
		Production Capacity	5	[30,31,35,51,53]
		Reliability	6	[31,36,37,53,54,55]
		Possibility of acquiring original technology	1	[37]
		Availability	6	[29,30,34,35,36,51]
		On grid access	1	[36]
		Installed capacity	1	[31]
		HR experts	5	[29,31,36,54,55]
		Programmable/Predictability	4	[31,53,54,55]
		Feasibility	3	[31,54,55]
		Climate	1	[29]
		Energy intensity (2010=100)	1	[50]
		Flexibility	1	[44]
		Primary energy ratio	2	[37,42]
		Storability	1	[30]
Environmental	15	CO2 emission	3	[35,36,51]
		Air pollution	4	[30,44,54,55]
		Greenhouse gas emissions	3	[31,42,53]
		Land use/requirement	8	[29,31,34,36,37,51,54,55]
		Impact on environment	6	[29,31,34,36,44,45]
		Potential for reduction of greenhouse gases	3	[37,43,50]
		Water consumption	2	[43,45]
		Human health impact	1	[29]
		Waste disposal	4	[31,45,54,55]
		Other environmental effects	3	[29,31,43]
		Renewables share overall	1	[50]
		Energy savings	1	[50]
Social	13	Social acceptability	6	[29,31,36,37,54,55]
		Job creation	10	[29,31,34,36,43,50,51,53,54,55]
		Social Benefits	2	[29,36]
		External costs (human health)	2	[42,50]
		Maintain country’s leading position	1	[34]
		Tax increase	1	[43]
		Technical innovation promoting degree	1	[43]
		Energy related expenditures of households	1	[50]
		Sustainability	1	[31]
		Durability	1	[31]
		Distance to user	2	[29,31]
Political	11	Policy	5	[29,31,37,54,55]
		Political acceptance	6	[31,34,51,53,54,55]
		National economic benefits	2	[36,50]
		National energy security	3	[36,37,43]
		Relocation and rehabilitation	2	[29,37]
		Geo-political factors	2	[37,44]
		Government support	1	[30]
Market	1	Domestic market size and competitiveness	1	[38]
		Global market size and competitiveness	1	[38]
		Competitive power of domestic technology	1	[38]

shows the most commonly used criteria and subcriteria within the context of decision-making problems on energy issues. Columns under # show how many criteria and subcriteria appear out of a total of 16 analysed works.

There is no unanimity regarding the number of criteria to use in each case or the sub-criteria to consider within each of the criteria, but there is broad consensus regarding the main criteria affecting energy analysis (economic, technical -and technological-, environmental, and political-social), regardless of the type of problem (energy-related decision processes, renewable energy analysis, selecting power plant locations, and energy evaluations) or the geographical focus. Börcsök et al. [45] employed these first-level criteria to determine the optimal country-specific criteria weights for long-term energy planning in Europe. Their research revealed that the Eastern European region displayed significant sensitivity to investment costs. In contrast, countries with a heavy reliance on renewable or nuclear energy sources showed a predominant influence of environmental factors. In a different location, Ghana, Sarkodie et al. [54] evaluate five renewable energy resources for power generation versus thirteen subcriteria included in the four aforementioned first-level criteria. Commencing with the identification of the same criteria, Solangi et al. [30] concluded that economic and land acquisition were the most significant criteria and sub-criteria, respectively in their study of eight different sites considered for the optimal location of a wind power project in Pakistan. Kahraman also used these criteria to determine the best energy policy for Turkey [53,55], while Maghsoodi did a similar analysis for Iran [56].

In some works [26,30], the predominance of the economic over the other three first-level criteria in energy planning and management decisions was noted; this prioritization is often driven by the imperative to ensure financial viability and cost-effectiveness. Economic considerations are paramount because they directly impact on the affordability of energy projects, influencing investment decisions, pricing strategies, and the overall economic health of a region. While technical efficiency, social acceptance, and environmental sustainability are crucial, the ability to secure funding, achieve economic returns, and maintain competitive energy prices often dictates the feasibility and long-term success of energy initiatives.

Table 3. Other data of the references used for the identification of the main criteria.

Reference	[35]	[37]	[43]	[32]	[55]	[53]	[30]	[44]	[51]	[46]	[54]	[56]	[38]	[31]	[46]	[36]
Alternatives	5	4		7	9	5	8	3	5	9	5	6		8	9	13
Experts	20			3	4	4	5	4	8		25			9
Criteria	4	5	4	6	4	4	5	3	4	5	4	3	5	4	2	3
Subcriteria	14	20	9	29	17	17	16	11	12	7	13	11	17	9	5	7
Country	Saudi Arabia	Pakistan		Turkey	Turkey	Turkey	Pakistan	China	EU	EU	Ghana	Iran	Korea	Saudi Arabia	United Kingdom	Spain

displays additional information extracted from the references used for the identification of the main criteria.

Other recent examples of MCDM methodologies applied to energy planning issues are Hernández-Torres et al. [57], Loftipour et al. [58], Parvaneh et al. [59] and Arikan Kargi et al. [60].

3. Proposed Model

In this work, a hierarchical model (see Figure 3) was prepared, containing the objective at the top level (assessment of power generation technologies and BESS in a National Energy System), followed by the range of criteria and subcriteria defined. These include the most common ones found in the literature (Economic, Environmental, Technical and Social). At the bottom level, a set of 10 alternatives can be found, of which 7 are existing and 3 are considered to have a high potential for future use.

This model, which will be applied with all the methodologies described in Section 4, uses the following selected alternatives and criteria:

3.1. Selected Alternatives

The ten power technologies considered as alternatives can be divided into two categories: those generally present in current generation mixes, including both non-renewable technologies like Nuclear, Coal, Gas (both Combined Cycle Gas Turbine (CCGT) and Combined Heat and Power (CHP)), and renewable sources (Wind, Hydro, PV). The second category includes technologies that are not yet present in current national mixes but are close to commercial feasibility and will likely spread in the near future (Green Hydrogen, Battery Energy Storage Systems (BESS) and Small Modular Reactors (SMR)). Figure 4 shows the share of electricity production by source in the world in 2024.

Technologies that rely on fossil fuels (coal, gas) are non-renewable and emit CO₂, contributing to climate change. Nuclear fission technology, which utilizes radioactive minerals such as uranium or plutonium, is also non-renewable, although it does not emit CO₂. Renewable technologies include Wind, PV and Hydroelectric among others. For our world average study, only existing sources with a current share bigger than 5% were considered. National energy mixes normally include very different energy sources, as it can be seen in Figure 5, where the cases of USA, Norway, China and France are depicted. In the USA, the biggest share is occupied by natural gas with around 45%, while in Norway ca. 90% is hydro, in China there is almost 60% of coal and in France, nuclear energy accounts for almost 70% of the total. Each case would require separate modelling with the assessment of specific groups of experts. With our combined method, this can be done both easily and accurately.

3.2. Selected Criteria

Criteria and subcriteria were defined through a deep cross-check of the most recurrent ones found in the related literature review. The ones finally considered were: Economic, Environmental, Technical and Social.

At the next level, sub-criteria for each of the four main blocks were, for the economic criterion: investment cost, operating cost and market price. For the environmental criterion: noise, CO₂ emissions and waste. The technical criterion was divided into operational and structural sub-criteria, The operational sub-criteria were start-up time, programmability and efficiency, while the structural ones were lifetime and construction time. For the social criterion, job creation and public acceptance were selected, according to the results found in the literature review shown in Section 2.2.

4. Methodology

To systematically assess expert perspectives, a structured questionnaire was developed to capture the expert panel’s evaluation of the relative importance of criteria influencing electricity generation technology assessments and also the experts’ judgements about technologies for each criterion. This questionnaire also made it possible to obtain a profile of each expert in terms of educational background and general and specific experience in different fields of the energy sector, so that individual relevance weights of each expert could be calculated.

After calculating the individual weights of each expert, an “Analytic Hierarchy Process (AHP)” method was applied. Based on the judgements of paired comparisons, the individual importance weights associated with each criterion were obtained. Afterwards, given the potential heterogeneity among the expert panel members, a consensus method was incorporated to facilitate the convergence of their opinions and avoid subjectivity. This consensus method involved making iterative modifications to their initial judgements until final weights were agreed upon. Then, with these consensual definitive weights, the fuzzy judgements given by the experts for alternatives vs criteria were used through VIKOR to obtain the ranking of the alternatives. Finally, as a validation, the Best-Worst Method (BWM) was used to confront the results obtained with AHP + Consensus for the criteria weights, and fuzzy TOPSIS was deployed to validate the ranking results previously obtained with fuzzy VIKOR for the ranking of technologies. Results are explained in Section 5.

Figure 6 shows the steps followed in our methodology:

4.1. Methodologies for the Combined Hybrid Decision Model (AHP + Fuzzy VIKOR)

4.1.1. Data Collection and Relevance Weights of Each Expert

The participant experts provided details about their educational background, work experience and familiarity with the different criteria. They were selected from several multinational energy utilities on the basis of their recognised knowledge of the electricity sector, each specialising in different criteria. Considering the differences in professional branch, studies, experience and field of knowledge, their individual importance weights were calculated following Equation (1), inspired on the formulation adapted from [61,62].

$${\rho }_i={\displaystyle \frac{\left(\frac{{PA}_i}{\mathit{max}\left\{{PA}_k\right\}}+\frac{{ES}_i}{\mathit{max}\left\{{ES}_k\right\}}+\frac{{SD}_i}{\mathit{max}\left\{{SD}_k\right\}}+\frac{\sum _{m=1}^4{KD}_{m,i}}{10}\right)}{7}}$$

(1)

where:

-

${\rho }_i=$ Relevance weight of the expert “i”.

-

${PA}_i=$ Years of professional activity of Expert “i”; $max\left\{{PA}_k\right\}=$ Maximum among all experts.

-

${ES}_i=$ Years of experience specialized in the Electricity Sector of Expert “i”; $max\left\{{ES}_k\right\}=$ Maximum among all experts.

-

${SD}_i=$ Studies degree of expert “i” [scale: 1-non-university degree, 2-bachelor’s degree, 3-master’s degree, 4-PhD]; $max\left\{{SD}_k\right\}=$ Maximum among all experts.

-

${KD}_{m,i}=$ Knowledge degree of the expert “i” (Likert scale [0–10]) in “m” different fields related to the Energy Sector (in our case, 4 fields: Economy, Environment, Technics and Society).

Experts’ relevancies obtained from Equation (1) must be normalised so that they sum up the unity.

4.1.2. AHP (Weights of the Criteria)

Experts weighed the importance of criteria and sub-criteria using paired comparison matrices based on a Saaty [63] scale (see

Table 4. Saaty’s Fundamental Pairwise Comparison Scale.

Intensity	Importance of One Over Another	Explanation
1	Equal importance	Two activities contribute equally to the objective
3	Moderate importance	Experience or judgements slightly favours one criterion over another
5	Essential or strong importance	Experience or judgements strongly favours one criterion over another
7	Very strong importance	An activity is strongly favoured, and its dominance demonstrated in practice
9	Extreme importance	The evidence favouring one activity over another is of the highest possible
2, 4, 6, 8	Intermediate values	When compromise is needed

).

The steps to obtain the relative weights of the criteria are summarized below:

Step 1: Pairwise Comparison Matrixes

Experts develop importance comparison measures between criteria. Pairwise Comparison Matrices (PCMs) are constructed using expert judgments and reciprocal values (see Figure 7-left).

Step 2: Calculation of Priorities

The approximate eigenvector method is used to determine the priorities of each PCM after normalising each PCM according to its sum of columns [I*_ij] (Figure 7-central). The vector of priorities is obtained as the average of rows of its normalised matrix (Figure 7-right).

Step 3: Consistency of Judgements of each Expert

Consistency Ratios (CR) are calculated to ensure consistency and rationality of the PCMs.

CR is calculated as the quotient of the Consistency Index CI and the Random Index RI. See Equation (2), where ${“\lambda }_{max}”$ is the highest eigenvalue of the PCM and “n” its dimension.

$$\mathrm{C}\mathrm{R}={\displaystyle \frac{\mathrm{C}\mathrm{I}}{\mathrm{R}\mathrm{I}}} \mathrm{C}\mathrm{I}={\displaystyle \frac{{\lambda }_{max}-n}{n-1}} \mathrm{R}\mathrm{I}=(\mathrm{T}\mathrm{a}\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} \mathrm{o}\mathrm{f} \mathrm{“}\mathrm{n}”)$$

(2)

Step 4: Aggregation of PCMs from Experts

PCMs are aggregated using the weighted geometric mean, also considering the normalized relevance weights determined for each expert, calculated according to Section 4.1.1.

$$G_{ij}={\prod }_{\mathrm{k}=1}^{\mathrm{p}}{\left({\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}}\right)}^{{\mathsf{\rho }}_{\mathrm{k}}}$$

(3)

4.1.3. Consensus Method

To reduce the heterogeneity of the expert judgements, the iterative consensus procedure by Dong and Saaty [64,65,66,67] was applied, starting from the initial aggregated matrix calculated as in Equation (4):

$${\mathrm{G}\mathrm{t}=\mathrm{G}}_{\mathrm{i}\mathrm{j}}^{\mathrm{t}}={\prod }_{\mathrm{k}=1}^{\mathrm{p}}{\left({\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k},\mathrm{t}}\right)}^{{\mathsf{\rho }}_{\mathrm{k}}}$$

(4)

The steps are detailed below:

Step 1. Calculate the Group Compatibility Indices (${\mathrm{GCI}}_{\mathrm{k}}$) of each expert k with the last aggregated matrix,

which measures the discrepancies between each expert’s PCMs and the aggregated group matrix, according to Equation (5).

$${\mathrm{G}\mathrm{C}\mathrm{I}}_{\mathrm{k}}{=\mathrm{d}(\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k}},{\mathrm{G}}_{\mathrm{i}\mathrm{j}})={\displaystyle \frac{1}{{\mathrm{n}}^2}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{{\mathrm{G}}_{\mathrm{i}\mathrm{j}}·\mathrm{I}}_{\mathrm{j}\mathrm{i}}^{\mathrm{k}}$$

(5)

Step 2. Modify the previous PCMs or expert relevance weights for greater consensus.

The expert most discrepant from the consensus (h) is encouraged to adjust their judgements. If accepted, their new PCM (consistent) is calculated following Equation (6) (where α∈[0, 1] represents his willingness to change). If rejected, their relevance weight decreases according to Equation (7) (where β∈[0, 1] represents his adjustment penalty) affecting the weights of the other experts “z” according to Equation (8).

$${\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{h},\mathrm{t}+1}={\left({\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{h},\mathrm{t}}\right)}^{\mathsf{\alpha }}·{\left({\mathrm{G}}_{\mathrm{i}\mathrm{j}}^{\mathrm{t}}\right)}^{\left(1-\mathsf{\alpha }\right)}$$

(6)

$${\mathsf{\rho }}_{\mathrm{h}}^{t+1}={\mathsf{\rho }}_{\mathrm{h}}^t·\mathsf{\beta }+{\mathsf{\rho }}_{\mathrm{h}}^t·\left(1-\mathsf{\beta }\right)·{\mathsf{\rho }}_{\mathrm{h}}^t$$

(7)

$${\mathsf{\rho }}_{\mathrm{z}}^{t+1}={\mathsf{\rho }}_{\mathrm{z}}^t+{\mathsf{\rho }}_{\mathrm{z}}^t·\left(1-\mathsf{\beta }\right)·{\mathsf{\rho }}_z^t$$

(8)

Step 3. Calculate the new aggregated matrix for the next iteration (t+1) using the modified PCMs and/or updated values of ${\mathsf{\rho }}_k^{t+1}$, according to Equation (4) for instant (t+1): ${\mathrm{G}(\mathrm{t}+1)=\mathrm{G}}_{\mathrm{i}\mathrm{j}}^{\mathrm{t}+1}=\prod _{\mathrm{k}=1}^{\mathrm{p}}{\left({\mathrm{I}}_{\mathrm{i}\mathrm{j}}^{\mathrm{k},\mathrm{t}+1}\right)}^{{\mathsf{\rho }}_k^{t+1}}$

Step 4. Continue the iterations until a stop condition is reached, which could be:

(a)

All experts reach an acceptable level of consensus (in our case all (${\mathrm{G}\mathrm{C}\mathrm{I}}_{\mathrm{k}})$are less than 1.01 (1%)).

(b)

All experts reject the modification of their PCMs.

(c)

A predetermined number of iterations is completed (10 in this case).

The resulting importance weights obtained with this AHP+Consensus method, after validation, will be used in subsequent methods.

4.1.4. Fuzzy VIKOR (Ranking of Alternatives)

VIKOR is a distance-based multi-criteria decision method developed by Opricovic [68,69,70,71,72,73,74,75,76,77,78] to handle complex systems with conflicting criteria, focusing on maximizing group utility and minimizing individual regret. Fuzzy VIKOR extends the method to handle subjectivity and/or imprecise data.

Step 1. Determination of the Fuzzy Decision Matrix $\left[{\tilde{X}}_{ij}\right]$ by averaging the fuzzy numbers based on expert judgements given for each alternative A_i regarding each criterion C_j (see Figure 8-left).

Step 2. Normalization of the Fuzzy Decision Matrix $\left[{\tilde{V}}_{ij}\right]$ by dividing previous ${\tilde{X}}_{ij}$ by the maximum value of each criterion {C_ij} (see Figure 8-central).

Step 3. Weighing of the Fuzzy Decision Matrix $\left[{\tilde{P}}_{ij}\right]$ by multiplying previous ${\tilde{V}}_{ij}$ by the weight Wj of the corresponding criterion -determined by AHP+Consensus- (see Figure 8-right).

Step 4. Obtention of f⁺ and f⁻: After normalizing the Fuzzy Decision Matrix, determine the best (f⁺) and worst (f⁻) fuzzy values for each alternative-criterion set.

Step 5. Obtention of ${\tilde{S}}_i$, ${\tilde{R}}_i \mathrm{a}\mathrm{n}\mathrm{d} {\tilde{Q}}_i$: The three fuzzy VIKOR matrix functions (${\tilde{S}}_i=$ Utility function; ${\tilde{R}}_i=$ Regret function; ${\tilde{Q}}_i=$ VIKOR index) are calculated, as in Equations (9)–(11):

$${\tilde{S}}_i={\sum }_{j=1}^n{W}_j\left({\displaystyle \frac{{\tilde{V}}_j^{+}-{\tilde{V}}_{ij}}{{\tilde{V}}_j^{+}- {\tilde{V}}_j^{-}}}\right)$$

(9)

$${\tilde{R}}_i={Max}_j\left[W_j\left({\displaystyle \frac{{\tilde{V}}_j^{+}-{\tilde{V}}_{ij}}{{\tilde{V}}_j^{+}-{\tilde{V}}_j^{-}}}\right)\right]$$

(10)

$${\tilde{Q}}_i=v\left({\displaystyle \frac{{\tilde{S}}_i-{\tilde{S}}^{-}}{{\tilde{S}}^{+}-{\tilde{S}}^{-}}}\right)+\left(1-v\right)\left({\displaystyle \frac{{\tilde{R}}_i-{\tilde{R}}^{-}}{{\tilde{R}}^{+}-{\tilde{R}}^{-}}}\right)$$

(11)

being ${\tilde{S}}^{+}={Max}_i{\tilde{S}}_i$, ${\tilde{S}}^{-}={Min}_i{\tilde{S}}_i$, ${\tilde{R}}^{+}={Max}_i{\tilde{R}}_i$, ${\tilde{R}}^{-}={Min}_i{\tilde{R}}_i$

These three fuzzy VIKOR functions require defuzzification—in our case by the centroid method- to obtain the crisp values of S, R and Q, and the ranking.

Step 6. Acceptability conditions: The ranking of alternatives is made according to Q. Among the range of compromise solutions, two conditions must be met.

Condition 1 (Equation (12)) is an acceptable benefit:

$$Q\left(A^{\left(M\right)}\right)-Q\left(A^{\left(1\right)}\right)\ge {\displaystyle \frac{1}{\left(m-1\right)}}$$

(12)

where $A^{\left(i\right)}$ are the classified alternatives, m is the number of alternatives (in our case 10), and M is the alternative against which the first one is compared to in each iteration.

Condition 2 (Equation (13)) is acceptable stability: Alternative $A^{\left(1\right)}$ by Q must also be the first one by S and R.

$$Q\left(A^{\left(1\right)}\right)=S\left(A^{\left(1\right)}\right)=R\left(A^{\left(1\right)}\right)$$

(13)

If both conditions are not fulfilled:

(1)

If Condition 1 is not met, iterations must be made with the next alternatives until it is fulfilled.

The last acceptable compromise solution is the one corresponding to the position M-1.

(2)

If Condition 2 is not met, the two first-ranked solutions that meet Condition 1 are accepted.

4.2. Methodologies for the Validation (BWM+ Fuzzy TOPSIS)

4.2.1. Best-Worst Method (Weights of the Criteria)

The Best-Worst Method (BWM) is a refined paired-comparison decision-making approach created by Rezai in 2015 [79,80,81,82,83,84,85] that evaluates multiple alternatives based on specific criteria. It has become a very used method in multi-criteria decision-making. It involves identifying the best and worst criteria, conducting pairwise comparisons, and solving a max-min problem to determine their weights. The best alternative is chosen based on these weights, and a consistency test is conducted to ensure reliability. BWM outperforms the Analytic Hierarchy Process (AHP) in consistency ratio, requiring less comparison data and producing more consistent results. Once the criteria and subcriteria have been established, the following steps are:

Step 1: Determine the best or most important and the worst or least important criteria.

Step 2: Determine the preference of the best criterion over all the other criteria using the Saaty scale 1–9,

Step 3: Determine the preference of all the criteria over the worst criterion, also in the Saaty scale 1–9.

Step 4: Determine the optimal weights of the criteria and subcriteria ($w_1^{*}$, $w_2^{*}$, …, $w_n^{*}$), for which each pair of w_B/w_j and w_j/w_W, has w_B/w_j = a_Bj and w_j/w_W = a_jW.

To satisfy these conditions, a solution is needed where the maximum absolute differences $\left|{\displaystyle \frac{w_B}{w_j}}-a_{Bj}\right|$ and $\left|{\displaystyle \frac{w_j}{w_W}}-a_{jW}\right|$for all j are minimized. Under the two weight constraints (non-negativity and sum = 1), this can be expressed as in Equation (14):

$${\mathit{min}max}_j\left\{\left|{\displaystyle \frac{w_B}{w_j}}-a_{Bj}\right|,\left|{\displaystyle \frac{w_j}{w_W}}-a_{jW}\right| \right.$$

(14)

         subject to:

         $\sum _j{w}_j$ = 1 and w_j ≥ 0 for all j,

which can also be expressed like in Equation (15):

$$\begin{array}{l}\min \xi \\ \mathrm{subject} \mathrm{to}:\\ \left|{\displaystyle \frac{w_B}{w_j}}-a_{Bj}\right|\le \xi \hspace{1em}\hspace{1em}\mathrm{for} \mathrm{all} j\\ \left|{\displaystyle \frac{w_j}{w_W}}-a_{jW}\right|\le \mathsf{\xi }\hspace{1em}\hspace{1em}\mathrm{for} \mathrm{all} j\\ {\sum }_j{w}_j=1 \mathrm{and} w_j\ge 0 \mathrm{for} \mathrm{all} j\end{array}$$

(15)

Solving either Equation (14) or Equation (15), the optimal weights ($w_1^{*}$, $w_2^{*}$, …, $w_n^{*}$) and ξ^* are obtained.

Step 5: Consistency ratio

Consistency decreases when a_Bj × a_jW is lower or higher than a_BW, or equivalently a_Bj x a_jW ≠ a_BW. The highest inequality occurs when a_Bj and a_jW have the maximum value (ξ). As a result of assigning the maximum value by a_Bj and a_jW, ξ is a value that should be subtracted from a_Bj and a_jW and added to a_BW or, as in Equations (16) and (17):

(a_Bj − ξ) × (a_jW − ξ) = (a_BW + ξ)

(16)

As for the minimum consistency, a_Bj = a_jW = a_BW:

(a_BW − ξ) × (a_BW − ξ) = (a_BW + ξ) → ξ² − (1+2 a_BW) ξ + (a_BW² − aBW) = 0

(17)

The maximum ξ (max ξ) is determined by solving for different values of a_BW ∈ (1, 2, …, 9), obtaining the consistency index (see

Table 5. Consistency index.

Consistency Index (CI)
aBW	1	2	3	4	5	6	7	8	9
Consistency Index	0	0.44	1	1.63	2.3	3	3.73	4.47	5.23

), which are then used to calculate the consistency ratio (see Equation (18)):

Consistency ratio = ξ/Consistency Index

(18)

4.2.2. Fuzzy TOPSIS (Ranking of Alternatives)

The TOPSIS method, proposed by Cheng and Hwang in 1992 [86,87,88], is a distance-based multi-criteria method for obtaining rankings of alternatives based on their similarity to an ideal solution, the best result being as distant from the negative ideal solution and as close to the positive ideal solution as possible.

This paper uses a fuzzy version of this methodology (FTOPSIS) to reflect the imprecision of the experts’ ratings on each alternative. The triangular fuzzy numbers ${\tilde{X}}_{ij}=\left(a_{ij}, b_{ij}, c_{ij}\right)$follow a fuzzy scale of unit variances: $\tilde{0}=\left(\mathrm{0,0},1\right), \tilde{1}=\left(\mathrm{0,1},2\right), \tilde{2}=\left(\mathrm{1,2},3\right), \dots , \tilde{9}=\left(\mathrm{8,9},10\right), \widetilde{10}=\left(\mathrm{9,10,10}\right).$For the importance weights of the criteria W_j, the crisp values derived from AHP + Consensus are taken.

The formulation of FTOPSIS is summarised below:

Steps 1–3 described in Section 4.1.4 for FVIKOR are identical for FTOPSIS.

Step 4. Calculation of FPIS and FNIS based on the previous weighted matrix, considering the type of each criterion (“max”—the bigger the better- or “min” —the smaller the better-) according to Equation (19).

$${\tilde{P}}_j^{+}=\left\{\begin{array}{c}max \left\{{\tilde{P}}_{ij}\right\} if C_j is “max”type\\ min \left\{{\tilde{P}}_{ij}\right\} if C_j is “min”type\end{array}\right. { \tilde{P}}_j^{-}=\left\{\begin{array}{c}min \left\{{\tilde{P}}_{ij}\right\} if C_j is “max”type\\ max \left\{{\tilde{P}}_{ij}\right\} if C_j is “min”type\end{array}\right.$$

(19)

FPIS: Ideal fuzzy alternative ${\tilde{A}}_j^{+}=({\tilde{P}}_1^{+},{\tilde{P}}_2^{+},\dots ,{\tilde{P}}_n^{+})$

FNIS: Anti-ideal fuzzy alternative ${\tilde{A}}_j^{-}=({\tilde{P}}_1^{-},{\tilde{P}}_2^{-},\dots ,{\tilde{P}}_n^{-})$

Step 5. Calculation of distances to FPIS and FNIS

FPIS (${\mathrm{D}}_{\mathrm{i}}^{+}$) and FNIS (${\mathrm{D}}_{\mathrm{i}}^{-}$) are calculated according to Equations (20) and (21), based on the triangular fuzzy numbers.

$${\mathrm{D}}_{\mathrm{i}}^{+}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{dist(\tilde{P}}_{ij}-{\tilde{\mathrm{P}}}_{ij}^{+}) {\mathrm{D}}_{\mathrm{i}}^{-}={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{dist(\tilde{P}}_{ij}-{\tilde{\mathrm{P}}}_{ij}^{-})$$

(20)

$${dist(\tilde{P}}_{ij}-{\tilde{\mathrm{P}}}_{ij}^{*})=\sqrt{{\displaystyle \frac{1}{3}}·\left[{\left(P_{ij}^L-P_{ij}^{*L}\right)}^2+{\left(P_{ij}^M-P_{ij}^{*M}\right)}^2+{\left(P_{ij}^U-P_{ij}^{*U}\right)}^2\right]}$$

(21)

Step 6. Calculation of the Closeness Coefficient and the final ranking

Once $D_i^{+}$ and $D_i^{-}$ have been calculated, the Closeness Coefficient (CC_i) of each alternative is derived using Equation (22):

$$\mathrm{C}\mathrm{C}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{i}}^{-}}{\left({\mathrm{D}}_{\mathrm{i}}^{+}-{\mathrm{D}}_{\mathrm{i}}^{-}\right)}}$$

(22)

The values of the Closeness Coefficients lie within the interval [0,1], ranking the alternatives from highest to lowest. In other words, values closer to 1 indicate better solutions.

5. Results, Validation and Discussion

In this Section, the methods described in Section 4 (Methodology) were applied to determine the weights of the criteria and the ranking of the studied technologies. For the criteria weights, the assessments obtained from the experts’ responses were used both in AHP+Consensus and in BWM. For the ranking of alternatives, the criteria weights obtained from AHP+ Consensus were used.

5.1. Methodologies for the Combined Hybrid Decision Model (AHP + Fuzzy VIKOR)

5.1.1. Relevance Weights of Each Expert

According to Section 4.1.1, experts were weighed according to Equation (1), obtaining a set of values that were then normalised to be in the interval [0,1], as seen in

Table 6. Relevance weights of each expert.

Relevance weights of experts	Exp. 1	Exp. 2	Exp. 3	Exp. 4	Exp. 5	Exp. 6
Experts’ individual experience:
Years of Professional Activity (PA)	28	22	30	42	29	29
Years within the Energy Sector (ES)	28	22	25	42	27	29
Academic Degree (AD)	4	4	4	4	4	4
Knowledge Degree in energy sector fields (KD):
Economic Knowledge (KDEc)	8	6	9	5	8	8
Environmental Knowledge (KDEnv)	6	9	9	6	7	9
Technical Knowledge (KDTech)	7	7	8	7	8	8
Social Knowledge (KDSoc)	6	9	7	3	7	7
Expert Relevance	1.298	1.400	1.509	1.179	1.405	1.483	SUM:
Normalized Expert Relevance	0.157	0.169	0.182	0.142	0.170	0.179	1.000

:

5.1.2. Weights of the Criteria Using AHP

As said in Section 4.1.2, criteria are compared with each other at each level by all the experts, obtaining the corresponding PCMs ([I_ij]). Subsequently, after normalising them [I^*_ij], their eigenvector of weights [W_i] is determined, and its consistency checked.

Table 7. PCM, Autovector and 1st Level Criteria Consistency Analysis (Expert 1).

Expert 1
ρ1 = 0.157		[Iij]					[I*ij]				Wi
	C1	C2	C3	C4		C1	C2	C3	C4			Consistency
C1	1.0	2.0	2.0	2.0	C1	0.40	0.36	0.50	0.29	C1	0.39	0.041	CI
C2	0.5	1.0	0.5	2.0	C2	0.20	0.18	0.13	0.29	C2	0.20	0.882	RI
C3	0.5	2.0	1.0	2.0	C3	0.20	0.36	0.25	0.29	C3	0.27	0.046	CR
C4	0.5	0.5	0.5	1.0	C4	0.20	0.09	0.13	0.14	C4	0.14	0.090	Threshold
Sum	2.5	5.5	4.0	7.0						Sum	1.00	OK

illustrates the results of this process for Expert 1 in the subsystem formed by first level criteria of the model (C1 to C4). For this expert, economic criteria hold greater importance compared to environmental criteria, with a value of 2. In contrast, technical criteria have a higher importance than the environmental criteria with a score of 2 as well. It is also observed that this expert is consistent in his/her judgements, since his/her consistency ratio is lower than the threshold for n = 4 (CR = 0.046 < 0.090).

Finally, by aggregating the (consistent) PCMs of the six experts using the weighted geometric mean -Equation (3)-, we obtain the initial aggregation results (G0) illustrated in

Table 8. PCM, Autovector and Consistency analysis of 1st Level Criteria (Group of experts).

Group of Experts
		G0 = [G0ij]					[G0*ij]				W0i
	C1	C2	C3	C4		C1	C2	C3	C4			Consistency
C1	1.00	0.97	1.75	2.04	C1	0.32	0.31	0.36	0.31	C1	0.32	0.002	CI
C2	1.03	1.00	1.42	2.13	C2	0.33	0.32	0.29	0.32	C2	0.32	0.882	RI
C3	0.57	0.70	1.00	1.45	C3	0.18	0.22	0.21	0.22	C3	0.21	0.003	CR
C4	0.49	0.47	0.69	1.00	C4	0.16	0.15	0.14	0.15	C4	0.15	0.090	Threshold
Sum	3.09	3.14	4.86	6.61						Sum	1.00	OK

. In these results, criteria C1 (Economic) and C2 (Environmental) emerge as the most important, with similar relative weights (0.32). Additionally, the aggregated PCM of all experts demonstrated good consistency.

These steps were applied to each subsystem of the model, obtaining the local weights of each criterion across all hierarchical levels. To determine the global weights at the lowest hierarchical level, the weights of the criteria at each level were multiplied in a downward chain. This process yielded the global weights for all criteria, which were then used in all the other methods tested. The final results of this procedure are summarized in

Table 9. Results of the AHP method. Overall weighting.

Criteria/Subcriteria			Local Weights			Global Weights	ID
1st level	2nd Level	3rd Level	1st Level	2nd Level	3rd Level
Economic		Investment cost	0.32		0.434	0.141	C 1.1
		Operation cost			0.236	0.077	C 1.2
		Market price			0.330	0.107	C 1.3
Environmental		Noise	0.32		0.087	0.027	C 2.1
		CO2 Emissions			0.618	0.196	C 2.2
		Waste			0.295	0.093	C 2.3
Technical	Operational	Start-up time	0.21	0.721	0.180	0.027	C 3.1.1
		Programmable			0.344	0.052	C 3.1.2
		Efficiency			0.476	0.071	C 3.1.3
	Structural	Lifetime		0.279	0.699	0.041	C 3.2.1
		Construction time			0.301	0.017	C 3.2.2
Social		Job creation	0.15		0.418	0.063	C 4.1
		Public acceptance			0.582	0.088	C 4.2
					Sum:	1.000

.

5.1.3. Consensus Method

Figure 9 illustrates the calculations corresponding to Iterations 1 and 6 of the consensus procedure described in Section 4.1.3. In Iteration 1, Expert 2 was the furthest from the initial aggregate matrix G0 and accepted the modification of his/her PCM, resulting in the aggregate matrix G1. Note that $\alpha$ is 0.5, indicating moderate willingness to change from Expert 2. In Iteration 6, Expert 2 was again the furthest, but in this case, $\alpha$ was 0.2, revealing higher willingness to change and obtaining the aggregate matrix G6. After meeting a stopping condition at Iteration 10, the last results in the Figure show the final aggregate matrix ($\mathrm{G}9$), the weighting vector of the four Level 1 criteria (${W9}_i)$: 0.32 for C1, 0.34 for C2, 0.18 for C3, and 0.16 for C4), and the corresponding consistency analysis.

The same procedure was applied to all subsystems within the hierarchical framework, yielding local weights for criteria at each level. These local weights were then used to calculate the new composite weights, as presented in

Table 10. Overall weighting after the consensus procedure.

Criteria/Subcriteria			Local Weights			Global Weights	ID
1st Level	2nd Level	3rd Level	1st Level	2nd Level	3rd Level
Economic		Investment cost	0.32		0.354	0.114	C 1.1
		Operation cost			0.322	0.104	C 1.2
		Market price			0.323	0.104	C 1.3
Environmental		Noise	0.34		0.072	0.024	C 2.1
		CO2 Emissions			0.653	0.219	C 2.2
		Waste			0.276	0.092	C 2.3
Technical	Operational	Start-up time	0.18	0.661	0.23	0.028	C 3.1.1
		Programmable			0.389	0.046	C 3.1.2
		Efficiency			0.381	0.046	C 3.1.3
	Structural	Lifetime		0.339	0.696	0.043	C 3.2.1
		Construction time			0.304	0.019	C 3.2.2
Social		Job creation	0.16		0.33	0.054	C 4.1
		Public acceptance			0.67	0.109	C 4.2
					Sum:	1.000

.

5.1.4. Fuzzy VIKOR

As indicated in Section 4.1.4, Steps 1 and 2 start from the normalised matrix of alternative assessments $\left[{\tilde{V}}_{ij}\right]$. The parameter V was taken as 0.5 since it was the result of obtaining consensus using the Dong-Saaty method.

The fuzzy scale used for VIKOR assessments was 0–10 with fuzzy triangular numbers (see

Table 11. Fuzzy scale for VIKOR assessments.

Crisp	l	m	u
0	0	0	1
1	0	1	2
2	1	2	3
3	2	3	4
4	3	4	5
5	4	5	6
6	5	6	7
7	6	7	8
8	7	8	9
9	8	9	10
10	9	10	10

below).

Table 12. Matrix of normalised fuzzy valuations of alternatives for all criteria, best and worst solutions and weighted matrix for the calculation of the VIKOR matrix functions.

		Investment Cost			Operation Cost			…			Job Creation			Public Acceptance
	A1	0.08	0.20	0.31	0.58	0.68	0.79				0.79	0.91	1.00	0.07	0.18	0.29
	A2	0.43	0.55	0.67	0.33	0.44	0.54				0.75	0.87	0.96	0.21	0.32	0.43
	A3	0.71	0.82	0.94	0.44	0.54	0.65				0.55	0.66	0.77	0.46	0.57	0.68
	A4	0.61	0.73	0.84	0.42	0.53	0.63				0.45	0.57	0.68	0.55	0.66	0.77
	A5	0.76	0.88	0.98	0.72	0.82	0.91				0.34	0.45	0.57	0.71	0.82	0.93
Vij	A6	0.27	0.39	0.51	0.70	0.81	0.91		…		0.49	0.60	0.72	0.46	0.57	0.68
	A7	0.78	0.90	1.00	0.86	0.96	1.00				0.30	0.42	0.53	0.82	0.93	1.00
	A8	0.24	0.35	0.47	0.28	0.39	0.49				0.51	0.62	0.74	0.64	0.75	0.86
	A9	0.37	0.49	0.61	0.53	0.63	0.74				0.34	0.45	0.57	0.68	0.79	0.88
	A10	0.20	0.31	0.43	0.51	0.61	0.72				0.68	0.79	0.91	0.21	0.32	0.43
FPIS		0.78	0.90	1.00	0.86	0.96	1.00		…		0.79	0.91	1.00	0.82	0.93	1.00
FNIS		0.08	0.20	0.31	0.28	0.39	0.49				0.30	0.42	0.53	0.07	0.18	0.29
Wj			0.114			0.104			…			0.054			0.109
	A1	0.06	0.11	0.22	0.01	0.05	0.12				−0.02	0.00	0.04	0.06	0.11	0.19
	A2	0.01	0.06	0.14	0.05	0.09	0.19				−0.01	0.00	0.05	0.05	0.09	0.16
	A3	−0.02	0.01	0.07	0.03	0.08	0.16				0.00	0.03	0.09	0.02	0.05	0.11
	A4	−0.01	0.03	0.09	0.03	0.08	0.16				0.01	0.04	0.11	0.01	0.04	0.09
	A5	−0.02	0.00	0.06	−0.01	0.03	0.08				0.02	0.05	0.13	−0.01	0.02	0.06
M	A6	0.03	0.08	0.18	−0.01	0.03	0.08		…		0.01	0.03	0.10	0.02	0.05	0.11
	A7	−0.03	0.00	0.05	−0.02	0.00	0.04				0.02	0.05	0.14	−0.02	0.00	0.04
	A8	0.04	0.09	0.19	0.05	0.10	0.20				0.00	0.03	0.10	0.00	0.03	0.07
	A9	0.02	0.07	0.15	0.02	0.06	0.13				0.02	0.05	0.13	−0.01	0.02	0.07
	A10	0.04	0.09	0.19	0.02	0.06	0.14				−0.01	0.01	0.07	0.05	0.09	0.16

illustrates the results obtained according to Step 3 of the best (${\tilde{V}}_j^{+})$ and worst ${(\tilde{V}}_j^{-})$fuzzy solutions and the matrix ${M= W}_j\left({\displaystyle \frac{{\tilde{V}}_j^{+}-{\tilde{V}}_{ij}}{{\tilde{V}}_j^{+}- {\tilde{V}}_j^{-}}}\right),$which will allow in a further step to calculate the VIKOR matrix functions. For size reasons, only the two first and the two last criteria are shown.

Table 13. Results of fuzzy matrices ${\tilde{S}}_i$, ${\tilde{R}}_i \mathrm{a}\mathrm{n}\mathrm{d} {\tilde{Q}}_i$.

		Sj			Rj			Qj
A1	0.16	0.53	1.31	0.06	0.11	0.22	−0.77	0.52	1.88
A2	0.29	0.70	1.55	0.14	0.22	0.33	−0.40	0.98	2.43
A3	0.11	0.47	1.22	0.07	0.14	0.22	−0.78	0.53	1.80
A4	0.16	0.55	1.36	0.09	0.16	0.26	−0.67	0.67	2.02
A5	−0.07	0.22	0.85	0.02	0.05	0.13	−1.10	0.05	1.21
A6	−0.04	0.27	0.89	0.03	0.08	0.18	−1.02	0.19	1.36
A7	−0.11	0.17	0.77	0.02	0.05	0.14	−1.12	0.01	1.15
A8	0.15	0.55	1.41	0.03	0.10	0.33	−0.86	0.50	2.29
A9	0.08	0.45	1.23	0.01	0.07	0.26	−0.99	0.30	1.91
A10	0.14	0.51	1.28	0.04	0.09	0.19	−0.83	0.45	1.77
	S+	0.29	0.70	1.55	R+	0.14	0.22	0.33
	S−	−0.11	0.17	0.77	R−	0.02	0.05	0.13

shows the results obtained for the fuzzy matrices ${\tilde{S}}_i$, ${\tilde{R}}_i \mathrm{a}\mathrm{n}\mathrm{d} {\tilde{Q}}_i$ according to the formulation from Equations (9)–(11) in Section 4.1.4.

The defuzzified values of S, R and Q for all the alternatives and their ranking are shown in

Table 14. VIKOR Indexes S, R and Q and Ranking of Alternatives.

	S	Ranking		R	Ranking		Q	Ranking
A1—Nuclear	0635	7		0.127	6		0.538	7
A2—Coal	0.811	10		0.229	10		1.000	10
A3—Combined Cycle	0.566	5		0.142	7		0.522	6
A4—CHP	0.656	8		0.166	9		0.674	9
A5—Wind	0.308	2		0.063	1		0.053	2
A6—Hydro	0.348	3		0.094	3		0.181	3
A7—PV	0.249	1		0.067	2		0.014	1
A8—Green Hydrogen	0.663	9		0.143	8		0.610	8
A9—Storage	0.552	4		0.100	4		0.382	4
A10—SMR	0.614	6		0.107	5		0.458	5

:

The three renewable alternatives achieve the best results. However, they do not have the same ranks according to S, R and Q. This means they are compromise solutions. The acceptability conditions must be checked: Condition 1 (Acceptable benefit): According to Equation (12) in Section 4.1.4, the first alternative that meets this condition is Alternative 7 (PV), which is ranked first. Condition 2 (Acceptable stability): According to Equation (13) in Section 4.1.4, this condition is not met, since ranks of the first, second and third ranked alternatives are not the same in S, R and Q. Therefore, Alternatives 7 (PV) and 5 (Wind) are the first-ranked compromise solutions for FVIKOR.

A sensitivity analysis was conducted to explore the changes in ranking of the studied alternatives for different values of V (V= 0, 0.2, 0.4, 0.5, 0.6, 0.8 and 1), and the results are shown in Figure 10:

It can be seen that alternatives A5 (Wind), A6 (Hydro) and A7 (PV) are always at the top three positions of the ranking.

5.2. Methodologies Used for the Validation (BWM + Fuzzy TOPSIS)

5.2.1. BWM (Weights of the Criteria)

According to Section 4.2.1, Steps 1, 2 and 3 of the procedure to obtain the weights of the criteria are represented in

Table 15. Analysis of Best to Others and Others to Worst in each subsystem.

Level 1 Criteria						Economic Subcriteria
	Best			Worst			Best		Worst
	Environmental	Economic	Technical	Social			Investment Cost	Operation Cost	Market Price
BO->	1	1.15	1.65	2.1		BO->	1	1.09	1.1
	2.1	1.83	1.27	1	<-OW		1.1	1.01	1	<-OW
Operational subcriteria						Environmental subcriteria
	Best		Worst				Best		Worst
	Programmable	Efficiency	Start-Up Time				CO2 Emissions	Waste	Noise
BO->	1	1.03	1.66			BO->	1	2.72	8.06
	1.66	1.61	1	<-OW			8.06	2.97	1	<-OW
Structural subcriteria						Technical subcriteria
	Best	Worst					Best	Worst
	Lifetime	Construction time					Operational	Structural
BO->	1	2.29				BO->	1	1.95
	2.29	1	<-OW				1.95	1	<-OW
						Social subcriteria
							Best	Worst
							Social acceptance	Job creation
						BO->	1	0.49
							2.03	1	<-OW

:

Step 4: After applying the constraint formulas, the optimal criteria and subcriteria weights ($w_1^{*}$, $w_2^{*}$, …, $w_n^{*}$) are obtained, as shown in

Table 16. Weights of all the criteria using BWM.

Criteria/Subcriteria			Local Weights			Global Weights	ID
1st Level	2nd Level	3rd Level	1st Level	2nd Level	3rd Level
Economic		Investment cost	0.33		0.333	0.111	C 1.1
		Operation cost			0.333	0.111	C 1.2
		Market price			0.333	0.111	C 1.3
Environmental		Noise	0.33		0.091	0.030	C 2.1
		CO2 Emissions			0.727	0.242	C 2.2
		Waste			0.182	0.061	C 2.3
Technical	Operational	Start-up time	0.17	0.661	0.333	0.037	C 3.1.1
		Programmable			0.333	0.037	C 3.1.2
		Efficiency			0.333	0.037	C 3.1.3
	Structural	Lifetime		0.339	0.696	0.039	C 3.2.1
		Construction time			0.304	0.017	C 3.2.2
Social		Job creation	0.17		0.33	0.055	C 4.1
		Public acceptance			0.67	0.112	C 4.2
					Sum:	1.000

.

5.2.2. Fuzzy TOPSIS (Ranking of Alternatives)

Steps 1 to 3 of the procedure described in Section 4.2.2 were followed. The fuzzy scale used for TOPSIS assessments was the same one as for VIKOR (see Table 11).

Table 17. Aggregation, normalisation and weight of fuzzy valuations for ‘Investment Cost’ across alternatives.

Alternatives	Exp1			…			Exp6			Aggregated Mean			Normalised Assessment			Weighted Assessment
A1—Nuclear	0	1	2				4	5	6	0.67	1.67	2.67	0.08	0.20	0.31	0.01	0.02	0.04
A2—Coal	2	3	4				6	7	8	3.67	4.67	5.67	0.43	0.55	0.67	0.05	0.06	0.08
A3—Combined Cycle	3	4	5				7	8	9	6.00	7.00	8.00	0.71	0.82	0.94	0.08	0.09	0.11
A4—CHP	4	5	6				6	7	8	5.17	6.17	7.17	0.61	0.73	0.84	0.07	0.08	0.10
A5—Wind	5	6	7		…		5	6	7	6.50	7.50	8.33	0.76	0.88	0.98	0.09	0.10	0.11
A6—Hydro	1	2	3				4	5	6	2.33	3.33	4.33	0.27	0.39	0.51	0.03	0.04	0.06
A7—PV	5	6	7				6	7	8	6.67	7.67	8.50	0.78	0.90	1.00	0.09	0.10	0.11
A8—Green Hydrogen	2	3	4				3	4	5	2.00	3.00	4.00	0.24	0.35	0.47	0.03	0.04	0.05
A9—Storage	2	3	4				5	6	7	3.17	4.17	5.17	0.37	0.49	0.61	0.04	0.06	0.07
A10—SMR	0	1	2				4	5	6	1.67	2.67	3.67	0.20	0.31	0.43	0.02	0.04	0.05
							Max:			8.50					Wi:	0.11

shows the calculations performed for the Criterion “Investment Cost”.

The last three columns present the aggregated fuzzy ratings for this criterion, calculated as the arithmetic mean of expert judgements across all alternatives ${(\tilde{\mathit{X}}}_{\mathit{i}\mathit{j}})$. Then, these ratings were normalised according to the maximum value of their right vertices (${\tilde{\mathit{V}}}_{\mathit{i}\mathit{j}}$) and finally they were weighted by the weights obtained after the consensus procedure (${\tilde{\mathit{P}}}_{\mathit{i}\mathit{j}}$). For size reasons, only judgements from Experts 1 and 6 are shown.

Table 18. Results of weighted fuzzy ratings, ideal solutions (FPIS and FNIS), distances between alternatives and ideal solutions, Closeness Coefficients and ranking of alternatives according to FTOPSIS.

	Investment Cost			…			Public Acceptance				D+	D−	CC	Ranking
A1	0.01	0.02	0.04				0.01	0.02	0.03	A1	0.34	0.29	0.459	9
A2	0.05	0.06	0.08				0.02	0.04	0.05	A2	0.46	0.18	0.279	10
A3	0.08	0.09	0.11				0.05	0.06	0.07	A3	0.29	0.34	0.543	5
A4	0.07	0.08	0.10				0.06	0.07	0.08	A4	0.33	0.30	0.472	8
A5	0.09	0.10	0.11		…		0.08	0.09	0.10	A5	0.12	0.51	0.806	2
A6	0.03	0.04	0.06				0.05	0.06	0.07	A6	0.18	0.46	0.722	3
A7	0.09	0.10	0.11				0.09	0.10	0.11	A7	0.09	0.54	0.859	1
A8	0.03	0.04	0.05				0.07	0.08	0.09	A8	0.31	0.33	0.517	6
A9	0.04	0.06	0.07				0.07	0.09	0.10	A9	0.25	0.38	0.600	4
A10	0.02	0.04	0.05				0.02	0.04	0.05	A10	0.32	0.31	0.490	7
FPIS	0.09	0.10	0.11		…		0.09	0.10	0.11
FNIS	0.01	0.02	0.04				0.01	0.02	0.03

illustrates the normalised and weighted results of alternatives for all the criteria, as well as the calculation of the positive (FPIS) and negative (FNIS) ideal fuzzy solutions, the distances of each alternative to these ideal solutions (D+ and D−), the Closeness Coefficient of each alternative and their final ranking. For size reasons, only the first and the last criteria are shown.

5.3. Comparison of Results

Weights of the criteria:

In

Table 19. Comparison of weights between AHP+Consensus and BWM.

Criteria/Subcriteria			Global Weights		Diff (%)
1st Level	2nd Level	3rd Level	AHP + Consensus	BWM
Economic		Investment cost	0.114	0.111	3%
		Operation cost	0.104	0.111	−7%
		Market price	0.104	0.111	−6%
Environmental		Noise	0.024	0.030	−21%
		CO2 Emissions	0.219	0.242	−10%
		Waste	0.092	0.061	52%
Technical	Operational	Start-up time	0.028	0.037	−25%
		Programmable	0.046	0.037	26%
		Efficiency	0.046	0.037	24%
	Structural	Lifetime	0.043	0.039	8%
		Construction time	0.019	0.017	9%
Social		Job creation	0.054	0.055	−2%
		Public acceptance	0.109	0.112	−2%
		Sum:	1.000	1.000	3.8%

a comparison is made between the final weights obtained using AHP + Consensus and the ones with BWM, with quite analogous outcomes. The criteria with the lowest weights are the ones which experienced the most significant variations, while the total average difference was only 3,8%. In fact, consistency with BWM was higher while the computational effort was much smaller.

Ranking of alternatives:

Table 20. Comparison of rankings obtained with FVIKOR and FTOPSIS.

#	Ranking by Technology	FVIKOR	FTOPSIS	Ranking by Technology	#
1	PV	A7	A7	PV	1
2	Wind	A5	A5	Wind	2
3	Hydro	A6	A6	Hydro	3
4	Battery Storage (BESS)	A9	A9	Battery Storage (BESS)	4
5	Small Modular Reactor (SMR)	A10	A3	Combined Cycle	5
6	Combined Cycle	A3	A8	Green Hydrogen	6
7	Nuclear	A1	A10	Small Modular Reactor (SMR)	7
8	Green Hydrogen	A8	A4	CHP	8
9	CHP	A4	A1	Nuclear	9
10	Coal	A2	A2	Coal	10

depicts a comparison between the ranking of alternatives using FVIKOR and the one obtained with FTOPSIS.

In view of the results, it can be concluded that the rankings derived from FVIKOR and FTOPSIS exhibit a high degree of similarity, with the top three alternatives being the same renewable technologies (PV, Wind and Hydro) and the one at the bottom being Coal.

5.4. Discussion

The results of the criteria weights in Section 5.1.2 and Section 5.1.3 (AHP + Consensus) and Section 5.2.1 (BWM) were highly consistent, while the rankings obtained in Section 5.1.4 (FVIKOR) and Section 5.2.2 (FTOPSIS) were highly coincident for the evaluated alternatives. According to the assessments of our experts, Renewable energy alternatives dominated the top positions, with PV (A7) ranking first, followed by Wind (A5) and Hydro (A6). Conversely, fossil-fuel-based alternatives (particularly Coal (A2) and CHP (A4)), along with large Nuclear plants (A1) consistently ranked lowest.

In fact, the alternatives with best combined scores in economic and environmental criteria emerged as the winners. Nuclear energy, although non-CO₂-emitting, has a very high investment cost and this, together with its very poor social acceptance led this technology to a low position in the ranking. The energy mix resulting from the assessment of this panel of experts would promote the installation of renewable energies to slow down environmental degradation.

Photovoltaic energy has also topped the ranking in several studies conducted in recent years in different countries. In an analysis using a hybrid MCDM method by Zhao and Guo in China [15], PV was positioned ahead of wind energy. Another work by Çolak et al. [32] obtained similar results for Turkey, when choosing only among renewable alternatives. The results obtained from the research conducted by Taylan et al. [31] in Saudi Arabia, which employed several methods (fuzzy AHP, fuzzy VIKOR, and fuzzy TOPSIS) to assess the alternatives, indicate that PV technology also ranked first. Other analyses have produced similar results to the ranking obtained in our study. However, differences in the timing of the investigations, the diversity of the countries involved and their power generation mixes may always lead to variations in the outcomes. For example, the study by Amer et al. [37] and the research conducted by Solangi et al., both in Pakistan [34] reveal minor differences. In the first case, the results were: Biomass > Wind > Solar thermal, while in the second case, the results were Wind > Hydro > PV. Despite the similarity of criteria, the weights assigned to the criteria led to different solutions, also influenced by the evolution of the countries’ energy and social situation. The study by Galiano et al. (Spain, 2023) [89] gave the same results obtained in our paper, confirming through the use of Integrated Assessment Models (IAMs) the expected growth in the share of renewable sources in the Spanish energy mix to reach the Net-zero scenario in 2050. Other studies related to prospective generation scenarios in Spain [52,90,91,92,93] also align with the results presented in this work. Our findings align with studies such as Lu & Liu [94], who highlighted the critical balance between cost, reliability, and environmental protection in community energy systems, reinforcing the need for multi-criteria frameworks in energy policy decisions.

However, results of the different studies are highly variable depending on the assignments of the experts for the different criteria affecting each alternative. Our combined method shows that, with the judgements made by our panel of experts, the results remain consistent across different multi-criteria decision methods. In other words, the ranking remains consistent regardless of the multi-criteria decision methods used to derive the solutions.

6. Conclusions

The assessment of power generation technologies for national energy mixes using economic, environmental, technical, and social criteria is a complex multi-criteria decision-making problem. In the current context of an energy transition throughout the world to achieve the goal of climate neutrality or net-zero emissions by 2050, accurately assessing energy production technologies is particularly relevant and even critical for policy-makers and investors. Historically, the selection of these technologies was primarily based on investment and technical criteria; however, this approach is no longer adequate. In our research, experts in the electricity generation sector provided their assessments through a questionnaire, expressing their opinions on the weights of the criteria and the alternatives under consideration. Given the current state of the sector and the global objectives to mitigate climate change, the participating experts ranked environmental and economic criteria as the most significant ones, with CO₂ emissions being the top sub-criterion, followed by investment costs. It is important to note that other experts’ assessments on specific countries’ energy mixes will surely lead to different results, which is obvious due to the highly different available energy sources.

In this study, AHP was firstly combined with a consensus method to determine the importance weights of the criteria, aiming to reduce subjectivity and to account for the educational and/or professional diversity of the experts. The Best-Worst Method (BWM) was used to verify the consistency of the results with AHP and the consensus method. The results with BWM were completely similar to those of AHP+Consensus, while the computational load was much smaller. The weights obtained were used in all the methods deployed, minimizing the need of further consultation rounds with experts. Fuzzy VIKOR was the selected method to obtain the ranking of alternatives, and validation was made using fuzzy TOPSIS. Fuzzy sets for the assessments of the experts of criteria with respect to each alternative. Since both FVIKOR and FTOPSIS are distance-based methods, the results are based on calculating the geometric distance between each alternative and the ideal solution. Additionally, this work considers a wide variety of alternatives, both existing (conventional and renewable) and emerging, such as Battery-storage (BESS), Small Modular Reactors (SMR) and Hydrogen. This diversity was aimed to represent the current reality of an average energy mix in the world and anticipate its possible evolution. The analysis of these emerging technologies using multi-criteria decision-making methods had not yet been sufficiently explored.

The global results obtained for our world average energy source scenario indicate that PV, Wind and Hydro energy technologies were the highest-rated alternatives across all methods employed. The large-scale adoption of renewable energies, including utility-scale and residential self-consumption projects, reduces dependence on conventional fossil fuels, decreases energy imports and leverages the countries’ local energy sources. Currently, PV and Wind energy already have a significant share in some energy mixes like California or Texas in the USA, Spain and Portugal in Europe or in China, where the increase is being really fast. A combination of multiple renewable technologies can achieve energy independence over time and foster long-term sustainable development. This increase in the share of renewables touches the quadrilemma question posed in the introduction section. On the positive side, it significantly contributes to improving the living standards, reducing fossil fuel imports and ensuring environmental sustainability simultaneously. On the other hand, this increase makes energy systems more unpredictable and therefore less controllable by energy system operators. As an example, Spain and Portugal have been recently powered exclusively by renewable energies for entire days. On the negative side, Spain suffered a general black-out on 28th April that had the whole country without electricity for around 18 h.

The results obtained after the application of the different MCDM methods are an answer to the research questions posed in the introduction. Regarding whether the trend of increasing renewable energy installations will continue, the rankings obtained consistently show a clear preference for PV, Wind, and Hydro, all of them renewable generation technologies. The question of whether the emerging technologies considered in this study (Hydrogen, Battery-Storage (BESS) and SMRs) are already commercially feasible, the rankings obtained were intermediate or low, respectively. Storage and SMRs ranked fourth and fifth, while Hydrogen ranked ninth, according to our experts’ judgments. It appears that Hydrogen has not reached yet a competitive cost, while the installation of Battery-Storage units is already growing in some countries or regions. Despite SMRs ranking favorably (5th), few units are being installed yet throughout the world. We will need to wait and observe whether these still emerging technologies reduce their costs and/or enhance their evaluation results and, consequently, accelerate their deployment rate.

A general conclusion of this study is that the predominance of renewable energy in the results reflects a balance between economic (cost reduction) and environmental (CO₂ emission reduction) objectives, which aligns with the global goals of neutral emissions in 2050.

To further underscore the methodological and practical contributions of this study, our hybrid model uniquely integrates structured group consensus with uncertainty-aware ranking capabilities, advancing beyond conventional MCDM approaches in energy planning. By combining AHP with a formal consensus mechanism, we reconcile divergent expert perspectives into robust criteria weights, avoiding the oversimplification of averaging individual judgments. The subsequent application of fuzzy-VIKOR captures the inherent ambiguity in evaluating emerging technologies like Hydrogen, BESS and SMRs, providing more realistic rankings than traditional crisp methods. This modular framework, validated through BWM and fuzzy-TOPSIS respectively, not only reduces computational redundancy but offers policymakers a flexible tool adaptable to diverse national contexts. Crucially, the model’s design bridges theoretical rigor with implementation needs, enabling both comprehensive technology assessments and responsive energy strategy adjustments as new data on renewables and storage solutions emerge.

Finally, this work can be extended in future studies. Despite its contributions, our study has limitations due to its qualitative nature, which involves expert assessments for the criteria weights and for the alternatives ranking. This limitation could be solved if only quantitative data were used, but this might lead to the loss of valuable information about the interpretation of those quantitative data. Another limitation is that the use of only AHP + Consensus for criteria weights and VIKOR for alternatives ranking may not be sufficient for complex decisions in real-world energy planning or policy. To mitigate this, the results were validated using BWM for criteria weights and TOPSIS for alternatives ranking. The significant alignment between the results obtained underscores the reliability of the proposed combined method. The gains in accuracy, computational effort, and consistency obtained by employing multiple MCDM methodologies suggest that incorporating other MCDM approaches can lead to more informed and effective decision-making processes. Future studies could use more recent MCDM methods, such as FUCOM (FUll COnsistency Method) [95], IDOCRIW (Integrated Determination of Objective CRIteria Weights) [96], or MABAC (Multi-Attribute Border Approximation Area Comparison) [97], to further refine the analyses. New entrants to the energy sector like financial entities [98]-which own no physical assets- also bring interesting new approaches that are worth investigating in the near future. Integrating these new methods with the ones used in our work could broaden their applicability for different countries, scenarios and players.