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Article

A Fuzzy-Machine Learning Framework for Energy Efficiency Optimization and Smart Transition Analysis in European Economies

by
Ionuț Nica
1,
Irina Georgescu
1,* and
Jani Kinnunen
2
1
Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, 010552 Bucharest, Romania
2
Department of Information Systems, Åbo Akademi University, Tuomiokirkontori 3, 20500 Turku, Finland
*
Author to whom correspondence should be addressed.
Electronics 2026, 15(2), 276; https://doi.org/10.3390/electronics15020276
Submission received: 10 December 2025 / Revised: 25 December 2025 / Accepted: 6 January 2026 / Published: 7 January 2026
(This article belongs to the Special Issue New Trends in Energy Saving, Smart Buildings and Renewable Energy)
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Abstract

This study aims to identify and interpret latent energy-economic typologies across European economies and to assess whether their energy transition paths exhibit convergence or persistent structural divergence. To achieve this objective, the paper investigates the energy–economic structure of thirteen European economies between 2000 and 2024 using an integrated fuzzy–machine learning framework. Eight indicators related to renewable energy, energy efficiency, emissions, electricity use, digitalization, investment, urbanization and economic development were analyzed to identify structural typologies across countries. Using the Fuzzy C-Means algorithm, four distinct clusters were identified: (i) moderately developed economies with balanced renewable adoption and energy efficiency, (ii) structurally integrated economies with medium energy intensity and stable economic performance, (iii) an emerging economy with persistent structural constraints, and (iv) advanced high-performance economies engaged in accelerated energy transition. To validate the fuzzy classification, Random Forest and XGBoost models were trained based on the same indicators, achieving high predictive accuracy (94% and 92%, respectively). Feature importance analysis reveals that CO2 emissions, energy efficiency and urbanization play the most significant roles in differentiating country profiles. The proposed framework provides a comprehensive approach for understanding energy transition heterogeneity, structural convergence and the drivers shaping the evolution of European energy–economic systems.

1. Introduction

The energy transition has become one of the defining processes of European economies over the past two decades [1,2,3]. Countries in Europe are trying, at different paces, to modernize their energy infrastructure [4,5], reduce carbon emissions [6,7] and adopt digital technologies to support a more efficient and smarter energy system [8,9]. However, these transformations are not happening uniformly. They are influenced by the economic structure, the level of digitalization, the institutional capacity and the historical legacies of each country. As a result, the energy-economy systems in Europe are evolving in a complex way, with sometimes converging, sometimes diverging trajectories, difficult to capture using traditional methods.
Despite the strong policy commitment to decarbonization and renewable energy expansion, the European energy transition faces a series of structural and systemic obstacles. Recent studies highlight challenges related to insufficient investment in energy storage, grid congestion, limited interconnection capacity, and increasing system instability caused by the high variability of renewable energy sources [10]. These constraints affect the reliability of power systems and slow down the pace of convergence across European economies, particularly in countries with weaker infrastructure or limited investment capacity. As a result, the energy transition in Europe unfolds unevenly, reinforcing structural heterogeneity and divergent adjustment paths among countries.
Recent literature has shown a growing interest in approaches that can describe this structural diversity without forcing countries into rigid categories. Classical clustering methods or linear econometric models often assume clear boundaries between groups, although in reality energy transitions are gradual, and economies are frequently in intermediate zones. Moreover, the relationships between energy consumption, CO2 emissions, digitalization and economic performance are often nonlinear, influenced by structural factors that change over time.
This complexity highlights a gap in the literature: there are few works that combine a fuzzy approach, capable of capturing hybrid natures and overlaps between country profiles, with modern machine learning methods that can validate and interpret these groupings in a robust way. Especially for Central and Eastern Europe—a region undergoing accelerated transformation—there are still few analyses that integrate energy transition, digitalization, and economic development into a common framework.
To address this gap, this study proposes a Fuzzy–Machine Learning framework applied to a set of thirteen European economies, over a 25-year period (2000–2024). Fuzzy C-Means is used to identify typologies of energy–economy systems, allowing each country to have different degrees of membership in multiple clusters. PCA is introduced to reduce dimensionality and visually understand the latent structure of the data. In addition, Random Forest and XGBoost models are used to externally validate the fuzzy clusters and to identify the indicators that contribute most to the differentiation of countries.
The scientific literature shows that classical clustering methods have significant difficulties in identifying overlapping structures and gradual transitions, because they impose rigid boundaries between groups. For example, Budayan et al. [11] demonstrate that, in the analysis of strategic groups, traditional methods cannot capture the simultaneous membership of entities in several typologies, while Self-Organizing Maps and Fuzzy C-Means approaches manage to more accurately highlight “fuzzy” structures and intermediate positions. Classical clustering methods assume that economies can be neatly assigned to a single structural category. In reality, especially in times of economic and energy transformation, this assumption is rarely valid, as countries simultaneously combine characteristics belonging to several typologies [12,13]. Similarly, traditional econometric models tend to describe average and relatively stable relationships, which makes it difficult to capture gradual adjustment processes and divergent transition trajectories [14,15].
The fuzzy approach allows overcoming these limitations, offering the possibility for an economy to belong simultaneously to several typologies, with different degrees of membership. This aspect is particularly relevant in the analysis of energy transition, where changes are progressive and economic structures frequently remain mixed for long periods [16,17,18]. The integration of machine learning methods complements this perspective by validating fuzzy typologies and identifying the main factors that differentiate energy-economic profiles, capturing nonlinear relationships and complex interactions between indicators [19,20,21]. Also, the integration of fuzzy logic with machine learning methods provides an appropriate framework for the analysis of complex and uncertain systems, allowing the representation of gradual transitions, hybrid structures and incomplete information, where both classical statistical methods and standard machine learning models encounter limitations [22]. In this sense, fuzzy–machine learning frameworks have demonstrated the ability to combine predictive performance with interpretability, being successfully used in integrated sustainability and economic performance assessments [23].
Through this integrated approach, the paper makes three major contributions. First, it offers a flexible and reality-based way to represent energy transitions, avoiding rigid classifications. Second, it highlights the differences and similarities between European economies, placing advanced countries, transition economies and emerging energy systems in the same framework. Third, it demonstrates that machine learning techniques can strengthen fuzzy analysis, both by validating the coherence of clusters and by highlighting the role of each indicator in structuring them.
Thus, the study provides a clear perspective on how European economies are evolving in terms of energy, digital and economic aspects. The proposed framework brings added clarity to a field characterized by complexity and dynamism, showing where each country is positioned in this process and how energy-economic structures are reconfigured over time.
The paper is organized in a way that follows the natural progression of the analysis. After introducing the European context and the reasons why these economies are worth studying together, Section 2 explains in a way that is understandable to the reader what data was used and why, how the indicators were constructed, and what methodological tools were used—from heatmaps and principal component analysis, to Fuzzy C-Means and machine learning models. Section 3 brings to the fore the results: how countries cluster, how they evolve over time, and how well these patterns can be reproduced by Random Forest and XGBoost models. In Section 4, these results are placed in a broader economic perspective, discussing what they mean for Europe’s energy and digital transitions. Section 5 discusses the robustness of the results, the rationale for indicator selection, and the added value of the proposed fuzzy–machine learning framework. The paper concludes, in Section 6, with the main conclusions, the limitations of the study, and some realistic future research avenues.

2. The Stage of Knowledge in the Field

2.1. Machine Learning Approaches for Energy Efficiency and Smart Energy Systems

This stream of research focuses on the use of machine learning techniques to improve energy efficiency through prediction, optimization, and intelligent control, predominantly at the level of networks, buildings, and localized energy systems.
Over the past decade, the scientific literature has undergone a profound transformation in the way energy efficiency and the transition to sustainable systems are approached, as digital technologies and artificial intelligence have begun to redefine energy infrastructures and decision-making processes. Initial research focused mainly on specific technical optimizations, such as improving the performance of wireless networks or managing digital traffic. For example, Imran et al. [24] review how machine learning (ML) can improve the energy efficiency of wireless networks, focusing on its integration into self-organizing network functions. It highlights ML-based improvements in self-configuration, self-optimization, and self-healing, as well as applications in resource allocation, traffic prediction, and cognitive radio.
Deep learning has become a powerful tool for dealing with the growing complexity of modern wireless communication systems, particularly in optimizing energy efficiency for distributed cooperative spectrum sensing. In a deep learning framework which combines graph neural networks and reinforcement learning, He and Jiang [25] prove how cooperative spectrum sensing can be optimized by learning efficient sensing strategies directly from network topology and interaction patterns. By their approach, energy efficiency is improved while maintaining high sensing accuracy.
Venugopal et al. [26] propose a Reinforcement Learning–based Energy-Efficient Communication Protocol (RL-EECP) to address persistent challenges in AI- and IoT-enabled wireless sensor networks, including energy constraints, security, and network flexibility. Their protocol combines sleep scheduling, data fusion, and adaptive node prioritization to extend network lifetime. RL-EECP achieves superior performance compared to existing approaches. Pham et al. [27] propose a Random Forest (RF)–based prediction model to forecast short-term, hourly energy consumption across multiple buildings, using five year-long datasets to evaluate its performance. Their results prove that the RF approach outperforms M5P and Random Tree techniques during several forecasting horizons. Their tool would help building owners and facility managers improve energy efficiency.
Zekić-Sušac et al. [28] investigate how Big Data platforms and machine learning can be integrated into an intelligent system for dealing with energy efficiency in the public sector, focusing on Croatian public buildings. Using deep neural networks, regression trees, and RF techniques, they propose the MERIDA system to support smart city energy management through predictive analytics and digital transformation.
Harrouz et al. [29] propose PUMA-GRID, a hybrid clustering and routing protocol that integrates the Puma Optimization Algorithm with grid-based multi-hop routing to improve energy efficiency and extend the lifetime of wireless sensor networks. The simulation results show that PUMA-GRID outperforms LEACH, AEO-based methods, and previous PUMA variants in different base-station placements.

2.2. AI-Driven Energy Transition, Smart Cities, and Sustainability Perspectives

These studies emphasize the systemic nature of the energy transition, highlighting the interaction between digitalization, sustainability, and economic transformation.
Nižetić et al. [30] highlight the critical role of energy transition in reducing dependence on fossil fuels and mitigating environmental impacts. This shift assumes intertwined economic, social, political, and technological challenges. Advances in smart and sustainable technologies, ranging from smart cities to decarbonization, are presented. They support energy transition goals highlighting the need to assess digitalization from resource and environmental perspectives.
Şerban et al. [31] discuss the Smart Energy domain within Future Smart Cities Research. The need for advanced AI- and ML-driven optimization, smarter networks, and improved renewable energy infrastructure is emphasized. The efficiency of transformation processes in the EU, the evolving structure of renewable energy sources, labor productivity and investment patterns, and the role of AI in shaping future smart cities are discussed.
Peng et al. [32] investigate how AI-based multi-energy optimization can improve rural energy planning and support carbon-neutral development. A geographically adaptive framework applied to three counties across China is proposed. Their findings validate the Porter hypothesis through and introduce a coal-coupled biomass model that informs sustainable energy decisions.
Hinov [33] states that the next major evolution in the electricity sector is the emergence of Energy Intelligence (EI), where predictive analytics, adaptive control, and material-aware design are embedded directly into power-conversion hardware. An EI reference architecture is shown, proving how AI converges with WBG-based converter design. A sustainability-focused roadmap for building intelligent, resilient, and self-optimizing energy systems is proposed.

2.3. Fuzzy and Hybrid Decision-Making Approaches in Energy and Digital Transformation

A complementary stream of literature integrates fuzzy logic with machine learning and optimization techniques to address uncertainty, qualitative assessments, and hybrid decision-making in energy systems.
Eti et al. [34] develop a three-stage decision-making model that integrates machine learning and Fermatean fuzzy logic to identify performance indicators for digital transformation in renewable energy projects. Their results show that qualified personnel and strong government support are the most critical factors. The proposed hybrid model improves accuracy by reducing uncertainty and weighting expert judgments.
Aldulaimi and Çevik [35] propose an intelligent MPPT strategy for grid-connected photovoltaic systems that combines an Adaptive Neuro-Fuzzy Inference System (ANFIS) with Particle Swarm Optimization (PSO) to optimize tracking accuracy, speed, and power quality under varying environmental conditions. The ANFIS-PSO controller outperforms conventional MPPT methods by identifying the global maximum power point, reducing THD, and maintaining high efficiency in dynamic and partial-shading scenarios. The ANFIS-PSO controller is suitable for next-generation smart PV systems.

2.4. Synthesis and Research Gap

All these studies, together, indicate that there is a strong convergence between machine learning techniques, digitalization and energy efficiency optimization. There is also a high interest in fuzzy and hybrid approaches that help manage uncertainty and quality assessments in energy-related decision-making processes. However, the existing literature remains largely fragmented, with most contributions focusing on specific technologies, localized systems or sector-level applications.
At the macroeconomic level, there is still a lack of comparative analyses that integrate fuzzy clustering and machine learning to examine how national economies differ in terms of energy efficiency, renewable integration, digitalization, and economic performance over time. In particular, European economies—especially those in Central and Eastern Europe—are underrepresented in studies that jointly address gradual energy transitions and mixed structural configurations.
This study addresses this gap by proposing an integrated fuzzy–machine learning framework that captures both the hybrid nature of energy–economic structures and the nonlinear relationships shaping energy transition trajectories across European economies.

3. Data Collection and Methodology

3.1. Data Collection

The set of countries analyzed in this paper was selected to capture the structural and institutional diversity of European energy systems, essential for a fuzzy–machine learning framework aimed at optimizing energy efficiency and understanding the smart transition. The list includes, according to Table 1, both European Union member states (Bulgaria, Croatia, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia and Slovenia) and two economies located on the periphery of the EU or outside the bloc, but relevant for regional comparison (Switzerland and the Republic of Moldova). The presence of most Central and Eastern European countries allows capturing a broad spectrum of energy development trajectories, characterized by economic convergence, accelerated modernization, and varying levels of integration into European policies on decarbonization and digitalization. At the same time, the inclusion of Switzerland provides a benchmark of “advanced performance” in energy efficiency and smart infrastructure [36,37], while the Republic of Moldova provides a useful contrast for understanding the structural limitations and energy vulnerabilities of the region’s emerging economies [38,39]. This group of countries therefore allows for the analysis of diverse patterns of energy consumption, technological adoption, investment, environmental pressures and urban transformations. At the same time, the selection maximizes the comparative relevance of the results: it provides a coherent framework for studying European energy convergence, but also the differences that persist between advanced, transition and emerging economies. This diversity is essential for the robust assessment of fuzzy relationships and for the performance of machine learning algorithms in identifying energy transition patterns.
In Table 2, we present the role of each indicator used in the analysis, along with its conceptual relevance for the energy-economy dynamics. We believe that the selection of variables captures essential dimensions of the processes analyzed: energy transition (RNEC), energy efficiency (GDPEU), environmental pressure (CO2) and energy intensity (EPC). At the same time, the inclusion of the IUI indicator as a proxy for digitalization and the GCS as a proxy for investment capacity allows highlighting the potential of each country for structural modernization. Urbanization (UPA) is treated as a major demographic factor, with a direct impact on energy demand. Finally, GDP per capita was introduced as a general measure of economic development. Overall, we observe that high values of these indicators can reflect both technological progress and structural transformation, as well as increasing pressures on the environment and resources. All data was taken from the World Bank.

3.2. Fuzzy Clustering Approach (Fuzzy C-Means)

Considering that the selected European economies do not strictly belong to a single category, the energy transition is gradual, and infrastructure, energy mix and digitalization evolve at different rates, we consider the fuzzy approach appropriate.
To characterize the energy and economic structure of the analyzed countries, but also to substantiate the fuzzy clustering process, three complementary exploratory analysis tools were integrated: temporal heatmaps, fuzzy membership matrix and principal component analysis (PCA). Heatmaps were constructed for each indicator, using normalized values and organized in a country × year structure. These representations help us identify gradual transitions, detect divergent routes and delimit similar regional patterns in advance that can influence the clustering results. Basically, we will use heatmaps not for classification, but for visual validation of the existence of natural groupings in the data.
To identify latent structures in the multidimensional energy–digitalization landscape of the selected European economies, we apply the Fuzzy C-Means (FCM) clustering algorithm [48,49,50]. Unlike hard clustering techniques such as K-Means, FCM allows each country to belong to multiple clusters simultaneously, with different degrees of membership [51,52]. This property is essential for modeling economic systems characterized by gradual transitions, hybrid configurations and overlapping development trajectories, as is the case with European energy transitions.
Appendix A reports the standard mathematical formulation of the Fuzzy C-Means algorithm for completeness and reproducibility.
From an economic perspective, the fuzzy membership degrees capture the extent to which a country’s energy–economic profile aligns with a given cluster prototype. High membership values indicate strong structural coherence with a dominant development pattern, while intermediate values reflect hybrid or transitional configurations, allowing us to identify economies that simultaneously exhibit characteristics of multiple energy transition pathways.
To ensure the robustness of the fuzzy clustering results, the optimal value k was determined using two standard fuzzy validity indices: Partition Coefficient (PC) [53] and Modified Partition Coefficient (MPC) [54,55]. Both indices must be maximized to illustrate the optimal number of clusters. It is also important to mention that before clustering, all variables were standardized to avoid dominating the algorithm by variables with different scales. The data set has a panel structure, for the period 2000–2024, and fuzzy analysis was applied both on the average values for stable structural typologies, and on panel data, to detect dynamics over time.
To reduce dimensionality, but also to validate the fuzzy clusters, we used PCA [56]. The eight variables will be projected into the space of the first two principal components, which cumulatively explain the dominant proportion of the total variance. Through PCA Biplot we will evaluate how countries naturally group in the energy-economic space, but we will also understand the direction of influence of each indicator.

3.3. Rationale for Machine Learning-Based Validation

While fuzzy clustering provides a flexible framework for identifying latent energy–economic typologies, its results are primarily descriptive and exploratory in nature [11,57]. To enhance the robustness and credibility of the identified clusters, an external validation step is required. In this study, Random Forest and XGBoost models are employed as supervised learning tools to validate the fuzzy clustering outcomes [58,59]. Specifically, the fuzzy cluster assignments are treated as target labels, and the same set of energy, economic, and digitalization indicators is used as input features. High predictive accuracy indicates that the fuzzy clusters capture consistent and learnable patterns in the data, rather than arbitrary groupings. Random Forest is selected for its robustness to multicollinearity [60], nonlinear relationships [61], and noise [62], as well as for its strong performance in high-dimensional settings. XGBoost complements this approach by offering superior predictive power and the ability to model complex interactions through gradient boosting [63,64]. Together, these models provide a complementary validation framework that strengthens confidence in the fuzzy clustering results and supports their economic interpretability.

3.4. Supervised Machine Learning for Cluster Prediction and Feature Importance Analysis

3.4.1. Random Forest

To validate the cluster structure obtained by fuzzy clustering, we applied a Random Forest (RF) model as a multi-class classification method [65]. The model was trained using energy and economic indicators as explanatory variables, and the fuzzy cluster labels (obtained by maximum membership) were used as the target variable. In the Python implementation in Google Colab, the RF model was configured with 300 trees (n_estimators = 300), a value selected to stabilize performance and reduce prediction variance. Setting random_state = 42 ensured reproducibility of the results. The model was trained by splitting the data into training and testing subsets (train–test split), followed by generating predictions for the test set.
The model performance is evaluated through the confusion matrix and associated metrics such as accuracy, precision, recall and F1-score. These metrics allowed us to verify the degree to which the model could reproduce the structure of the previously identified clusters. We also extracted the importance of the variables (feature importance), providing information on the indicators that contribute most to the differentiation of the clusters.
We consider RF to be suitable for our study because it efficiently handles non-linear relationships between indicators and provides interpretable explanations regarding the variables that most influence cluster membership.

3.4.2. XGBoost

XGBoost (Extreme Gradient Boosting) was introduced as a complementary evaluation method, due to its ability to model complex interactions and provide high performance in multi-class classification [66].
The model is based on the incremental optimization of a loss function by sequentially adding weak decision trees [19]. Each tree corrects the residual errors of the previous trees, according to the general formulation according to relation (1):
y ^ ( t ) = y ^ t − 1 + f t ( x )
where in Equation (1), f t ( x ) is the tree added at step t, selected so as to minimize:
L ( t ) = ∑ i l ( y i ,   y ^ t + Ω ( f t ) )
where in Equation (2), the Ω ( f t ) penalty controls the complexity of the model through the number of leaves and the magnitude of their weights, preventing overfitting.
The model was trained using the same energy and economic indicators as explanatory variables, and the cluster labels were treated as the target variable. The implementation was performed in Python (version 3.12.12), using the XGBoost package (version 3.1.2). The model parameters included 300 estimators, a low learning rate to stabilize the boosting process, and setting the parameter max_depth = 3 to prevent overfitting. The model was trained using the standard gradient boosting method, in which decision trees are added sequentially to correct the residual errors of the previous steps. After training on the training set, the model performance was evaluated on the test set, generating accuracy, confusion matrix and performance indicators (precision, recall, F1-score).

4. Results

The values presented in Table 3 highlight clear distinctions between the energy and economic dimensions studied over the period 2000–2024. On average, nations exhibit a moderate degree of renewable energy (RNEC ≈ 2.85) and energy efficiency (GDPEU ≈ 2.44), while CO2 emissions are low but fluctuating (CO2  ≈ 1.78). Electricity use (EPC ≈ 8.37) and the level of digitalization (IUI ≈ 3.91) are higher, reflecting a modernization of infrastructure. Economic indicators (GDP ≈ 9.45) and those relating to energy consumption (UPA ≈ 4.12; GCS ≈ 3.21) present constant values, with somewhat lower fluctuations (small standard deviations), suggesting regional uniformity. Asymmetry indicates slightly uneven distributions, but without extreme variations, and kurtosis shows slightly more concentrated values compared to a normal distribution. In conclusion, the information provides a vision of a stable energy-economic profile, but with considerable differences between states in terms of digitalization, energy consumption and economic development.
Figure 1 shows the normalized evolution of the eight indicators analyzed for the thirteen countries, during 2000–2024. RENEC shows a gradual increase in almost all countries, with visible accelerations after 2010, in line with European policies on energy transition. The GDPEU indicator shows moderate but stable improvements, especially in countries such as Switzerland, Slovenia and Croatia. CO2 show a visible decline in most countries, reflecting industrial modernization and the shift to cleaner energy sources.
EPC increases slightly over time in most countries, but with important variations between advanced countries and Eastern European economies. IUI has the clearest upward trend of the entire set of indicators: all countries move from low values in the early 2000s to very high levels after 2015, signaling digital convergence. The GCS indicator is much more volatile, with distinct episodes of growth and decline, suggesting changes in policies or institutional dynamics specific to each country. UPA remains relatively stable in structure, but shows persistent differences between developed and transition countries. Finally, GDP confirms the largest disparities: Switzerland remains consistently in the upper range, while Moldova and Bulgaria are placed at the lower end of the normalized scale. Overall, developments show a general trend of energy and digital modernization, but also persistent structural differences between the economies analyzed.
Figure 2 illustrates the evolution of the FPC coefficient as a function of the number of clusters (k). It is observed that the FPC values gradually decrease as k increases from 4 to 10, indicating a decrease in the clarity and separation between clusters. In particular, the highest level of FPC occurs at k = 4, suggesting that this division generates the most coherent and distinct fuzzy structure of the data. After this point, the coefficient continues to decrease, which shows that adding additional clusters does not bring a gain in interpretability, but on the contrary leads to greater overlaps between groups. Therefore, the results show that the optimal solution for classifying the dataset is the 4-cluster configuration, which maximizes internal cohesion and fuzzy separation between countries.
Figure 3 shows the values of the MPC for various values of the number of clusters k. It is observed that the MPC reaches the highest levels in the range k = 3–5, with a local maximum at k = 4. This indicates a well-defined fuzzy structure, in which the memberships are sufficiently clear, and the overlaps between clusters remain small. After k = 5, the MPC drops sharply, which reflects a deterioration in the quality of the partitioning: as the number of clusters increases, the groups become less distinct, and the degree of ambiguity in the assignment of observations increases. Although there are small fluctuations at k = 8 and k = 9, the values remain substantially lower than in the 4-cluster configuration. The results thus confirm that k = 4 represents the optimal solution, being the point at which the clarity of the partitioning and the fuzzy separation reach their maximum level.
Considering both indices jointly (FPC and MPC), k = 4 emerges as the most robust solution, being the only configuration at which both FPC and MPC indicate maximum partition quality.
Figure 4 illustrates the dynamics of European countries’ membership in the four identified clusters, over the period 2000–2024. Two major patterns are observed: structural stability for some economies and significant transitions for others. Countries such as Czechia, Estonia and Switzerland present a constant positioning in the same cluster (cluster 1), suggesting a clearly defined energy and economic profile, without major structural changes over time. In contrast, countries such as Croatia, Latvia, Slovenia and Romania have undergone transitions between clusters, reflecting reconfigurations in their energy performance, investment or emission intensity. A special case is Moldova, which remains stable in cluster 3 throughout the period, indicating a persistent energy model, but less convergent with the EU dynamics. Also, starting with 2011–2012, a general trend of migration towards cluster 4, associated with economies characterized by the intensification of the energy transition and increased efficiency, is noted. This development suggests both regional convergence and the direct effect of European policies on renewable energy, digitalization and emission reduction.
Figure 5 shows how the thirteen European economies are distributed in the space defined by the first two principal components, which together explain almost 70% of the total variation in the data. The representation highlights the deep patterns of the energy-economic structure and how these align with the clustering obtained by Fuzzy C-Means. The arrows from Figure 5 represent the loadings of the standardized indicators. Although some vectors and labels partially overlap due to the two-dimensional projection, their directions and relative magnitudes remain clearly distinguishable and are explicitly discussed in the text.
The RNEC and GDPEU indicators are oriented towards the upper part of the graph, suggesting that economies located in this area—such as Romania, Latvia, Croatia and Lithuania—combine a higher level of renewable energy and better energy efficiency. This also explains why these countries form Cluster 1: they are economies in an active process of energy modernization, with visible progress in the green transition. On the right side of the graph we find the vectors associated with economic development and social infrastructure: GDP, UPA, IUI and GCS. The countries located in this direction—especially Estonia, Slovenia and Switzerland—present characteristics of advanced economies: high incomes, consolidated urbanization, strong digitalization and superior investment capacity. This profile justifies their membership in Cluster 4, even if the internal differences between these three states lead to slightly divergent development models.
The CO2 vector is clearly oriented towards the bottom of the graph, indicating that countries in this area—such as the Czech Republic and the Slovak Republic—face higher levels of per capita emissions and energy structures still dependent on fossil fuels. This positioning explains why these economies belong to Cluster 2, characterized by a slower energy transition and greater pressure on the environment. The EPC, oriented towards the lower right, suggests that countries in this area have higher electricity consumption per capita, reflecting more energy-intensive industrial sectors or different consumption styles. Slovenia, for example, is positioned close to the EPC direction, indicating an energy model with a significant share of electricity consumption. Moldova is placed far to the left of the graph, far from any cluster, which confirms its distinct profile: low energy consumption, modest economy and an energy structure different from that of the Central European states. This isolation justifies why Moldova forms Cluster 3 alone.
Overall, the biplot validates the structure of the fuzzy clusters: each group occupies a coherent area in the principal component space, and the variable vectors very clearly indicate the energy-economic dimensions that separate the states from each other—green transition at the top, economic development on the right, and emissions intensity at the bottom of the graph.
Figure 6 summarizes the structural differences between the four fuzzy clusters through the average values of energy, environmental and economic indicators. The analysis highlights four distinct typologies of energy–economy systems in Central and Eastern Europe. Cluster 1 is characterized by a high level of energy efficiency (EPC = 8.1) and a high GDP per capita (GDP = 9.3), lead by a considerable share of renewable energy (RNEC = 3.3). This profile suggests relatively stable economies, with moderate energy transition and solid economic performance. Cluster 2 presents similar values for EPC (8.5) and GDP (9.4), but a lower level of CO2 emissions (2.0), indicating a more efficient and sustainability-oriented energy structure. High urbanization and balanced energy consumption suggest integrated economies well connected to the European energy market. Cluster 3, on the other hand, is marked by the lowest values of EPC (7.7) and GDP (7.8), as well as the lowest level of renewable energy (RNEC = 2.5). This profile reflects economies in transition, with lower energy and digital investments and a more modest capacity for decarbonization. Cluster 4 is distinguished by the highest level of GDP per capita (GDP = 10.3) and energy efficiency (EPC = 8.8), together with a relatively low level of emissions (CO2 = 2.1). This combination suggests highly performing, resilient economies deeply engaged in the advanced energy transition. Overall, the heatmap confirms the existence of clear development patterns, in which economic performance correlates with energy efficiency and the advance of the green transition, while less developed economies exhibit a slower pace of structural transformations.
Table 4 shows how the countries are grouped into the four clusters identified by the Fuzzy C-Means algorithm, together with the average membership degree that reflects the internal coherence of each group. Cluster 3 (Moldova) stands out with an exceptionally high membership value (≈0.99), indicating a very compact and internally consistent profile. This result confirms that Moldova behaves as an outlier within the regional energy–economic system: it combines the lowest levels of energy consumption and GDP per capita with structural vulnerabilities and limited integration into European energy frameworks, which position it at a significant distance from the rest of the countries included in the analysis.
Clusters 1 and 2 gather economies that share similar structural features but are still undergoing transitions, reflected by moderate membership values (0.69–0.81). According to fuzzy classification theory, countries with membership values below 0.7 should be interpreted as hybrid economies—states whose energy and economic structures simultaneously display elements belonging to several cluster profiles. This explains why the countries in Cluster 2, for instance, combine industrial legacies with ongoing modernization, resulting in mixed or evolving structural configurations.
Cluster 4, consisting of Estonia, Slovenia and Switzerland, groups high-performing economies but with the lowest average membership ( ≈ 0.65). This suggests the presence of mixed development models: although all three countries share strong digital infrastructure, high economic performance and overall energy efficiency, their structural trajectories differ considerably. Estonia’s rapid progress is driven primarily by digitalization and technological adoption [67,68,69], Slovenia exhibits a more balanced evolution influenced by its industrial base and service sector [70,71], while Switzerland represents a mature, innovation-driven economy with long-standing efficiency and stability [72,73,74]. These differences naturally reduce the compactness of the cluster, even though the countries converge on several key dimensions.
Overall, Table 4 highlights that fuzzy clustering not only identifies the dominant structural patterns across European economies, but also uncovers hybrid configurations and outlier behaviors—elements that are often masked by traditional, hard clustering techniques.
Figure 7 shows the performance of the Random Forest model in classifying countries into the four previously defined fuzzy clusters. The main diagonal concentrates most of the observations, indicating a very good accuracy of the model. Cluster 1 is correctly classified in 13 cases, with no false positives in the other clusters, which shows a clear delimitation of this group. Cluster 2 presents two classification errors in Cluster 1 and three in Cluster 4, but with 24 correct classifications, maintaining a high performance. Cluster 3 is identified almost perfectly, with 28 correct classifications and only one observation incorrectly interpreted as cluster 2. Cluster 4 is correctly classified in 27 cases, with only three observations incorrectly assigned to cluster 2. Overall, the matrix highlights that Random Forest reproduces the structure of fuzzy clusters very well, with minimal errors and a clear distribution of observations on the diagonal. The limited deviation indicates that the model adequately captures the identified energy-economic typologies and can be considered a robust method for validating fuzzy clustering.
Figure 8 illustrates the performance of the XGBoost model in reproducing the four fuzzy clusters identified based on the average of the energy-economic indicators. The confusion matrix shows that the model performs very well, maintaining a dominant diagonal distribution, which highlights the consistent fit between the actual and predicted clusters. Cluster 1 is perfectly identified: all 13 observations are correctly classified, which shows the high separability of this group from the others. Cluster 2 shows three misclassifications in Cluster 1, but 23 observations are correctly assigned, maintaining a solid performance. Cluster 3 is almost perfectly identified, with 28 correct classifications and no misassignments in clusters 1 or 4. Cluster 4 is correctly classified in 26 cases, with three observations assigned to cluster 2 and one to cluster 3. This is the only cluster where XGBoost makes additional errors compared to Random Forest, suggesting a slight structural overlap of variables between clusters 2–4. Overall, XGBoost reproduces the structure of fuzzy clusters very well, with a performance comparable to Random Forest, although with slightly more errors for cluster 4. However, the overall accuracy remains very high, robustly validating the fuzzy clustering and the consistency of the identified groups.
Table 5 presents the performances of the Random Forest and XGBoost models in reproducing the four fuzzy clusters identified in the energy and economic analysis. Both models achieve high scores, confirming the stability and coherence of the cluster structure. Random Forest achieves the best accuracy (0.94), as well as the highest precision and recall values, indicating a superior ability to distinguish between clusters even in overlapping areas. XGBoost offers very close performances, with values of 0.92–0.93, suggesting that the cluster structure is robust and easy to reproduce regardless of the ML algorithm used. Overall, the results show that the machine learning models successfully validate the fuzzy classification, highlighting the consistency of the energy-economic patterns in the region.
Figure 9 highlights the contribution of each indicator to the classification of countries into the four fuzzy clusters, based on the Random Forest model. It follows that CO2 emissions are the strongest predictor, suggesting that differences between countries are significantly marked by carbon intensity and energy structure. The next factor in importance is UPA (urban population accessing basic services), which indicates that the level of urbanization and access to utilities considerably influences the energy-economic profile of countries. EPC and RNEC also have relatively high weights, which shows that energy efficiency and renewable energy production are essential in delimiting the clusters. In contrast, indicators such as GCS, IUI and GDPEU have lower importance, suggesting that differences between countries in these dimensions are more subtle or less relevant in structuring the fuzzy groupings. Overall, the analysis highlights that energy transition and emissions intensity are the elements that most strongly differentiate countries in the region, reflecting divergences in the pace of energy modernization and consumption patterns.

5. Discussion

5.1. Reliability of the Long-Term Analysis (2000–2024)

The covered timespan (2000–2024) represents a period marked by major structural changes in European economies: EU enlargement, accelerated digitalization, policy reforms and external shocks such as the global financial crisis of 2008–2010. These events influenced energy consumption, investment patterns and economic performance. The applied machine-learning framework is appropriate for this context, since it relaxes the assumptions of linearity and parameter stability that characterize econometric models, allowing for nonlinear dynamics and structural changes in the data-generation process [75].
Fuzzy clustering allows countries to gradually change their degree of membership among clusters, capturing transitional phases than regime shifts.
The normalized indicators, panel-based heatmaps and time-averaged values reduce the influence of crisis-related fluctuations, focusing mainly on persistent patterns. The post-2010 shifts in cluster memberships, especially the migration to more advanced clusters are in line with policy development at the European level. Even if short-term shocks are present in data, the applied methods capture long-run structural dynamics through clustering rather than short-term disturbances. These findings are consistent with previous studies documenting heterogeneous and uneven energy transition paths across European economies, particularly between Western and Central–Eastern regions.

5.2. Rationale for Indicator Selection

The selection of indicators is based on theoretical relevance and consistency with previous literature on energy transition and economic development. Renewable energy consumption, energy efficiency, CO2 emissions and electricity consumption reflect energy systems and environmental pressure. GDP per capita is a proxy for economic development, while gross capital formation reflects investment and modernization capacity. Urbanization reflects demographic and infrastructure effects on energy demand. Internet use is a proxy for digitalization, nowadays a main driver of smart energy systems.

5.3. Complexity and Added-Value of the Proposed Framework

The proposed framework combines several complementary components. Fuzzy clustering captures country heterogeneity and hybrid development paths that cannot be obtained by hard clustering. PCA reduces dimensionality and preserves the dominant variance structure. The supervised machine-learning methods XGBoost and Random Forest are validation tools which test the consistency of the fuzzy clusters.
This framework is also informative. It addresses classification, validation and interpretation. Compared to existing studies that rely either on clustering or on predictive models alone, the proposed framework integrates classification, validation, and interpretation within a unified analytical pipeline. This integration enhances the robustness and credibility of the identified typologies, particularly in contexts characterized by gradual transitions and mixed structural configurations.

6. Conclusions and Policy Recommendations

Our findings show that Europe’s energy and economic dynamics remain deeply heterogeneous, even in the context of almost a quarter of a century marked by convergence, accelerated digitalization and decarbonization pressures. Fuzzy analysis allowed the capture of intermediate degrees of development and structural transitions, avoiding rigid classifications that would have masked fine differences between economies. The four clusters identified describe a coherent picture of the region: advanced economies, with a consolidated energy profile; integrated economies, in rapid transition; economies with moderate rates of transformation; and, finally, economies still at a structural distance from the European average. Validation carried out using Random Forest and XGBoost confirms the robustness of these typologies, with both models reproducing the obtained groupings with high accuracy and highlighting the essential role of emissions, energy efficiency and urbanization in distinguishing these profiles.
Taken together, the results suggest that the European energy transition is not only a technological process, but a systemic phenomenon, in which the pace of modernization depends on the economic structure, investment capacity, the level of digitalization and the way urbanized societies adapt their consumption. Economies located in clusters with modest performance are not necessarily “left behind”, but are at a different stage of transformation, influenced by institutional, technological and demographic constraints. From this perspective, public policies should go beyond uniform logic and adopt differentiated interventions: intensifying investments in renewable energy and efficiency in transition countries; accelerating digitalization in economies that have already stabilized their energy structure; strengthening infrastructure and interconnections in more vulnerable economies; and maintaining the pace of innovation in advanced countries, which can act as regional benchmarks.
With respect to the research questions posed in the introduction, the results indicate that the European energy-economic structure follows a pattern of partial convergence. Even if several Central and European countries exhibit gradual convergence toward more advanced energy profiles, some structural gaps exist between performing economies and structurally constrained ones. At the extremes the divergence is present.
The fuzzy clustering and machine learning validation prove that the main drivers of these dynamics are CO2 emissions intensity, energy efficiency and urbanization. Renewable energy consumption supports convergence, but it is not among the main drivers.
At the same time, the study has some limitations inherent to the quantitative approach. The indicators used capture only part of the complexity of the energy-economy system; factors such as the quality of governance, sectoral structure or political volatility can significantly influence the analyzed trajectories. In addition, fuzzy classification captures similarities and differences, but does not allow the establishment of causal relationships, and the transformation of fuzzy membership into rigid labels for validation by machine learning inevitably reduces the nuances present in the initial structure.
Future research directions can deepen these aspects through dynamic models that explicitly track migration between clusters, by integrating additional institutional or technological indicators, or by using econometric models capable of capturing the causality between energy transition, digitalization and economic development. Combining fuzzy techniques with agent-based modeling or simulation tools could provide additional insight into how public policies influence, over time, the evolution of each economy.
Overall, the study provides a comprehensive framework for understanding European energy convergence and highlights that differences between economies are not just deviations from an ideal path, but the expression of distinct paces of adaptation, governed by structural, institutional and socio-technological factors. These results can support policymakers in formulating more context-sensitive policies and, at the same time, can form the foundation for future research that deepens the internal mechanisms of the green transition.

Author Contributions

Conceptualization, I.N. and I.G.; methodology, I.N. and I.G.; software, I.N.; validation, I.N., I.G. and J.K.; formal analysis, I.N.; investigation, I.N. and I.G.; resources, I.N. and I.G.; data curation, J.K.; writing—original draft preparation, I.N.; writing—review and editing, I.N., I.G. and J.K.; visualization, I.N., I.G. and J.K.; supervision, I.N.; project administration, I.N. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the EU’s NextGenerationEU instrument through the National Recovery and Resilience Plan of Romania—Pillar III-C9-I8, managed by the Ministry of Research, Innovation and Digitization, within the project entitled “Place-based Economic Policy in EU’s Periphery—fundamental research in collaborative development and local resilience. Projections for Romania and Moldova (PEPER)”, contract No. 760045/23.05.2023, code CF 275/30.11.2022.

Data Availability Statement

Data are available upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
FCMFuzzy C-Means
MLMachine Learning
RFRandom Forest
XGBoostExtreme Gradient Boosting
PCAPrincipal Component Analysis
FPCFuzzy Partition Coefficient
MPCModified Partition Coefficient
GDPGross Domestic Product
CO2Carbon Dioxide Emissions
RNECRenewable Energy Consumption
GDPEUGDP per unit of Energy Use (Energy Productivity)
EPCElectric Power Consumption
IUIIndividuals using the internet
GCSGross Capital Formation
UPAUrban population
EUEuropean Union
CEECentral and Eastern Europe

Appendix A

FCM estimates cluster centers by minimizing the following objective function describe in equation [52] (A1):
J m U ,   c 1 ,   … ,   c k = ∑ i = 1 n ∑ j = 1 k u i j m | | x i − c j | | 2
where in relation (A1), x i represents the vector of variables for country i , c j is the center of cluster j , u i j is the degree of membership of country i in cluster j , with 0 ≤ u i j ≤ 1 , m represents the fuzziness exponent (often set to 2), and k is the number of clusters.
Minimizing J m determines the optimal position of the centers and the distribution of memberships.
The algorithm alternates between two updates:
(i)
Updating cluster centers, according to Equation (A2):
c j = ∑ i = 1 n u i j m x i ∑ i = 1 n u i j m
(ii)
Updating the membership matrix, according to relation (A3):
u i j = 1 ∑ h = 1 k x i − c j x i − c h 2 m − 1
These two steps are repeated until convergence (standard criterion: successive differences < 10 − 5 ) [76]. The degree of membership u i j is not a probability, but an indicator of the coherence of each country with the cluster profile. The membership matrix is used to interpret the quality of clustering. The interpretation of the membership values does not follow a universally fixed threshold in the FCM literature. Instead, researchers typically adopt analytical cut-offs to distinguish between strong, moderate, and weak membership, based on the general principles of fuzzy set theory introduced by Zadeh [12] and the FCM formalization proposed by Bezdek [13]. In this study, we follow a common interpretative practice in applied fuzzy clustering: values above 0.8 are treated as strong affinity to the cluster prototype, values between 0.5 and 0.8 indicate transitional or hybrid profiles, while values below 0.5 reflect weak similarity or ambiguous positioning. These thresholds do not represent theoretical constraints, but analytical conventions that support the economic interpretation of cluster coherence.
We will consider if u i j ≥ 0.8 , then the economic and energy structure is similar to the cluster core, if 0.5 < u i j < 0.8 then we have a hybrid economy, in transition, but with predominant affinity, and if u i j ≤ 0.5 then the positioning may be ambiguous, or a dual structure.

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Figure 1. Heatmap of key indicators across European Economies (normalized 0–1).
Figure 1. Heatmap of key indicators across European Economies (normalized 0–1).
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Figure 2. Fuzzy partition coefficient.
Figure 2. Fuzzy partition coefficient.
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Figure 3. Modified partition coefficient.
Figure 3. Modified partition coefficient.
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Figure 4. Fuzzy cluster evolution in the European Energy-Economy System.
Figure 4. Fuzzy cluster evolution in the European Energy-Economy System.
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Figure 5. PCA Biplot of country means with fuzzy cluster assignments.
Figure 5. PCA Biplot of country means with fuzzy cluster assignments.
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Figure 6. Cluster profiles based on mean indicator values.
Figure 6. Cluster profiles based on mean indicator values.
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Figure 7. Confusion matrix—Random Forest.
Figure 7. Confusion matrix—Random Forest.
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Figure 8. Confusion matrix—XGBoost.
Figure 8. Confusion matrix—XGBoost.
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Figure 9. Feature importance—Random Forest Classifier.
Figure 9. Feature importance—Random Forest Classifier.
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Table 1. Grouping of the selected European economies included in the analysis.
Table 1. Grouping of the selected European economies included in the analysis.
CategoryCountriesDescription
EU Member States—Central and Eastern Europe (CEE)Bulgaria, Croatia, Czechia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovak Republic, SloveniaRepresent economies characterized by structural transformation, EU energy policy alignment, convergence processes, and heterogeneous trajectories of digitalization and efficiency improvements [40,41,42,43].
Advanced Non-EU High-PerformerSwitzerlandProvides an upper-benchmark reference for energy efficiency, technological sophistication, innovation capacity, and smart transition maturity [44,45,46].
EU Neighborhood/Emerging
Energy System		MoldovaRepresents a structurally constrained economy with lower energy efficiency, higher vulnerability to external shocks, and limited integration into EU energy frameworks. Offers contrast and highlights divergence patterns [47].
Table 2. Description and theoretical justification of the selected indicators.
Table 2. Description and theoretical justification of the selected indicators.
CodeIndicatorDescriptionConceptual Relevance
RNECRenewable energy consumption (% of total final energy consumption)Indicates how much of a country’s energy mix is renewableHigher values = stronger renewable adoption
GDPEUGDP per unit of energy use (constant 2021 PPP $ per kg of oil equivalent)Measures efficiency of energy use in generating economic outputHigher values = greater efficiency
CO2Carbon dioxide (CO2) emissions excluding LULUCF per capita (t CO2e/capita)Environmental impact of energy consumptionHigher values = higher environmental pressure
EPCElectric power consumption (kWh per capita)Overall energy demand per capitaHigher values = more energy-intensive economies
IUIIndividuals using the Internet (% of population)Digitalization levelHigher values = more advanced digital capabilities
GCSGross capital formation (% of GDP)Investment capacityHigher values = stronger capital accumulation
UPAUrban population (% of total)Degree of urbanizationHigher values = more urbanized society
GDPGDP per capita (constant 2015 US$)Economic developmentHigher values = richer economies
Table 3. Summary Statistics.
Table 3. Summary Statistics.
RNECGDPEUCO2EPCIUIGCSUPAGDP
Mean2.852.441.788.373.913.214.129.45
Median2.922.421.778.384.213.204.209.46
Maximum3.783.482.859.014.573.774.3411.41
Minimum1.301.690.857.530.242.563.747.20
Std. dev.0.540.360.420.380.740.170.160.78
Skewness−0.670.440.33−0.26−2.040.30−0.720.15
Kurtosis2.863.112.662.197.413.492.624.49
Table 4. Fuzzy cluster composition and dominant membership levels.
Table 4. Fuzzy cluster composition and dominant membership levels.
ClusterCountriesMembership
1Croatia, Latvia, Lithuania, Romania0.81
2Bulgaria, Czechia, Hungary, Poland,
Slovak Republic		0.69
3Moldova0.99
4Estonia, Slovenia, Switzerland0.65
Table 5. Performance metrics for the ML models used to validate the fuzzy clusters.
Table 5. Performance metrics for the ML models used to validate the fuzzy clusters.
MLAccuracyPrecisionRecallF1-Score
Random Forest0.940.930.950.94
XGBoost0.920.910.930.91
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Nica, I.; Georgescu, I.; Kinnunen, J. A Fuzzy-Machine Learning Framework for Energy Efficiency Optimization and Smart Transition Analysis in European Economies. Electronics 2026, 15, 276. https://doi.org/10.3390/electronics15020276

AMA Style

Nica I, Georgescu I, Kinnunen J. A Fuzzy-Machine Learning Framework for Energy Efficiency Optimization and Smart Transition Analysis in European Economies. Electronics. 2026; 15(2):276. https://doi.org/10.3390/electronics15020276

Chicago/Turabian Style

Nica, Ionuț, Irina Georgescu, and Jani Kinnunen. 2026. "A Fuzzy-Machine Learning Framework for Energy Efficiency Optimization and Smart Transition Analysis in European Economies" Electronics 15, no. 2: 276. https://doi.org/10.3390/electronics15020276

APA Style

Nica, I., Georgescu, I., & Kinnunen, J. (2026). A Fuzzy-Machine Learning Framework for Energy Efficiency Optimization and Smart Transition Analysis in European Economies. Electronics, 15(2), 276. https://doi.org/10.3390/electronics15020276

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