Long-Term Building Renovation Strategies—F-TOPSIS Analysis of Solutions Applied in the Chosen European Union Countries

Abstract

The article analyzes long-term renovation strategies in EU member countries using the F-TOPSIS method, focusing on chosen criteria such as CO₂ emission reductions, renovation rates, energy savings, investment requirements, and overall strategy quality. High-performing countries, such as Finland and Spain, demonstrate the importance of clear targets, robust planning, and substantial financial commitments. In contrast, several countries show gaps in strategic detail or ambition, highlighting challenges in achieving EU climate neutrality goals. The methodology underscores the effectiveness of multi-criteria decision-making tools in assessing complex renovation strategies. The findings emphasize the need for harmonized metrics and innovative approaches, such as digital tools like building renovation passports.

1. Introduction

As part of the Paris Agreement under the United Nations Framework Convention on Climate Change at the 21st Conference of the Parties, in 2015, it was agreed to limit the global temperature increase to 1.5 °C above pre-industrial levels by 2050. Achieving this goal necessitates a reduction in energy demand wherever feasible, including the construction sector, which accounts for approximately 28% of total energy-related CO₂ emissions according to the report of the International Energy Agency (IEA 2019). Research presented in [1] emphasizes the critical role of reducing carbon emissions through fuel substitution in building decarbonization.

One of the key elements in achieving the European Union (EU)’s decarbonization objectives is the energy renovation of buildings [2]. Recognizing the importance of this challenge, the European Commission has implemented numerous initiatives to enhance the energy performance of buildings within EU member countries. According to the Energy Performance of Buildings Directive (EPBD), all EU member countries have established independent certification systems for energy performance, supported by independent mechanisms for inspection and verification. However, current practices and tools for assessing and certifying energy performance across the EU face several challenges. The revised Directive (EU) 2024/1275 of the European Parliament and of the Council of 24 April 2024 on the energy performance of buildings (recast) (text with relevance to the EEA) [3] holds significant potential for advancing energy efficiency in the EU building sector, including measures aimed at accelerating the renovation rate to make buildings more energy efficient.

One solution supported by the European Commission as part of climate action is the introduction of so-called building renovation passports (BRPs). While there is no universally accepted definition of a BRP, its purpose aligns with initiatives in member countries. A BRP is generally seen as a tool designed to encourage cost-effective renovations through a “tailored roadmap for the deep renovation of a specific building in a maximum number of steps that will significantly improve its energy performance” [3]. According to [4,5], a BRP can also be identified as a certification that documents building characteristics and technological data through various records (professional technical reports, official declarations, system installation manuals, etc.). BRPs outline the scope of actions, sequence, and estimated costs for improvements toward more energy-efficient buildings, while also setting long-term ambitions (e.g., goals for 2050) within short- and medium-term renovation strategies.

Given emerging challenges, the literature increasingly addresses both decarbonization and energy efficiency improvements in EU buildings. Various renovation models can be found in the literature [6,7]. One project promoting the concept of building renovation is ALDREN (Alliance for Deep Renovation in Buildings Implementing the European Common Voluntary Certification Scheme). The authors describe it as a European Common Voluntary Certification Scheme aimed at encouraging deep renovations toward the nearly-zero-energy buildings (NZEB) standard for existing buildings. This protocol is currently applied to 15 demonstration buildings across five European countries: France, Italy, Spain, Slovakia, and the United Kingdom [8].

Analyses of construction materials, including recycled insulation materials, are also explored in the literature to assess their suitability and effectiveness in enhancing building energy standards [9]. Studies in [10] reveal that decarbonization scenarios in EU countries remain insufficient for achieving significant reductions in carbon emissions. Research in [11] evaluates the impact of buildings on global warming throughout their lifecycle. Advanced modeling studies in [12] leverage the PRIMES-BuiMo model to develop cutting-edge innovative pathways and strategies for decarbonizing the EU building sector, with case studies in Sweden and Greece.

The widespread implementation of comprehensive energy renovations is hampered by a number of EU barriers [8,13]. The basic ones include:

• Limited number of technological solutions that work in the existing environment;
• Materials and labor costs are not affordable in all cases;
• Limited knowledge of construction workers in the field of comprehensive renovation of buildings;
• Difficulties in adapting the supply chain;
• Owners are often not ready to undertake renovation in terms of knowledge about the building’s condition and finances;
• Unified energy requirements and renovation definition;
• Costs of renovations;
• Sources of financing;
• Energy prices do not significantly burden the budget, so there is no impulse to improve the current situation.

In [14], a review of current financing practices for energy renovations was conducted, examining several innovative instruments for their potential to address longstanding barriers to investments in energy efficiency.

The improvement of energy efficiency, as well as the achievement of a bigger percentage of energy-efficient building stock in EU member countries, is inseparable from the maintenance strategies, which have to be planned in a proper way. Many scientists have discussed the broad topic of building maintenance, focusing on, for example, methods of maintenance prioritization [15], improvement actions in building maintenance management [16], the provision of guidelines on maintenance decision making [17], procedures and determination of factors affecting building maintenance success [18], and the implementation of extensive models for use in building maintenance processes like the multi-criteria decision-making model developed in [19], as well as a maintenance cost estimation model assessment for buildings [20]. In the paper [21], the authors emphasize the need for sustainable maintenance strategies due to the serious maintenance issues faced by heritage buildings, including, for instance, infrequent maintenance, repairs, or funding shortages.

The EU, recognizing that energy-efficient building stock is critical to achieving decarbonization goals and improving quality of life, has established a legal framework consisting of the Energy Performance of Buildings Directive and the Energy Efficiency Directive. Since 2014, all EU member countries are required to develop a long-term renovation strategy every three years. These strategies aim to support the transformation of national building stocks into highly energy-efficient and emission-free assets by 2050, contributing to the goals outlined in EU member countries’ national energy and climate plans [22].

The evaluation of EU Member States’ strategies in implementing the requirements of these directives, including the planning and execution of long-term renovation strategies, has been addressed in studies such as [23,24,25,26,27]. Despite the emphasis placed on the importance of developing and implementing of the long-term renovation strategies, the literature lacks precise definitions, indicators, and conceptual frameworks that would facilitate the formulation and practical execution of these strategies by EU countries. General guidelines indicate that renovation plans must include at least: an overview of the national building stock for different building types; a roadmap with nationally established targets for 2030, 2040, and 2050 (including a range of progress indicators); an overview of planned policies and measures; and an outline of the investment needs and financing sources for their implementation.

By 31 December 2025, all EU Member States are required to prepare a draft of a national building renovation plan, which will be evaluated by the European Commission. The final plan must be submitted by 31 December 2026. This creates an urgent need for the proper development of these plans to ensure compliance with EU regulations and the achievement of long-term renovation objectives.

This study examines the long-term renovation strategies of selected EU countries using the F-TOPSIS method for evaluation. The assessment criteria applied in this study aim to provide a more detailed framework for the general EU guidelines on renovation plans. The findings are intended to assist EU Member States in improving the structure and presentation of their renovation strategies while identifying potential gaps that may hinder the achievement of long-term goals. The results will highlight key elements and indicators presented in national plans that determine their overall quality and effectiveness.

2. Building Renovation Strategies in EU Countries

2.1. Current Status of Buildings in EU Member Countries

The energy performance of many buildings in the EU is low, as these structures were constructed before the introduction of modern energy requirements. Simultaneously, the European Commission estimates that by 2050, approximately 85–95% of existing buildings will still be in use. Only 11% of the current building stock in the EU undergoes either full or partial renovations annually. These renovations typically focus on reducing energy consumption, often without upgrading building technical systems or installing renewable energy sources. The weighted annual rate of energy renovations is low, standing at just 1%.

Due to the insufficient pace of building stock renovations in the EU, the European Commission adopted the “Renovation Wave for Europe” initiative in October 2020. Its primary goal is to double the annual energy renovation rate by 2030 and support comprehensive renovations [27,28]. The plan outlines ambitious targets alongside significant challenges and barriers to be addressed for the European building stock. Figure 1 shows the number of buildings that were being renovated in each EU member country in 2016, based on data sourced from [29].

The level of energy demand reduction, in alignment with the first principle of energy efficiency, can be defined using various approaches. One possible method involves applying the commonly accepted definition of “deep renovation”, achieving at least a 60% reduction in energy consumption. This definition was utilized in the EU’s flagship study titled “Comprehensive study of building energy renovation activities and uptake of nearly zero-energy buildings in the EU”, published in 2019 [28]. An alternative approach involves modeling outcomes under different decarbonization scenarios. Example thermal modernization scenarios are presented in Section 2.2 of this paper, based on the renovation strategy for Poland, published in 2022 [30].

2.2. Example Scenarios: Poland

2.2.1. Scenario 1: Rapid and Deep Thermal Modernization

This scenario assumes widespread, deep thermal modernization of the building stock, starting with structures characterized by the lowest energy efficiency. It is the most ambitious and economically advantageous plan. Under this scenario, the average annual renovation rate is approximately 3%. A rapid reduction in the number of buildings with the lowest energy efficiency is observed, as they are prioritized for thermal modernization.

The rapid and deep thermal modernization scenario achieves its target outcomes with the fewest thermal modernization initiatives among all considered scenarios, avoiding the need for repeated investments associated with step-by-step modernization. This translates into a lower overall renovation rate, which remains below 3% until the second half of the 2040s. However, this scenario relies heavily on complex and capital-intensive investments. Its implementation may be challenging, as owners of poorly performing buildings often lack the financial resources necessary to undertake deep renovations.

Additionally, this scenario may delay the mobilization of financial resources from other building owners, including those already demonstrating high awareness and willingness to invest in modernization, provided they receive adequate support.

The impact of implementing this thermal modernization scenario on the energy efficiency distribution of buildings in Poland is illustrated in Figure 2.

2.2.2. Scenario 2: Step-by-Step Thermal Modernization

The second scenario envisions widespread thermal modernization of the building stock, wherein buildings in the poorest condition are upgraded gradually until they achieve the highest energy efficiency categories. Each stage of modernization addresses only a portion of the full scope of the thermal modernization work, allowing for a phased approach to achieving the target energy efficiency level. This strategy prevents a sudden surge in investment efforts and aggregate demand for the goods and services essential for these upgrades.

The process is planned from the outset with the final outcome in mind, ensuring consistency between the stages and avoiding duplication or counterproductive actions in subsequent phases. However, the ultimate outcome of this scenario is less effective than that of rapid and deep thermal modernization, owing to the lower economic and technical efficiency of actions carried out in multiple stages. Although the share of buildings with the lowest energy efficiency decreases more quickly than in the rapid deep modernization scenario, buildings with low energy performance indicators do not emerge simultaneously.

In the step-by-step thermal modernization scenario, the average annual renovation rate is high, approximately 4%. This rate results from the need to perform several investments between 2021 and 2050 for most buildings under this phased approach. The pace of thermal modernization accelerates rapidly, reaching very high levels toward the end of the analyzed period. While this scenario is easier to implement, it is less economically efficient. A significant limitation is the scale of required investments, as the proposed plan would necessitate renovation rates of 5–6% annually.

The impact of implementing this step-by-step thermal modernization scenario on the energy efficiency distribution of buildings in Poland is presented in Figure 3.

2.2.3. Scenario 3: Recommended Scenario

The recommended scenario combines the advantages of the two previous scenarios. It involves the rapid implementation of an initial stage of thermal modernization for buildings with the poorest energy efficiency, coupled with the promotion of deep thermal modernization in the near future. This is followed by the widespread adoption of high renovation standards across the entire market.

The final outcome of this scenario is comparable to that achieved under the rapid and deep thermal modernization scenario. This is due to the early initiation of gradually scaling investments in deep thermal modernization and the reduction in the number of stages required for step-by-step modernization. These measures enhance the economic and technical efficiency of the analyzed actions compared to the step-by-step modernization scenario. In this scenario, the average annual rate of thermal modernization is approximately 3.8%.

The impact of implementing this recommended scenario on the energy efficiency distribution of buildings in Poland is presented on Figure 4.

2.3. Assumptions of Building Renovation Strategies in EU Countries

Building renovations remain insufficient to achieve carbon neutrality by 2050 [31,32]. At the same time, investments in buildings can act as a catalyst for the construction sector and the broader economy. Renovation projects are labor intensive, creating jobs and driving investments often based on local supply chains. They generate demand for highly energy-efficient equipment, enhance climate resilience, and increase property value in the long term.

EU member countries have adopted varied approaches in their long-term renovation strategies, focusing on reducing CO₂ emissions and comprehensive building renovation.

Based on the European Commission’s guidelines on renovation plans, five criteria, described below, were selected for comparative analysis. The criteria selected relate to the basic measurable indicators to be achieved that have been declared by the countries analyzed. As the strategies are characterized by varying degrees of precision, the last criterion evaluates the completeness and quality of the strategies, focusing on the level of detail provided and the coherence of the plans. Criteria weights were not included in the analysis. Their determination would require further thorough research.

Criterion 1: CO₂ Emission Reduction

EU member countries continue to undervalue the construction sector’s role in achieving Europe’s climate neutrality. Reducing energy consumption and CO₂ emissions are critical aspects of building renovation. Analyses indicates that EU member countries should aim for a 100% reduction in CO₂ emissions by 2050 [1].

Criterion 2: Annual Renovation Rate

The goal of the Renovation Wave initiative is to at least double renovation rates from approximately 1% annually to 2% over the next decade and to ensure that renovations lead to higher energy efficiency and resource savings. Analysis by BPIE in the report “On the Road to a Climate-Neutral Europe” highlights the need to increase renovation rates to about 3% annually. Expected benefits include improved quality of life, reduced energy poverty, lower greenhouse gas emissions, support for digitization, improved reuse and recycling of materials, and additional jobs in the construction sector. Furthermore, all renovations should adhere to the nearly-zero-energy building principle, achieving the highest efficiency level for the building type while meeting remaining energy needs with renewable sources.

Criterion 3: Expected Energy Savings

Advancing energy efficiency is crucial for transitioning away from fossil fuels. In alignment with the IEA’s net-zero emissions scenario for the energy sector by 2050, accelerated energy efficiency improvements could account for over 70% of projected reductions in oil demand and 50% of reductions in gas demand by 2030. Reduced natural gas demand, largely achieved through measures such as building insulation and heating electrification, would exceed Europe’s total natural gas consumption in 2024.

Criterion 4: Total Investment Required

Implementing planned renovations requires substantial financial resources. Therefore, one criterion is the declaration of required funding in strategies. Higher investment levels typically correlate with more ambitious renovation plans.

Criterion 5: Overall Assessment

This criterion evaluates the completeness and quality of the strategies, focusing on the level of detail provided and the coherence of the plans.

To compare the long-term renovation strategies of EU member countries, the necessary data for selected EU member countries have been collected. The primary sources of information were the national renovation plans prepared in accordance with Article 2a of Directive 2010/31/EU of the European Parliament [33] and of the Council of 19 May 2010 on the energy performance of buildings, as amended by Directive (EU) 2018/844 of the European Parliament and of the Council of 30 May 2018 [34], uploaded on the official website of the European Commission [35]. However, the general nature of these guidelines results in varying levels of detail across the plans, making it difficult to extract specific indicators for planned targets in particular years and the procedures to achieve them.

Furthermore, some countries, such as Belgium, do not have a single national renovation strategy but rather separate strategies for different regions. The data were supplemented with information gathered from the analysis of European Commission legal acts and national regulations, including documents such as the Commission Staff Working Document [27].

For this study, countries were selected based on the availability of sufficient data to evaluate the criteria and the presence of a unified renovation strategy applicable at the national level. This ensured consistency in the comparative analysis, which allowed for a more structured evaluation of the renovation plans in line with EU objectives.

Key data supporting the evaluation and comparison of the long-term renovation strategies of EU member countries are summarized in

Table 1. Comparison of the long-term renovation strategies of EU member countries.

Country	Baseline Year	Reduction in CO2 Emissions	Renovation Assumptions	Total Investment Required	Expected Energy Savings	Overall Rating
Austria	2020	80%	Increase renovation rate from 1.5% to 3%	EUR 159 billion	68% by 2050 from 2015	good
Bulgaria	2020	None	Renovate 127,597,192 m2 of existing building area by 2050	EUR 67.5 billion	Not provided	weak
Croatia	2020	80%	4% annual rate until 2050; renovate 100% of existing buildings by 2050	EUR 51 billion	Not provided	good
Czech Republic	2020	40%	Increase annual renovation rate: 1.4% for single-family homes, 0.79% for multi-family residential, 2% for commercial and public buildings	EUR 33 billion	24% by 2050 on 2020 levels	good
Estonia	2020	90%	Renovate all existing buildings to nearly-zero-energy standards by 2050	EUR 21.6 billion	60% by 2050	sufficient
Finland	2020	92%	Detailed roadmap to 2050 with comprehensive milestones and indicators	EUR 24 billion	49% reduction in heating energy consumption	excellent
Germany	1990	100%	Increase annual renovation rates by 2030 to over 2% for single-family and twin buildings (current 1.3%) and over 2% for multi-family buildings (current 1.5%)	Not provided	55% reduction by 2030 compared to 2008	good
Greece	2015	100%	Double annual renovation rate to 1.6% by 2050 compared to 2015	Not provided	Not provided	weak
Lithuania	2020	100%	Increase renovation rates to 17% by 2030, 43% by 2040, 74% by 2050	EUR 53 billion	Not provided	weak
Poland	2020	None	Increase annual renovation rate to: 3.6% by 2030, 4.1% by 2040, 3.7% by 2050	EUR 36 billion	Not provided	sufficient
The Netherlands	1990	95%	Gradual thermal modernization of 1,500,000 buildings by 2030	Not provided	Not provided	excellent
Spain	2020	98.8%	Renovate 6.42% of homes by 2030; excellent strategy with detailed energy savings and benefits	EUR 143 billion (residential sector only)	37%	excellent

. The table provides a foundational reference for assessing and benchmarking these strategies.

3. Evaluation of Strategies Using F-TOPSIS Methods

3.1. TOPSIS and F-TOPSIS Methods

The fuzzy extension of the TOPSIS method was selected for the analysis. The TOPSIS method (technique for order preference by similarity to ideal solution) belongs to the class of multi-criteria methods utilizing reference functions, which are derived from taxonomic approaches. These methods are primarily designed for ranking purposes and often use patterns or benchmarks during their implementation.

TOPSIS is one of the most popular methods for solving discrete multi-criteria decision-making problems [36]. It is used to rank (or sort) decision alternatives based on their similarity to an ideal solution, which represents the most desirable option. This is achieved by minimizing the distance to the ideal solution (the reference ideal solution) while maximizing the distance from the anti-ideal solution (the reference anti-ideal solution). Distances between each alternative and the ideal and anti-ideal solutions are calculated, and these distances are used to determine a measure value.

The selection of this method was primarily driven by its effectiveness in solving problems similar to the one analyzed in this research. Additionally, it is a highly efficient technique with broad applicability across various decision-making contexts. As highlighted by Shih et al. [37], the TOPSIS method offers several advantages: it effectively represents rational human decision making, its scalar value simultaneously accounts for both the best and worst alternatives, it features a straightforward computational process, and the number of attributes does not affect the number of steps in the TOPSIS procedure. These characteristics make TOPSIS one of the most widely applied multi-criteria decision-making methods in academic research [38].

However, the traditional TOPSIS method has certain limitations, such as its reliance on Euclidean distance, which does not account for attribute correlation. This can lead to information redundancy and potentially influence the final results. Some of these drawbacks can be mitigated by using its fuzzy extension, which enhances the method’s ability to handle uncertainty and imprecise data, making it particularly suitable for evaluating complex renovation strategies.

The algorithm for the TOPSIS method was first introduced by Hwang and Yoon in 1981 [39], although some sources suggest that a similar approach was advocated much earlier by the Polish statistician Z. Hellwig [40]. In addition to its basic version, the TOPSIS method has interval and fuzzy variants.

3.1.1. Basic Model

In the basic model, the decision problem is discrete. We assume m alternatives and n criteria. The realization of the j-_th criterion for the i-_th alternative is represented as x_ij. This forms a data matrix:

X = [x_ij]

(1)

and a weight vector:

$$w=[w_1,w_2,\dots ,w_n]$$

(2)

Step 1 Construction of the normalized matrix:

$$z_{ij}={\displaystyle \frac{x_{ij}}{{max}_i{x}_{ij}}}$$

(3)

This creates the normalized decision matrix:

$$V=\left[w_j{z}_{ij}\right]$$

(4)

Step 2 The ideal solution (A⁺) and anti-ideal solution (A⁻) are determined:

$$A^{+}=\left\{v_1^{+},v_2^{+},\dots ,v_n^{+}\right\}$$

(5)

$$v_j^{+}=\left\{\begin{array}{c}{max}_i{v}_{ij},\hspace{1em}\hspace{1em}j\in I\\ {min}_i{v}_{ij},\hspace{1em}\hspace{1em}j\in J\end{array}\right.$$

(6)

$$A^{-}=\left\{v_1^{-},v_2^{-},\dots ,v_n^{-}\right\}$$

(7)

$$v_j^{-}=\left\{\begin{array}{c}{max}_i{v}_{ij},\hspace{1em}\hspace{1em}j\in J\\ {min}_i{v}_{ij},\hspace{1em}\hspace{1em}j\in I\end{array}\right.$$

(8)

where I is a set of criteria to be maximized (stimulants), and J is a set of criteria to be minimized (destimulants).

Step 3 The Euclidean distances of each alternative from the ideal and anti-ideal solutions are calculated:

$$d_i^{+}={\left(\sum _{j=1}^n{\left(v_{ij}-v_j^{+}\right)}^p\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}, i=\mathrm{1,2},\dots ,m$$

(9)

$$d_i^{-}={\left(\sum _{j=1}^n{\left(v_{ij}-v_j^{-}\right)}^p\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$p$}\right.}}, i=\mathrm{1,2},\dots ,m$$

(10)

Step 4 The ranking coefficient S_i for each alternative is computed to measure its similarity to the ideal solution:

$$S_i={\displaystyle \frac{d_i^{-}}{d_i^{-}+d_i^{+}}}, i=\mathrm{1,2},\dots ,m$$

(11)

The alternative with the highest S_i value is the most desirable solution.

3.1.2. Fuzzy Model

The fuzzy model refers to the concept of fuzzy sets, introduced into mathematics by L.A. Zadeh. The F-TOPSIS (fuzzy technique for order preference by similarity to ideal solution) method was proposed by Chen [41]. In this approach, the criteria values characterizing decision alternatives are represented as triangular fuzzy numbers. The algorithm follows the same steps as in the original TOPSIS method; however, it requires the use of fuzzy arithmetic to conduct computations. The decision matrix consists of fuzzy numbers. Thus, each element of the matrix now takes the following form:

$${\widehat{x}}_{ij}=\left(a_{ij},b_{ij}, c_{ij}\right)$$

(12)

where a_ij is the lower bound of the fuzzy number (pessimistic), b_ij is the most likely value (or mean value) of the fuzzy number, and c_ij is the upper bound of the fuzzy number (optimistic).

Normalization in the fuzzy decision matrix is performed using the following formulas:

$${\widehat{z}}_{ij}=\left({\displaystyle \frac{a_{ij}}{{max}_i{c}_{ij}}},{\displaystyle \frac{b_{ij}}{{max}_i{c}_{ij}}},{\displaystyle \frac{c_{ij}}{{max}_i{c}_{ij}}}\right), i\in I,J=1,\dots ,n$$

(13)

$${\widehat{z}}_{ij}=\left({\displaystyle \frac{{min}_i{a}_{ij}}{c_{ij}}},{\displaystyle \frac{{min}_i{a}_{ij}}{b_{ij}}},{\displaystyle \frac{{min}_i{a}_{ij}}{a_{ij}}}\right), i\in I,J=1,\dots ,n$$

(14)

The elements of the decision matrix V with weights are formed as follows:

$${\widehat{r}}_{ij}=w_j\otimes {\widehat{z}}_{ij}, i=1,\dots ,m,j=1,\dots ,n$$

(15)

The reference vectors have the following form:

$$A^{+}=\left({\widehat{v}}_1^{+},{\widehat{v}}_2^{+},\dots ,{\widehat{v}}_n^{+}\right)=\left(\begin{array}{c}max\\ i\end{array}{\widehat{r}}_{i1},\begin{array}{c}max\\ i\end{array}{\widehat{r}}_{i2},\dots ,\begin{array}{c}max\\ i\end{array}{\widehat{r}}_{in}\right)$$

(16)

$$A^{-}=\left({\widehat{v}}_1^{-},{\widehat{v}}_2^{-},\dots ,{\widehat{v}}_n^{-}\right)=\left(\begin{array}{c}min\\ i\end{array}{\widehat{r}}_{i1},\begin{array}{c}min\\ i\end{array}{\widehat{r}}_{i2},\dots ,\begin{array}{c}min\\ i\end{array}{\widehat{r}}_{in}\right)$$

(17)

The Euclidean distances of the analyzed objects from the ideal and anti-ideal solutions in the fuzzy model are determined using the following formula:

$$d(\tilde{a},\tilde{b})=\sqrt{{\displaystyle \frac{1}{2}}\left[{\left(a-a^{\prime }\right)}^2+{\left(b-b^{\prime }\right)}^2+{\left(c-c^{\prime }\right)}^2\right]}$$

(18)

3.2. Evaluation of Long-Term Renovation Strategies Using the F-TOPSIS Method

Linguistic Term and Triangular Fuzzy Number Scale for Criteria

In the context of the F-TOPSIS method, the linguistic variables are applied for evaluation of criteria. A linguistic variable uses words or phrases in natural or artificial language to describe the degree of a value. For instance, experts may assess the weights of criteria using terms such as “very important” and “not important”, and these assessments are subsequently converted into specific numerical values based on the principles of fuzzy sets. This approach is particularly useful under conditions of imprecision and uncertainty.

In the F-TOPSIS method, the values of criteria characterizing decision alternatives are expressed as triangular fuzzy numbers (Figure 5).

For each of the five evaluated criteria, considering their individual characteristics, a tailored fuzzy evaluation range was developed.

Criterion 1: Reduction of CO₂ emissions

For the reduction of CO₂ emissions, the criterion is assessed using a fuzzy scale (

Table 2. Linguistic term and triangular fuzzy number scale for criterion 1.

Linguistic Term	Fuzzy N.
No reduction	0, 1, 2
Less than 80%	1, 2, 3
More than 80% but less than 91%	2, 3, 4
Above 91%	3, 4, 5

), where the degree of reduction is represented by triangular fuzzy numbers (

Table 3. Number of CO₂ emissions reduction in chosen EU member countries and the given fuzzy numbers.

Country	Reduction in CO2 Emissions	Fuzzy N.
Austria	80%	2, 3, 4
Bulgaria	None	0, 1, 2
Croatia	80%	2, 3, 4
Czech Republic	40%	1, 2, 3
Estonia	90%	2, 3, 4
Finland	92%	3, 4, 5
Germany	100%	3, 4, 5
Greece	100%	3, 4, 5
Lithuania	100%	3, 4, 5
Poland	None	0, 1, 2
The Netherlands	95%	3, 4, 5
Spain	98.8%	3, 4, 5

).

Criterion 2: Annual Renovation Rate

For the annual renovation rate, the criterion is assessed using a fuzzy scale (

Table 4. Linguistic term and triangular fuzzy number scale for criterion 2.

Linguistic Term	Fuzzy N.
No Details	0, 1, 2
General Statement Without Specific Targets	1, 2, 3
Annual Renovation Rate of 4% or above	2, 3, 4
Annual Renovation Rate Below 4%	3, 4, 5

), where the degree of reduction is represented by triangular fuzzy numbers (

Table 5. Renovation assumptions in chosen EU member countries and the given fuzzy numbers.

Country	Renovation Assumptions	Fuzzy N.
Austria	Increase renovation rate from 1.5% to 3%	3, 4, 5
Bulgaria	Renovate 127,597,192 m2 of existing building area by 2050	1, 2, 3
Croatia	4% annual rate until 2050; renovate 100% of existing buildings by 2050	2, 3, 4
Czech Republic	Increase annual renovation rate to 1.4% for single-family homes, 0.79% for multi-family residential, 2% for commercial and public buildings	3, 4, 5
Estonia	Renovate all existing buildings to nearly-zero-energy standards by 2050	1, 2, 3
Finland	Presented a detailed roadmap to 2050, with a comprehensive range of milestones and indicators	2, 3, 4
Germany	Increase annual renovation rates by 2030 to over 2% for single-family and twin buildings (current 1.3%) and over 2% for multi-family buildings (current 1.5%)	3, 4, 5
Greece	Double annual renovation rate to 1.6% by 2050 compared to 2015	3, 4, 5
Lithuania	Increase renovation rates to 17% by 2030, 43% by 2040, 74% by 2050	1, 2, 3
Poland	Increase annual renovation rate to 3.6% by 2030, 4.1% by 2040, 3.7% by 2050	3, 4, 5
The Netherlands	Gradual thermal modernization of 1,500,000 buildings by 2030. The consultation process was highly collaborative, engaging the public in national climate and energy policy.	0, 1, 2
Spain	Renovate 6.42% of homes by 2030. Delivered the best overall strategy, with excellent detail on energy savings, wider benefits, and progress on the 2017 strategy.	1, 2, 3

).

Criterion 3: Expected energy savings

For the expected energy savings, the criterion is assessed using a fuzzy scale (

Table 6. Linguistic term and triangular fuzzy number scale for criterion 3.

Linguistic Term	Fuzzy N.
No details	0, 1, 2
Up to 30%	1, 2, 3
30–70%	2, 3, 4
Above 70%	3, 4, 5

), where the degree of reduction is represented by triangular fuzzy numbers (

Table 7. Expected energy savings in chosen EU member countries and the given fuzzy numbers.

Country	Expected Energy Savings	Fuzzy N.
Austria	68% by 2050 from 2015	2, 3, 4
Bulgaria	No details	0, 1, 2
Croatia	No details	0, 1, 2
Czech Republic	24% by 2050 on 2020 levels	1, 2, 3
Estonia	60% by 2050	2, 3, 4
Finland	49% reduction in heating energy consumption	2, 3, 4
Germany	A 55% energy reduction goal for 2030 compared to 2008	2, 3, 4
Greece	No details	0, 1, 2
Lithuania	No details	0, 1, 2
Poland	No details	0, 1, 2
The Netherlands	No details	0, 1, 2
Spain	98.8%	3, 4, 5

).

Criterion 4: Total Investment Required

For the total investment required, the criterion is assessed using a fuzzy scale (

Table 8. Linguistic term and triangular fuzzy number scale for criterion 4.

Linguistic Term	Fuzzy N.
No details	0, 1, 2
Up to EUR 50 billion	1, 2, 3
EUR 50 billion to EUR 100 billion	2, 3, 4
Above EUR 100 billion	3, 4, 5

), where the degree of reduction is represented by triangular fuzzy numbers (

Table 9. Total investment required to implement renovation plans in chosen EU member countries and the given fuzzy numbers.

Country	Total Investment Required	Fuzzy N.
Austria	EUR 159 billion	3, 4, 5
Bulgaria	EUR 67.5 billion	2, 3, 4
Croatia	EUR 51 billion	2, 3, 4
Czech Republic	EUR 33 billion	1, 2, 3
Estonia	EUR 21.6 billion	1, 2, 3
Finland	EUR 24 billion	1, 2, 3
Germany	No details	0, 1, 2
Greece	No details	0, 1, 2
Lithuania	EUR 53 billion	2, 3, 4
Poland	EUR 36 billion	1, 2, 3
The Netherlands	No details	0, 1, 2
Spain	EUR 143 billion inclusive of financing costs (residential sector only)	3, 4, 5

).

Criterion 5: Overall Assessment

For the overall assessment, the criterion is assessed using a fuzzy scale (

Table 10. Linguistic term and triangular fuzzy number scale for criterion 5.

Linguistic Term	Fuzzy N.
Weak	0, 1, 2
Sufficient	1, 2, 3
Good	2, 3, 4
Excellent	3, 4, 5

), where the degree of reduction is represented by triangular fuzzy numbers (

Table 11. Overall assessment of renovation plans in chosen EU member countries and the given fuzzy numbers.

Country	Overall Assessment	Fuzzy N.
Austria	Good	2, 3, 4
Bulgaria	Weak	0, 1, 2
Croatia	Good	2, 3, 4
Czech Republic	Good	2, 3, 4
Estonia	Sufficient	1, 2, 3
Finland	Excellent	3, 4, 5
Germany	Good	2, 3, 4
Greece	Weak	0, 1, 2
Lithuania	Weak	0, 1, 2
Poland	Sufficient	1, 2, 3
The Netherlands	Excellent	3, 4, 5
Spain	Excellent	3, 4, 5

).

The aggregate fuzzy decision matrix is presented in

Table 12. The aggregate fuzzy decision matrix.

	k1			k2			k3			k4			k5
Austria	2	3	4	3	4	5	2	3	4	3	4	5	2	3	4
Bulgaria	0	1	2	1	2	3	0	1	2	2	3	4	0	1	2
Croatia	2	3	4	2	3	4	0	1	2	2	3	4	2	3	4
Czech Republic	1	2	3	3	4	5	1	2	3	1	2	3	2	3	4
Estonia	2	3	4	1	2	3	2	3	4	1	2	3	1	2	3
Finland	3	4	5	2	3	4	2	3	4	1	2	3	3	4	5
Germany	3	4	5	3	4	5	2	3	4	0	1	2	2	3	4
Greece	3	4	5	3	4	5	0	1	2	0	1	2	0	1	2
Lithuania	3	4	5	1	2	3	0	1	2	2	3	4	0	1	2
Poland	0	1	2	3	4	5	0	1	2	1	2	3	1	2	3
The Netherlands	3	4	5	0	1	2	0	1	2	0	1	2	3	4	5
Spain	3	4	5	1	2	3	3	4	5	3	4	5	3	4	5

.

The normalized aggregate fuzzy decision matrix—using (13), (14)—is presented in

Table 13. The normalized aggregate fuzzy decision matrix.

	k1			k2			k3			k4			k5
Austria	0.4	0.6	0.8	0.6	0.8	1	0.4	0.6	0.8	0.6	0.8	1	0.4	0.6	0.8
Bulgaria	0	0.2	0.4	0.2	0.4	0.6	0	0.2	0.4	0.4	0.6	0.8	0	0.2	0.4
Croatia	0.4	0.6	0.8	0.4	0.6	0.8	0	0.2	0.4	0.4	0.6	0.8	0.4	0.6	0.8
Czech Republic	0.2	0.4	0.6	0.6	0.8	1	0.2	0.4	0.6	0.2	0.4	0.6	0.4	0.6	0.8
Estonia	0.4	0.6	0.8	0.2	0.4	0.6	0.4	0.6	0.8	0.2	0.4	0.6	0.2	0.4	0.6
Finland	0.6	0.8	1	0.4	0.6	0.8	0.4	0.6	0.8	0.2	0.4	0.6	0.6	0.8	1
Germany	0.6	0.8	1	0.6	0.8	1	0.4	0.6	0.8	0	0.2	0.4	0.4	0.6	0.8
Greece	0.6	0.8	1	0.6	0.8	1	0	0.2	0.4	0	0.2	0.4	0	0.2	0.4
Lithuania	0.6	0.8	1	0.2	0.4	0.6	0	0.2	0.4	0.4	0.6	0.8	0	0.2	0.4
Poland	0	0.2	0.4	0.6	0.8	1	0	0.2	0.4	0.2	0.4	0.6	0.2	0.4	0.6
The Netherlands	0.6	0.8	1	0	0.2	0.4	0	0.2	0.4	0	0.2	0.4	0.6	0.8	1
Spain	0.6	0.8	1	0.2	0.4	0.6	0.6	0.8	1	0.6	0.8	1	0.6	0.8	1

.

The final results (using (18)) are presented in

Table 14. Final results.

Country	d+	d−	Final Rating
Austria	0.3055	1.0456	0.7739
Bulgaria	1.0198	0.4472	0.3048
Croatia	0.7024	0.7303	0.5097
Czech Republic	0.6429	0.7832	0.5492
Estonia	0.7303	0.5774	0.4415
Finland	0.4899	0.4899	0.5000
Germany	0.6633	0.8944	0.5741
Greece	1.0392	0.6928	0.4000
Lithuania	0.9592	0.5657	0.3710
Poland	0.8944	0.6633	0.4258
The Netherlands	1.0392	0.6928	0.4000
Spain	0.4000	1.1136	0.7357

.

4. Discussion

Using the F-TOPSIS methodology, EU member countries were ranked based on their performance across five key criteria: CO₂ emission reduction, annual renovation rates, expected energy savings, total investments required, and overall assessment. Notable performers included Finland, Spain, and the Netherlands, which received “excellent” ratings due to comprehensive strategies and ambitious renovation goals.

In terms of CO₂ emission reduction goals, Germany, Greece, and Lithuania demonstrated strong commitments, aiming for a 100% reduction by 2050, consistent with EU climate neutrality targets. Conversely, some countries, including Bulgaria and Poland, lacked specific CO₂ reduction targets, highlighting critical gaps in their strategic planning. Regarding annual renovation rates, Spain and the Netherlands stood out for their well-defined pathways, with Spain targeting the renovation of 6.42% of its residential building stock by 2030. However, many countries struggled to meet the EU goal of 2% annual renovation rates, with several reporting figures closer to 1%, underscoring the need for accelerated action.

Investment requirements varied widely across EU countries, reflecting the scope and ambition of their strategies. For example, Austria and Spain reported significant planned investments of EUR 159 billion and EUR 143 billion, respectively, correlating with their ambitious goals. In contrast, countries such as Estonia and the Czech Republic reported much lower investment levels, indicative of narrower renovation scopes. Moreover, there are some EU countries like Germany, Greece, and the Netherlands that have not specified any investment requirements to implement their renovation plans.

The results reveal significant disparities in the ambition and implementation of renovation strategies across EU member countries. Countries with strong frameworks, like Austria and Spain, exemplify how clear targets and substantial investments can drive progress. Conversely, the lack of specific goals and limited financial resources in countries like, for instance, Bulgaria highlights the challenges of achieving EU-wide climate objectives. Overall, Austria and Spain achieved the highest final ratings, reflecting their comprehensive and ambitious approaches to building renovations. These countries exhibit well-defined strategies with high investment levels, robust CO₂ reduction goals, and significant progress toward energy savings. Germany and Czech Republic also performed well, indicating strong efforts to align their strategies with EU targets, though with room for further improvement. Countries such as Croatia, Finland, and Estonia displayed moderate alignment with the ideal solution. While these countries have made progress, they may lack certain aspects such as higher renovation rates or more ambitious energy savings targets. Poland, with a rating of 0.4258, falls within the moderate range but demonstrates gaps in both investment levels and strategic ambition. At the lower end, Bulgaria, Lithuania, Greece, and the Netherlands scored poorly, indicating significant challenges in their renovation strategies. These countries often lack detailed long-term plans, sufficient investments, or ambitious goals for CO₂ reduction and energy efficiency.

5. Conclusions

The results of the F-TOPSIS method analysis highlight the uneven progress among EU member countries in developing and implementing effective long-term renovation strategies. Countries with comprehensive frameworks, such as Finland and Spain, exemplify how clear targets, substantial financial commitments, and robust policy support can drive meaningful progress. Conversely, the lack of specific goals and limited financial resources in countries like Bulgaria and Poland underscores the challenges of achieving EU-wide climate objectives.

When compared to previous studies, such as those conducted by BPIE [17,18,24], the findings align with the notion that financing, technical capacity, and legislative coherence play pivotal roles in the success of renovation strategies. However, several challenges persist, including technical and economic barriers, high costs, limited technological solutions, and a shortage of skilled labor, continue to hinder renovation efforts. Policy and awareness gaps also exacerbate these challenges, as inconsistent definitions of “deep renovation” and varying baseline years impede meaningful cross-country comparisons. Despite these obstacles, the results indicate significant opportunities for improvement. Knowledge-sharing platforms could facilitate the exchange of best practices between leading nations and those lagging behind, enabling more uniform progress across the EU.

Future research should focus on exploring innovative financing mechanisms, particularly those targeting low-income households, to mitigate the financial burden of renovations. Additionally, the potential of digital tools, such as building renovation passports, to streamline renovation planning and implementation warrants further investigation. Finally, the development of harmonized metrics and standards for renovation goals could enable better cross-country comparisons and foster a more cohesive EU-wide approach.

In conclusion, while notable progress has been made in some EU member countries, substantial disparities remain, necessitating targeted actions to address the gaps identified. By leveraging the opportunities highlighted and addressing the challenges outlined, the EU can advance toward its climate neutrality objectives and ensure a sustainable future for its building stock.