Prioritizing the indicators of energy performance management: a novel fuzzy decision-making approach for G7 service industries

Energy performance management is a process used to monitor, evaluate, analyze, and improve the energy efficiency of a building or an organization. This process includes data collection, analysis, planning and implementation steps to manage energy consumption and energy performance. In this context, firstly, data on energy consumption and energy efficiency are collected (Karunanithi et al 2023). After that, the collected data is analyzed and performance indicators such as energy consumption, energy costs, energy efficiency indicators are calculated. This analysis is important for understanding energy use, identifying energy efficiency opportunities, and identifying weak spots. Based on the analysis results, energy performance targets are determined (Hakimi et al 2023). These goals may include reducing energy consumption, improving energy efficiency, and promoting sustainable energy use. Next, planned energy performance improvement steps are implemented. After the application, it is necessary to monitor and measure the energy performance (Kapp et al 2022). This situation allows to evaluate whether the determined targets have been achieved, to evaluate the effect of the improvements made and to take corrective measures if necessary.

Ensuring energy performance management is important in many ways. Energy performance management saves energy through monitoring, analysis, and improvement of energy consumption. Thanks to energy efficiency measures and strategies, energy resources are used more effectively, and energy costs are reduced (Ferrari et al 2023). In addition, energy performance management provides cost savings by increasing energy efficiency and reducing energy consumption. Less energy consumption means lower energy bills and significant savings in operating and usage costs. Energy performance management supports environmental sustainability by optimizing energy consumption. Energy saving reduces greenhouse gas emissions and ensures a more sustainable use of natural resources (Paramati et al 2022). This situation can minimize the negative effects on the environment. Energy performance management helps businesses monitor and improve their energy performance. More efficient use of energy ensures more reliable operation of energy systems, increases business continuity, and increases the competitiveness of the enterprise (Kostis et al (2022).

Different factors can affect energy performance management. Energy efficiency ensures that energy resources are used more effectively, which means energy savings. Less energy consumption reduces energy costs and ensures that energy sources can be used for a longer period (Paris et al 2022). System quality is very important for ensuring energy performance management. Accurate and reliable data is needed for energy performance management (Koutsandreas et al 2022). Energy consumption, energy costs and other performance indicators must be accurately measured and recorded. Quality systems reliably perform data collection, automation, and measurement, ensuring the precision and accuracy of data. To ensure energy performance management, effective legal regulations should also be provided (Zakari et al 2022). Energy performance regulations help set energy efficiency standards and targets. These standards and targets encourage buildings and organizations to achieve a certain level of energy efficiency (Alwaelya et al 2021, Mutalimov et al 2021).

There are many variables that have an important role on the effectiveness of energy performance management of buildings. In this context, to improve this performance, businesses need to make the necessary improvements for the development of these factors. However, these improvements also lead to an increase in the costs of the enterprises. In other words, if businesses carry out these improvement practices unplanned, this causes the costs to reach an uncontrollable level. Therefore, among these actions, the more important ones need to be determined. In this way, businesses will be able to use their limited budgets for more priority issues. This will also help increase productivity so that energy performance management should be improved without having high amount costs.

Accordingly, in this study, it is aimed to evaluate the main indicators of energy performance management system. In this way, a novel model is developed to make a priority analysis for the hospitals. In the first stage, five indicators of energy performance management system are identified by considering ISO 50006 standards. Moreover, these indicators are evaluated by using Spherical fuzzy CRITIC. In the second part of the proposed model, G7 countries are examined with fuzzy RATGOS technique.

Identifying the critical items for more effective energy performance management is a very difficult issue. Because of this situation, a comprehensive fuzzy decision-making model should be generated. However, existing models in the literature are criticized due to some reasons. The main drawback of these models is related to the uncertainty in this process (Alshamrani et al 2023, Majumder et al 2023). For example, the Euclidian distance is considered in the evaluations made by TOPSIS approach (Krishankumar and Ecer 2023). In this process, the distance to both positive and negative ideal results is used in the TOPSIS method (Corrente and Tasiou 2023). However, it is claimed that using the Euclidian distance is not correct to calculate the negative ideal result (Deng and Chen 2022). When these issues are taken into consideration, it is seen that a novel model should be created with a new ranking technique. Therefore, the main motivation in this study is to find the most significant variables of energy performance management via an original decision-making model in which a new ranking technique (RATGOS) is proposed.

The main contributions of the manuscript are explained as follows.

• (i)  
  Identification of the most significant indicators of the energy performance systems is an important novelty of this study. Different variables may have an influence on the performance of these systems. However, making improvements to these indicators leads to an increase in the costs of the companies (Manfren et al 2022). Hence, to prevent having too many costs, the more important indicators need to be determined. With the help of this issue, companies can use their limited budgets for more priority issues.
• (ii)  
  Making an evaluation for G7 countries also provides some advantages. G7 countries hold a crucial position in the global economy and are also responsible for a substantial proportion of the total greenhouse gas emissions across the globe. Consequently, these nations bear a heightened obligation to address environmental concerns. In these nations, a significant amount of energy is consumed by hospitals and buildings (Andersson and Thollander 2019).
• (iii)  
  The most significant methodological novelty of this study is proposing a new technique to the literature named RATGOS. Because of the criticisms to the currently ranking techniques in the literature, a new ranking technique (RATGOS) is created in this study. The geometric mean is used in the calculation process of the RATGOS. Hence, it is aimed to reach more effective solutions and minimize uncertainties in this process.
• (iv)  
  There are some advantages of using the CRITIC technique for weighting criteria. The main advantage of the CRITIC method is that it determines the objective criteria weights that include the contrast and conflict density in the structure of the decision problem (Amin et al 2022). Another advantage of the CRITIC method is that it normalizes the decision matrix by considering the ideal values of the cost and benefit criteria at the same time (Haktanır and Kahraman 2022). To make an effective priority analysis for the variables affecting energy performance management, the relationship between these factors should also be taken into consideration (Krishankumar et al 2022). Therefore, it seems that the CRITIC method, which uses the correlation relationship between the factors in the analysis process, is ideal for this study (Liu et al 2022).
• (v)  
  Selecting the indicators based on ISO 50006 standards also provides some advantages. ISO 50006 are international standards considered for energy performance management. These standards provide organizations with a framework for evaluating, improving, and tracking their energy performance (Fichera et al 2020). ISO 50006 provides a methodology and guidance for evaluating energy performance. Organizations can use this standard to objectively measure and analyze energy performance (Andersson et al 2021). Performance evaluation helps to identify critical indicators such as energy consumption, energy intensity, energy saving potential and to monitor performance. ISO 50006 provides guidance for improving energy performance (Batlle et al 2020). The standard provides a process for identifying, implementing, and monitoring energy efficiency measures. Organizations help to effectively manage energy saving projects and improvement activities.
• (vi)  
  Evaluating hospitals is another important contribution of this study. Hospitals have great potential in terms of energy efficiency due to long working hours, intensive energy use, and high carbon emissions. In other words, hospitals have a significant share in energy consumption, so providing energy efficiency is quite essential for this industry. Therefore, energy performance management of these buildings is important to achieve sustainability goals.

Literature is evaluated in the second part. Methodology is detailed in the following section. The fourth part consists of the results of the proposed model. The final sections explain the discussion and conclusions.

In this section, the results of the literature review are indicated based on each significant indicator of the energy performance management system. The summary of these studies is given in table A1. Many scholars in literature define that energy efficiency is an important indicator of the effective energy performance management system. Because of the environmental impacts and financial consequences of energy use, energy efficiency is an especially critical issue in the construction and operation of buildings and institutions (Sun et al 2022). Energy savings are achieved through reduced environmental consequences because of improved building energy efficiency (Siddik et al 2023). As a result, energy consumption and associated costs can be reduced by using energy-efficient devices (Chiu et al 2022). From a financial standpoint, this is a huge advantage. Therefore, the use of energy-saving technology in the G7 countries contributes to the adoption of an ecologically responsible approach by reducing the energy use of buildings and hospitals (Kanchiralla et al 2020). Popescu et al drew attention to the importance of system quality to increase energy efficiency in hospitals. Hospital HVAC and lighting systems were analyzed for this research to see how they are stacked up against each other in terms of energy efficiency and environmental friendliness (Zhang et al 2022). The research revealed that systems need to be redesigned, improved, and maintained to improve energy efficiency. Bampatsou and Halkos (2019) emphasized the importance of using smart building technologies to improve the quality of energy use in buildings. In this study, it is examined how smart building technologies can be used to increase the energy efficiency of buildings, reduce carbon footprint, and increase human comfort.

Moreover, the importance of technological improvement for energy performance management system is also highlighted in different studies. It is particularly important to have a high-quality system for efficient energy use (Jung and Jazizadeh 2019, Yasin et al 2023). System quality refers to a collection of energy-saving technologies installed in commercial and medical structures (Fichera et al 2020, Doğan et al 2022). These innovations are to reduce the environmental impact of buildings and hospitals and their energy use (Su et al 2022). Sharpe et al (2019) analyzed different strategies and policies that can be implemented in hospitals to increase energy efficiency. As a result of this article, they have shown that it is possible to reduce the energy consumption of hospitals by using the system dynamics model. Soni et al (2022) they examined the effect of increasing energy efficiency using solar energy in a hospital in Germany. The results of the study showed that the use of solar energy reduces energy consumption and provides hospital managers with significant savings.

Effective regulations play a critical role to improve energy performance management systems. Increasing energy demand, global climate change, and limited energy resources have made it necessary to regulate energy use. Building and healthcare facility energy consumption rules are becoming more important in this setting. About 40% of the total energy used in the G7 nations is used to power buildings (Dadi et al 2022). As a result, it presents a significant chance to cut down on carbon dioxide emissions by decreasing the amount of energy needed to power buildings (Chang and Hu 2019). To that end, codes have been drafted to mandate greater building efficiency when it comes to energy use (Batlle et al 2020). Energy labeling and building energy performance requirements are two areas where the European Union has adopted legislation (Eti et al 2023a). By mandating greater energy efficiency in buildings, the government hopes to cut down on energy use and greenhouse gas emissions (Lagrange et al 2020, Nundy et al 2021, Kou et al 2022, Xu et al 2022). Therefore, comparing the energy consumption of these areas to the market is crucial. This comparison creates a competitive environment among similar structures in terms of energy efficiency (Ding and Liu 2020). Among similar structures, those that are more efficient and consume less energy come to the fore and become more attractive. This, in turn, acts as an incentive mechanism to increase energy efficiency (Arjunan et al 2020). Comparing with the market is also important for measuring the level of energy efficiency. A building's or hospital's energy efficiency may be better understood when compared to that of other comparable buildings. The factors that affect a building's or hospital's energy usage may then be isolated, and from there, actions to increase efficiency can be devised (Kim et al 2019). Hashempour et al (2020) analyze how different strategies for energy conservation can affect hospital energy use in their article. Therefore, it shows that hospitals can save energy while also saving money by implementing appropriate energy efficiency measures. Schibuola and Tambani (2021) examined how important energy efficiency investments are in the commercial real estate sector. The bottom line is that energy efficiency investments can reduce the operating costs of buildings, increase tenant satisfaction, and increase building value.

Increasing energy demand should also be taken into consideration for the development of the energy performance management system. G7 countries consist of the most developed and economically powerful countries in the world. However, the demand for and use of energy in these nations is growing at an alarming rate (Yüksel et al 2022, Yan et al 2023). Population expansion, new manufacturing techniques, technical progress, and increased building energy use are all contributing elements (Ahmadi and Frikha 2022). For this reason, the G7 nations place a premium on the measurement and control of energy usage in buildings and hospitals to guarantee both energy efficiency and sustainability (Yang et al 2022). There are several advantages to assessing and controlling healthcare facilities' energy use. To begin with, lowering energy usage may lessen the financial burden on building and healthcare operations (Sohail et al 2023). In addition, cutting down on energy use may help create a more sustainable future by lessening the strain on the environment (Andersson et al 2021). The comfort of buildings and the contentment of hospital patients and visitors both rise when energy efficiency is improved (Sovacool et al 2022). Sahu et al (2022) and Coletta et al (2021) focus on the importance of increasing energy efficiency in buildings in their articles.

As a result of the literature review, it is possible to reach the following conclusions. Energy performance management is a very important issue in terms of sustainability. Moreover, energy management in hospitals has become very popular in the literature in recent years. There are many variables that have an important role on the effectiveness of energy performance management of buildings, such as energy efficiency, quality of the system and regulatory requirements. However, these improvements also lead to an increase in the costs of the enterprises. But hospitals and buildings are unlikely to improve each of these factors at the same time. Therefore, among these actions, the more important ones need to be determined. In this way, businesses will be able to use their limited budgets for more priority issues. Nevertheless, there are limited studies in literature that focused on the details of these issues. Hence, for satisfying this missing part, in this study, it is aimed to make a priority analysis for the indicators of energy performance management system with a novel methodology. On the other side, decision-making methodologies were also taken into consideration in some of these studies. However, these existing models are criticized by many researchers. One of the most significant criticisms is related to the ranking techniques. In this context, TOPSIS approach includes Euclidian distance in the calculation process. Nonetheless, some scholars criticized this situation while calculating the distance to the negative ideal result. By considering these factors, it is understood that a new ranking model should be generated to overcome these problems. For this purpose, RATGOS technique is proposed in this study newly by the authors. In the calculation steps of this approach, geometrical mean is taken into consideration.

This section consists of the operational steps of the decision-making techniques used in the proposed model.

3.1. Spherical Fuzzy CRITIC

The CRITIC method is used as a weighting method in solving decision making problems. The method in question calculates the weight of the criteria, taking into consideration the correlation between the criteria (Amin et al 2022, Krishankumar et al 2022). The steps of this method are given below (Haktanır and Kahraman 2022).

Step 1: Expert opinions are obtained and converted into fuzzy numbers with the help of the expressions in table 1. In this context, μ, v, and π membership, non-membership, and hesitancy degrees (Liu et al 2022).

Table 1. Linguistic variable for weighting.

	μ	v	π
1 (Absolutely low importance -ALI)	,1	,9	,1
2 (Very low importance-VLI)	,2	,8	,2
3(Low importance-LI)	,3	,7	,3
4 (Slightly low importance-SLI)	,4	,6	,4
5 (Equally importance-EI)	,5	,5	,5
6 (Slightly more importance-SMI)	,6	,4	,4
7 (High importance-HI)	,7	,3	,3
8 (Very high importance-VHI)	,8	,2	,2
9 (Absolutely more importance-AMI)	,9	,1	,1

Step 2: The arithmetic average (SWAM) of the obtained expert opinions is taken and the decision matrix (D) is created. In this process, equations (1) and (2) are used.

$$\begin{eqnarray}&&{SWAM}\left({D}_{s1},{D}_{s2},\ldots ,{D}_{{Sn}}\right)=\,\left\{\begin{array}{c}{\left[1-\displaystyle \prod _{i=1}^{n}{\left(1-{\mu }_{{D}_{{si}}}^{2}\right)}^{\frac{1}{n}}\right]}^{\frac{1}{2}},\\ \displaystyle \prod _{i=1}^{n}{v}_{{D}_{{si}}}^{\frac{1}{n}},\\ {\left[\displaystyle \prod _{i=1}^{n}{\left(1-{\mu }_{{D}_{{si}}}^{2}\right)}^{1/n}-\displaystyle \prod _{i=1}^{n}{\left(1-{\mu }_{{D}_{{si}}}^{2}-{\pi }_{{D}_{{si}}}^{2}\right)}^{1/n}\right]}^{1/2}\end{array}\right\}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}D=\left[\begin{array}{ccc}\left({\mu }_{11},{v}_{11}{\pi }_{11}\right) & \cdots & \left({\mu }_{m1},{v}_{m1},{\pi }_{m1}\right)\\ \vdots & \ddots & \vdots \\ \left({\mu }_{1n},{v}_{1n}{,\pi }_{1n}\right) & \cdots & \left({\mu }_{{mn}},{v}_{{mn}}{,\pi }_{1{mn}}\right)\end{array}\right]\end{eqnarray} \tag{ 2 }$$

Step 3: Using equations (3) and (4), the decision matrix is normalized, and the normalized matrix (X) is obtained. In this framework, V denotes the maximum operator, $\left({\mu }_{-},{v}_{-},{\pi }_{-}\right)$ show minimum optimal value and $\left({\mu }_{+},{v}_{+},{\pi }_{+}\right)$ indicate maximum optimal value.

$$\begin{eqnarray}&&{\widetilde{x}}_{{ij}}=\frac{1-\frac{{\mu }_{{ij}}^{2}{\rm{{\rm X}}}{\mu }_{-}^{2}+{v}_{{ij}}^{2}{\rm{{\rm X}}}{v}_{-}^{2}+{\pi }_{{ij}}^{2}{\rm{{\rm X}}}{\pi }_{-}^{2}}{{\mu }_{{ij}}^{2}{\rm{V}}{\mu }_{-}^{2}+{v}_{{ij}}^{2}{\rm{V}}{v}_{-}^{2}+{\pi }_{{ij}}^{2}{\rm{V}}{\pi }_{-}^{2}}}{1-\frac{{\mu }_{-}^{2}{\rm{{\rm X}}}{\mu }_{+}^{2}+{v}_{-}^{2}{\rm{{\rm X}}}{v}_{+}^{2}+{\pi }_{-}^{2}{\rm{{\rm X}}}{\pi }_{+}^{2}}{{\mu }_{-}^{2}{\rm{V}}{\mu }_{+}^{2}+{v}_{-}^{2}{\rm{V}}{v}_{+}^{2}+{\pi }_{-}^{2}{\rm{V}}{\pi }_{+}^{2}}}\,{\rm{for\; positive\; attributes}}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\widetilde{x}}_{{ij}}=\frac{1-\frac{{\mu }_{{ij}}^{2}{\rm{{\rm X}}}{\mu }_{+}^{2}+{v}_{{ij}}^{2}{\rm{{\rm X}}}{v}_{+}^{2}+{\pi }_{{ij}}^{2}{\rm{{\rm X}}}{\pi }_{+}^{2}}{{\mu }_{{ij}}^{2}{\rm{V}}{\mu }_{+}^{2}+{v}_{{ij}}^{2}{\rm{V}}{v}_{+}^{2}+{\pi }_{{ij}}^{2}{\rm{V}}{\pi }_{+}^{2}}}{1-\frac{{\mu }_{-}^{2}{\rm{{\rm X}}}{\mu }_{+}^{2}+{v}_{-}^{2}{\rm{{\rm X}}}{v}_{+}^{2}+{\pi }_{-}^{2}{\rm{{\rm X}}}{\pi }_{+}^{2}}{{\mu }_{-}^{2}{\rm{V}}{\mu }_{+}^{2}+{v}_{-}^{2}{\rm{V}}{v}_{+}^{2}+{\pi }_{-}^{2}{\rm{V}}{\pi }_{+}^{2}}}\,{\rm{for\; negative\; attributes}}\end{eqnarray} \tag{ 4 }$$

Step 4: With the help of equation (5), the correlation coefficient is calculated over the normalized matrix.

$$\begin{eqnarray}{\widetilde{\rho }}_{{jk}}=\displaystyle \sum _{i=1}^{m}\left({\widetilde{x}}_{{ij}}-{\widetilde{\mathop{x}\limits^{̅}}}_{j}\right)\left({\widetilde{x}}_{{ik}}-{\widetilde{\mathop{x}\limits^{̅}}}_{k}\right)/\sqrt{\displaystyle \sum _{i=1}^{m}{\left({\widetilde{x}}_{{ij}}-{\widetilde{\mathop{x}\limits^{̅}}}_{j}\right)}^{2}\displaystyle \sum _{i=1}^{m}{\left({\widetilde{x}}_{{ik}}-{\widetilde{\mathop{x}\limits^{̅}}}_{k}\right)}^{2}}\end{eqnarray} \tag{ 5 }$$

In this process, ${\widetilde{\mathop{x}\limits^{̅}}}_{j}$ and ${\widetilde{\mathop{x}\limits^{̅}}}_{k}$ values are the fuzzy average values of j and k criteria. This value is also calculated by equation (6).

$$\begin{eqnarray}{\widetilde{\mathop{x}\limits^{̅}}}_{j}=\frac{1}{n}\displaystyle \sum _{j=1}^{n}{\widetilde{x}}_{{ij}}\,i=1,2,\ldots ,m\end{eqnarray} \tag{ 6 }$$

Step 5: The standard deviation $(\widetilde{\sigma })$ is computed by equation (7).

$$\begin{eqnarray}{\widetilde{\sigma }}_{j}=\sqrt{\frac{1}{n-1}\displaystyle \sum _{j=1}^{n}{\left({\widetilde{x}}_{{ij}}-{\widetilde{\mathop{x}\limits^{̅}}}_{j}\right)}^{2}}\,i=1,2,\ldots ,m\end{eqnarray} \tag{ 7 }$$

Step 6: The index (C) value is calculated using equation (8).

$$\begin{eqnarray}&&{\widetilde{C}}_{j}={\widetilde{\sigma }}_{j}\displaystyle \sum _{k=1}^{n}(1-{\widetilde{\rho }}_{{jk}})\,j=1,2,\ldots ,n\end{eqnarray} \tag{ 8 }$$

Step 7: The weight (w) of each criterion is calculated by equation (9).

$$\begin{eqnarray}&&{\widetilde{w}}_{j}=\frac{{\widetilde{C}}_{j}}{\displaystyle \sum _{j=1}^{n}{\widetilde{C}}_{j}}\end{eqnarray} \tag{ 9 }$$

3.2. Fuzzy RATGOS

In this study, a new decision-making technique is proposed with the name of Ranking Technique by Geometric Mean of Similarity Ratio to Optimal Solution (RATGOS). Similar approaches in literature have been criticized in many ways. In this framework, the Euclidian distance is used in the analyzes made with the TOPSIS technique (Krishankumar and Ecer 2023). On the other hand, the distance to both positive and negative ideal results is considered in the TOPSIS method (Alshamrani et al 2023). In this process, it is claimed that it is not correct to use the Euclidian distance to calculate the negative ideal result (Deng and Chen 2022). When these issues are taken into consideration, it is seen that a new technique needs to be developed (Majumder et al 2023). To achieve this aim, the RATGOS method, in which the geometric mean is used, is recommended. In this study, the RATGOS method is considered together with fuzzy numbers. The details of the calculation steps of the method are given below.

Step 1: Expert opinions are taken and converted into fuzzy numbers using the linguistic expressions in table 2.

Table 2. Linguistic variables for ranking.

	a	b	c
1	0	0	,1
2	0	,1	,2
3	,1	,2	,3
4	,3	,4	,5
5	,3	,5	,7
6	,5	,6	,7
7	,7	,8	,9
8	,8	,9	1
9	,9	1	1

Step 2: The decision matrix ($\widetilde{S}$) is formed by averaging the triangular evaluations obtained with the help of equations (10) and (11).

$$\begin{eqnarray}\widetilde{S}=\left[\begin{array}{ccc}{\widetilde{s}}_{11} & \cdots & {\widetilde{s}}_{1n}\\ \vdots & \ddots & \vdots \\ {\widetilde{s}}_{m1} & \cdots & {\widetilde{s}}_{{mn}}\end{array}\right]\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{\widetilde{s}}_{{ij}}=\frac{{\widetilde{s}}_{{ij}}^{1}+{\widetilde{s}}_{{ij}}^{2}+\ldots +{\widetilde{s}}_{{ij}}^{k}}{k}\end{eqnarray} \tag{ 11 }$$

Step 3: The optimal value is determined for each criterion. In this process, equations (12) and (13) are used for benefit and cost criteria.

$$\begin{eqnarray}&&\widetilde{{optimal}}=\max {\widetilde{s}}_{j}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\widetilde{{optimal}}=\max 1/\widetilde{{s}_{j\,}}\end{eqnarray} \tag{ 13 }$$

Step 4: Each criterion is divided by the optimal value. Thus, both normalization ($\widetilde{A})$ is performed and the similarity ratio with respect to the optimal is calculated. In this process, equations (14)–(16) is taken into consideration.

$$\begin{eqnarray}&&\widetilde{A}=\frac{\widetilde{S}}{\widetilde{{optimal}}}\,{for}\,{benefit}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&\widetilde{A}=\frac{\widetilde{{optimal}}}{\widetilde{S}}\,{for}\,{cost}\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&\left({a}_{1},{b}_{1},{c}_{1}\right)\div\left({a}_{2},{b}_{2},{c}_{2}\right)=\left(\frac{{a}_{1}}{{c}_{2}},\frac{{b}_{1}}{{b}_{2}},\frac{{c}_{1}}{{a}_{2}}\right)\end{eqnarray} \tag{ 16 }$$

Step 5: These values are multiplied by the weights (w) to obtain the weighted normalization matrix ($\widetilde{T}$) by equations (17) and (18).

$$\begin{eqnarray}\widetilde{T}=\left[\begin{array}{ccc}{x}_{11},{y}_{11},{z}_{11} & \cdots & {x}_{1n},{y}_{1n},{z}_{1n}\\ \vdots & \ddots & \vdots \\ {x}_{m1},{y}_{m1},{z}_{m1} & \cdots & {x}_{{mn}},{y}_{{mn}},{z}_{{mn}}\end{array}\right]=w* \widetilde{A}\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&\lambda * \left(a,b,c\right)=\left(\lambda a,\lambda b,\lambda c\right)\end{eqnarray} \tag{ 18 }$$

Step 6: With the help of equation (19), the geometric mean ($\widetilde{G}$) of the weighted normalized matrix is taken.

$$\begin{eqnarray}&&\widetilde{{G}_{j}}=\left({g}_{1j},{g}_{2j},{g}_{3j}\right)=\left(\sqrt[n]{\displaystyle \prod _{i=1}^{n}{x}_{{ij}}},\sqrt[n]{\displaystyle \prod _{i=1}^{n}{y}_{{ij}}},\sqrt[n]{\displaystyle \prod _{i=1}^{n}{z}_{{ij}}}\right)\end{eqnarray} \tag{ 19 }$$

Step 7: The calculated ($\widetilde{{G}_{j}}$) values are defuzzified by equation (20) and alternatives can be ranked.

$$\begin{eqnarray}&&{G}_{j}=\frac{{g}_{1j}+{g}_{2j}+{g}_{3j}}{3}\end{eqnarray} \tag{ 20 }$$

The following subtitles give information about the results of the proposed model.

4.1. Identification of the criteria/alternatives and obtaining the expert evaluations

4.2. Computing the weights of the indicators

Expert opinions are converted into fuzzy numbers using the values in table 1. On the other hand, the decision matrix (D) is created with the help of equation (1). The details of this matrix are shown in table A3. Since all criteria are benefit, D matrix is normalized using equation (3) (table A4). Correlation coefficients are calculated with the help of equation (5) and shown in table A5. The standard deviation value of each criterion is calculated with the help of equation (7). Table A6 gives information about these values. In the last step, the importance weights of the criteria are calculated using equations (8) and (9). The results are presented in table 4.

Table 4. Index values (C) and criteria weights (W).

	C	W
Energy efficiency	,1755	,3075
Quality of system	,1387	,2429
Regulatory requirements	,0746	,1307
Benchmarking with the market	,0758	,1328
Evaluating energy demand	,1062	,1861

Also, the weights of the criteria are illustrated in figure 1.

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4.3. Ranking G7 countries

First, the expert opinions are converted into triangular fuzzy numbers. Then, with the help of equations (10) and (11), the decision matrix for the ranking is created. The triangular decision matrix is presented in table A7. Since the criteria are benefit, optimal values are calculated with the help of equation (12) and normalized with equation (14) (table A8). By using the weights obtained with Spherical fuzzy Critic and equation (17), a weighted normalized matrix was obtained. The resulting matrix is shown in table A9. G matrix is obtained by equation (19) and presented in table A10. Finally, the values in G matrix are defuzzified by using equation (20). The highest defuzzifed value gives information about the best alternative. The findings are indicated in table 5.

Table 5. Defuzzified values and ranking results.

	Defuzzied values	Ranking results
Canada	,0668	5
France	,1899	1
Germany	,0618	7
Italy	,0693	4
Japan	,1786	2
United Kingdom	,0657	6
United States	,0927	3

Figure 2 also explains the ranking results of G7 economies.

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It is identified that France is the most successful G7 economy with respect to the energy performance management. Japan and United States have also high performance in this respect. On the other side, United Kingdom and Germany are on the last ranks in this framework.

According to the results obtained in this study, the most important issue affecting the energy performance management process in hospitals was found to be ensuring energy efficiency. It is known that energy consumption is high in hospitals. Apart from this, energy is one of the largest components that make up the expenses of both hospitals and other buildings. In addition, energy prices can easily fluctuate as they are affected by economic crises and global events. Therefore, ensuring energy efficiency is very important for buildings. Accordingly, energy efficiency should be provided for hospitals to successfully realize energy performance management. To achieve this goal, hospitals need a good technological infrastructure. In addition, having qualified personnel who can use this advanced technology is another important factor that can affect the process. Except for this, measuring the amount of energy required by the hospital and acting accordingly will impress energy performance. Additionally, energy efficiency can be improved by comparing the practices of buildings and countries that are successful in energy performance management and energy efficiency.

Ensuring energy efficiency in buildings is also a very important issue. Buildings often account for a large portion of energy consumption. Energy efficiency measures reduce energy consumption in buildings and thus save energy. A well-insulated building reduces heating and cooling costs by making more efficient use of energy resources. Energy efficient buildings save on operating and usage costs, along with lower energy bills. Well-insulated buildings consume less energy and therefore reduce energy costs. In addition, the long-term economic return of energy-efficient technologies and systems can be high. On the other hand, energy efficient buildings comply with sustainability goals and create a green image. This is important for buildings' participation in certification programs and compliance with sustainable building standards. Energy efficient buildings encourage the spread of green construction practices and innovative solutions (Candila et al 2021, Saqib et al 2021, An et al 2020).

Many studies in the literature have emphasized that achieving energy efficiency plays an important role in energy performance management. Cai et al (2022) conducted a review of research examining energy performance improvement methods to ensure sustainable production. Accordingly, 166 articles were analyzed, and it was understood that ensuring energy efficiency has an important place in energy performance management. Santolamazza et al (2023) used a maturity model in their study on the energy performance management of companies in Italy. According to the study, which examined the reports of large companies in Italy, where it is obligatory to conduct energy audits every four years, companies that provide energy efficiency are more successful in the energy management process. Hasan and Trianni (2020) carry out a study examining the relationship between industrial energy efficiency and energy management processes. In the study, the importance of ensuring energy efficiency to reduce greenhouse gases and energy consumption was pointed up. Quiang et al (2023) managed a review study on energy management processes in green buildings. In the study, it is defined that buildings account for 40% of global energy consumption and that energy efficiency should be ensured. Castrillon-Mendoza et al 2020 investigated the relationship between climate change, carbon emissions, and energy consumption in industrialized countries with a case study. The importance of energy efficiency is also underlined in the study, which expresses the necessity of an environmentally friendly and cleaner production process. Apart from these, Flick et al (2020) and Manfren and Nastasi (2020) stated that calculating the amount of energy to be consumed in the energy performance management process also plays an important role.

According to another result obtained in our study, the quality of technological equipment used in service production has an important place in the measurement of energy performance. One of the biggest obstacles to the success of the energy performance management process is unnecessary and excessive energy consumption. Therefore, the establishment of a system that will prevent unnecessary and excessive energy consumption will contribute to the success of the energy performance management process. This will also contribute to reducing the costs of hospitals. Pappalardo and Reverdy (2020) ran a study covering technological infrastructure and energy performance management in buildings in France. According to the results of the study, the quality of the system has an important place in the energy performance management process. Hammad (2019) administered a study examining the reasons for the difference between predicted and actual energy consumption to increase efficiency in building energy performance. It is defined in the study results that the use of advanced technologies directly affects energy performance management. Al Hashmi et al made a study to reduce carbon emissions with multi-criteria decision-making techniques. According to the study conducted in Saudi Arabia, the increase in energy consumption should be prevented due to the increasing population. To achieve this goal, it is stated that technology should be utilized in addition to many other methods.

Energy performance management of buildings is especially important for developing countries. The population growth rate in developing countries is quite high. In addition, these countries are taking action to increase their economic growth. These issues cause the demand for energy to increase rapidly. Therefore, the high energy performance of buildings will contribute to the reduction of energy consumption in developing countries. Thus, a radical increase in energy demand will be prevented. Consequently, extraordinary increases in energy demand can be mitigated by managing the energy performance of buildings. So, energy performance management is more important for developing countries than for other countries. In this context, developing countries are analyzed in this study. According to the results of the analysis, the most successful country was China. This shows that China has taken more accurate steps to manage the energy performance of its buildings. Hence, it will also increase the economic performance of successful countries. These countries will be able to manage their energy demands and avoid extra costs. Then, developing countries that aim to grow economically but are less successful in the energy performance management process can achieve their goals by implementing the strategies outlined in this study. Sharma et al investigated the relationship between renewable energy and the ecological footprint of eight developing countries in Asia. In the study, which concluded that renewable energy reduces the ecological footprint, it was also stated that the energy consumption of developing countries is high. Shahbaz et al (2021) examined the impact of financial development on renewable energy demand in developing countries. Using data from 1994–2015 and including 34 countries, the study drew attention to the increase in energy demand in developing countries.

Fuzzy decision-making models were also taken into consideration in the literature regarding the subject of energy performance management systems. Zhao et al (2022) focused on the energy performance management in the microgrid systems. In this framework, they created a fuzzy decision-making model by integrating DEMATEL and TOPSIS techniques. Similarly, Fazeli et al (2022), Bilgili et al (2022) and Li et al (2022) also used TOPSIS methodology to measure energy performance for different country groups. However, TOPSIS methodology was also criticized by different scholars because of using the Euclidian distance to calculate the negative ideal result (Deng and Chen 2022, Corrente and Tasiou 2023). To overcome these criticisms, RATGOS technique is created by the authors in this study as a new ranking approach. On the other side, Jangre et al (2022), Tippu et al (2022) and Feng et al (2022) considered DEMATEL technique to weight the main indicators of energy performance management. However, the scholars criticized DEMATEL especially when there are symmetrical evaluations. In this process, it is claimed that the DEMATEL technique incorrectly calculates the importance weights of the criteria as equal (Özdemirci et al 2023). For handling these problems, CRITIC methodology is taken into consideration in this proposed model.

Main indicators of energy performance management system are evaluated. Within this framework, a novel model is generated to make a priority analysis. In the first stage, five indicators of energy performance management system are identified based on ISO 50006 standards. Additionally, these indicators are examined by using Spherical fuzzy CRITIC. In the second part of the proposed model, G7 countries are ranked with fuzzy RATGOS technique. It is concluded that energy efficiency is the most crucial indicator of energy performance management. Additionally, the quality of the system should also be taken into consideration in this context. However, the weights of the regulatory requirements and benchmarking are much lower than other factors. On the other side, based on the ranking results, it is identified that France is the most successful G7 economy with respect to the energy performance management. Japan and United States have also high performance in this respect. Nonetheless, United Kingdom and Germany are on the last ranks in this framework.

Identification of the most significant indicators of the energy performance systems is an important novelty of this study. With the help of this issue, companies can use their limited budgets for more priority issues. The most significant methodological novelty of this study is proposing a new technique to the literature named RATGOS. Existing similar techniques in literature are criticized because of some issues. Because of this issue, the RATGOS method, in which the geometric mean is used, is recommended. The main limitation of this study is that it focused only on hospitals in the analysis process. The issue of energy performance management is also important for other sectors. Therefore, future studies in other sectors such as textile and automotive can be considered in this context. On the other hand, G7 countries are taken into account in the analysis process of this study. On the other hand, the success of energy performance management is also very important for developing countries. In this context, these countries can be analyzed in a new study to be conducted.

Alexey Mikhaylov performed the work in Sections 3–6, which were funded by Russian Science Foundation (Agreement 23-41-10001), https://rscf.ru/project/23-41-10001/ Gabor Pinter performed the work in Sections 1–2, which been implemented Project no. RRF-2.3.1-21-2022-00009, titled National Laboratory for Renewable Energy has been implemented with the support provided by the Recovery and Resilience Facility of the European Union within the framework of Programme Széchenyi Plan Plus.

The data cannot be made publicly available upon publication because no suitable repository exists for hosting data in this field of study. The data that support the findings of this study are available upon reasonable request from the authors.