Tapio-Z Decoupling of the Valuation of Energy Sources, CO₂ Emissions, and GDP Growth in the United States and China Using a Fuzzy Logic Model

Abstract

Our contemporary society is powered by fossil fuels, which results in environmental catastrophes. The combustion of these materials results in the release of CO₂, which accelerates the progression of climate change and its catastrophic consequences. The environmental repercussions of fossil fuel extraction have been highlighted through research into alternative energy sources. This inquiry uses the Tapio-Z decoupling approach to assess energy inputs and emissions. Furthermore, the fuzzy logic model is used to inspect the economic growth of the USA and China, as well as the impact of environmental factors, energy sources, and utilization, through decoupling effects from 1994 to 2023. The findings are substantiated by the individual perspectives of the environmental factors regarding decoupling, which ultimately lead to the acquisition of valuable results. We anticipate a substantial reduction in the total volume of CO₂ emissions in both the USA and China. Compared to China, the USA shows a significant increase in CO₂ emissions due to its reliance on fossil fuels. It is evident that a comprehensive transition to renewable resources and a broad range of technology is required to mitigate CO₂ emissions in high-energy zones. In their pursuit of sustainability, these two nations are making remarkable strides. The percentage change in CO₂ emissions indicates that effective changes in economic growth, energy input, and energy utilization, particularly sustainable energy, transmute energy output, as does the sustained implementation of robust environmental protection policies. The percentage change in CO₂ emissions indicates a remarkable transformation in energy input, energy consumption, and economic growth. This transition has been most visible in the areas of energy transformation, sustainability, and the maintenance of strong environmental protection measures.

1. Introduction

It is a multifaceted endeavor with far-reaching consequences to assess the value of energy sources and CO₂ emissions. Environmental costs, market prices, social factors, and technological advancements all contribute to the evaluation of energy sources [1,2]. For instance, the environmental and social repercussions of fossil fuels may be substantial in the long term, despite their relative affordability in the short term. Environmental issues have generally become more prevalent on a global scale [3]. Energy use and economic growth are linked. Although more expensive, renewable energy sources provide long-term energy security and reduce pollution [4]. Carbon taxes and other pricing systems tax people for CO₂ emissions’ externalities. It is hard to price carbon since climate and technology changes are unpredictable. Accurate energy and CO₂ estimates are required to make educated decisions, achieve sustainable development, and create a low-carbon economy [5].

In this study, the economies of the USA and China are analyzed by utilizing a fuzzy logic model (F-LGM), and Tapio-Z (T-ZDP) decoupling is used to decouple the valuation of energy sources and CO₂ emissions [6]. This impact, which is predicated on the law of declining marginal returns, guarantees that each energy input element in the United States (USA) and China is being eliminated in its entirety [7]. Since their economic power and technological innovations make them global actors, these two nations have a more promising sustainability trajectory than others. They have high renewable energy targets, large expenditures in green technologies, comprehensive energy consumption and production regulations, and responsible resource management. In light of the rapid advancements in sustainable development, the economic elements in China are reorienting to prioritize the provision of high-quality stability and consistent economic growth. Despite their emphasis on environmental change and CO₂ emissions, energy supplies—oil, gas, and coal—have historically been the primary drivers of GDP in developing countries [8]. Economic expansion increases energy input and consumption, which increases CO₂ emissions, but countries are unwilling to compromise revenues for environmental protection. China’s rapid growth has long been expected to benefit the world’s largest economy [9,10].

We employed Tapio-Z decoupling (T-ZDP) in the fuzzy logic model (F-LGM) to evaluate energy sources and CO₂ emissions [11]. This approach involves categorizing environmental factors based on their impact on CO₂ emissions and development, as well as the energy source and utilization used for energy input and output [12]. It became the standard method for studying CO₂ emissions by dividing them by GDP, energy input, and consumption [13,14]. Previous studies have shown that decoupling causes economic growth to rebound from estimated or pattern correlations of indicators [15,16]. This research study further develops the decoupling concept by employing T-ZDP on an individual basis. The decoupling approach is utilized in situations in which two distinct indicators are going in opposite directions, climbing, or falling. Similarly, if one variable is going to increase, the other variable will drop, and this will occur with a decoupling attitude of ±. Indicator pairs are displayed by T-ZDP [17]. The decoupling lies between ±1 and ±2 is the result of a steady movement that occurs until T-ZDP is established. This is a steady movement that occurs together until T-ZDP is attained, resulting in a location that falls between ±1 and ±2. This study employs a stochastic methodology to examine the energy consumption and inputs of the population, with a particular emphasis on energy input and output. The F-LGM technique is currently being used to re-conceptualize its uniqueness and to evaluate the possible action of specific indicators in countries. This is the theory that is currently being used [18]. F-LGM-derived T-ZDP has been expanded to assess the impact of propelling forces on environmental change through CO₂ emissions [19]. As a result, the environmental factor and energy input are indicated by CO₂ emissions and GDP per capita in this study, while the energy source and utilization remain unaffected [20,21].

Four distinct fundamentals of study that are associated with decoupling approaches have been revealed to be of diminished significance in numerous studies conducted in the USA and China regarding CO₂ emissions in the significance of four distinct fundamentals of study that are associated with decoupling approaches. Firstly, the most critical aspect of the literature review is the identification of socio-economic driving factors of CO₂ emissions using the index decomposition T-ZDP extraction method and the structure decomposition model [22,23,24]. Secondly, the relevant features illustrate the associated evaluation policies of CO₂ emissions during a period of significant expansion in the USA and China. The third facet illustrates the economy’s expansion, while the fourth facet provides a literature review on the non-accounting of CO₂ emissions using F-LGM-derived T-ZDP techniques. Furthermore, there is a dearth of research on decoupling, which has implications for the correlation between CO₂ emissions and beta decoupling approaches. An investigation demonstrated a novel correlation between GDP-based CO₂ emissions, energy input and utilization, and fluctuations in energy sector development [13,25,26]. The T-ZDP approach was also demonstrated using F-LGM. It is challenging to provide energy sources to a strong economy such as the USA in the absence of new and extensive technology, which may be entirely absent from the current technological infrastructures of countries regarding development areas [4,27,28]. China’s unique position in globalization allows the country to leverage on its relative returns and apply cutting-edge energy extraction and usage technology. Exploring the relationship between energy output and economic development for individual environmental consequences, one study used energy input and usage to examine decoupling on several levels and with different methodologies [29]. The focus of this research was the decoupling of energy input and consumption through T-ZDP. The predicted results of the countries indicated that Groups A–F experienced both strong and moderate decoupling [30].

Considering the aforementioned, the primary objective of the present study is to examine the dynamic relationships between GDP growth, CO₂ emissions, and energy sources in the USA and China, with a specific emphasis on the decoupling of economic growth from environmental impact. In order to meet this objective, the subsequent tasks are addressed: (1) examining the historical trends of energy production and consumption, CO₂ emissions, and GDP growth; (2) utilizing the Tapio-Z decoupling technique to determine the decoupling status and trends in both countries; (3) constructing a fuzzy logic model to investigate the intricate relationships between energy sources, CO₂ emissions, and GDP growth; and (4) predicting future trends of these variables under various scenarios, taking into account potential decoupling pathways. The primary contribution of this study is the decoupling with T-ZDP, as we independently calculate decoupling using covariance and variance [31]. We employed the T-ZDP technique in previous research, as opposed to conventional decoupling methods. Regarding the first task, the causes of decoupling and economic growth perturbation from CO₂ emissions in the USA and China have generally been studied in the existing literature. Technological advancements and extraction were demonstrated. Relating to the second task, the environmental impact assessment (EIA) is a methodical process that assesses the potential environmental repercussions of a proposed project or policy. It considers a wide range of factors, including biodiversity loss, air and water pollution, and climate change. Consequently, EIA can aid in the identification of potential negative impacts and inform decision-making to mitigate them. In order to determine the significant influence of CO₂ emissions on economic development through energy input and utilization, it is essential to establish a more comprehensive and articulate methodology. As for task three, we intended (F-LGM) to expand the T-ZDP technique to include the investigation of CO₂ emissions based on GDP. Lastly, for task four, we examined the T-ZDP between the GDP, energy input, energy output, and CO₂ emissions of energy input and output of crude energy sources from 1994 to 2023 in Groups A to F. This research delineates an attentive approach to the T-ZDP technique and its causal factors in the most recent eras of the USA and China.

The first section introduces the study’s purpose and originality. The second section’s construct relationships are analyzed from the author’s standpoint. Section 2 presents the literature review. Section 3 covers data collection and methodology. The results, analysis, and discussion are presented in Section 4. The study ends with some conclusions and suggestions in Section 5.

2. Literature Review

2.1. Energy Sources and CO₂ Emissions

Fossil fuels, along with other sources of energy, have been the primary drivers of economic expansion for decades. They are the foundation upon which industrial civilizations have been built. Despite this, our dependence on them has ultimately led to a significant impact on the environment. As a result of the combustion of these fuels, which largely consist of coal, oil, and natural gas, CO₂ emissions and other greenhouse gases (GHGs) are emitted into the environment [32]. The warming of the planet and changes in climate are both caused by this process. The urgent requirement to mitigate these effects has resulted in a global shift towards energy sources that are more sustainable and less harmful to the environment [33,34]. Separating the detrimental impacts of the rapid economic expansion of China and the USA on the environment is one of the most significant hurdles [35]. This involves increasing economic output without negatively impacting the environment. In this study, we examine this connection using the Tapio-Z decoupling model (Appendix A). It differentiates between two types of decoupling: relative decoupling, in which environmental impacts are increasing at a slower rate than economic growth, and absolute decoupling, in which economic expansion is accompanied by a drop in environmental impacts [36].

Different case studies of decoupling may be found in China and the USA, two of the largest economies in the world and substantial contributors to GHG emissions. With China’s rapid economic growth, major environmental costs have frequently been incurred [26,37]. Decoupling has occurred, both relative and, in some instances, absolute, as a result of China’s recent implementation of policies that promote energy efficiency, renewable energy, and industrial restructuring [38]. Although it has historically been a big emitter, the USA has also taken steps to reduce its carbon footprint through the implementation of regulations, the development of technological improvements, and a transition towards cleaner energy sources [39]. On the other hand, the nation is confronted with difficulties in attaining full decoupling, especially in areas such as transportation [40]. The analysis is also based on the F-LGM, which can be a useful tool for analyzing the complex relationship between economic growth and environmental impact [41,42]. This study was carried out to differentiate the analyses. These models have the ability to provide insights into the possibility for decoupling and to guide policy decisions by considering a variety of elements, including technical improvements, rules and regulations enacted by the government, and societal considerations [43].

2.2. Industrial Sectors, Economic Growth, and CO₂ Emissions

The USA and China have been the focus of a recent study that investigated the intricate relationship that exists between industrialization, economic expansion, and CO₂ emissions [44]. It has been repeatedly demonstrated through research that there is a strong association between economic growth and greater energy consumption, which ultimately leads to higher levels of greenhouse gas emissions in both places. Since the beginning of industrialization in the USA, which was driven by fossil fuels, the country has accumulated a significant amount of carbon emissions [45]. The legacy of past emissions and the current dependency on fossil fuels for transportation and other sectors continue to pose significant challenges, despite the fact that the nation has made progress in diversifying its energy balance to include additional sources of renewable energy [14,46,47]. Nevertheless, China has experienced a rapid acceleration of its industrialization process over recent decades, which has led to a substantial rise in the amount of carbon dioxide emissions and the amount of coal that is used [16,48]. The sheer volume of China’s industrial production and energy demand is a huge barrier to the decoupling of economic growth from carbon emissions, despite the fact that China has been making significant investments in alternatives to fossil fuels, such as solar and wind power [49].

Furthermore, research has been conducted to identify the specific elements that are responsible for this association. The structure of the economy (for example, its reliance on heavy industries), technological developments in energy efficiency, energy intensity (the amount of energy consumed per unit of GDP), and government policies aiming to support economic growth and environmental sustainability are some of the elements that contribute to this phenomenon [50]. According to some research findings, China has achieved significant headway in recent years in terms of decoupling economic growth from carbon emissions. Despite this, new actions are necessary in order to speed up the transition to an economy with lower carbon emissions, including the following: encouraging environmentally responsible patterns of consumption, improving energy efficiency, and investing in technologies that utilize renewable energy sources [51].

When conducting research on the relationship between industrialization, economic growth, and CO₂ emissions in the USA and China, it is common practice to overlook important aspects of the relationship. Most research has focused on trends at the national level, ignoring the contributions of other sectors and variances at the regional level [52]. Rarely are investigations conducted into the consequences of social and environmental justice, and the effects that will be felt over the long term are typically ignored [53]. Furthermore, the dynamic and nuanced interactions that occur between these elements are usually missing from studies that have been conducted up until this point. A more comprehensive understanding of the challenges and opportunities associated with achieving sustainable economic growth while mitigating climate change in both countries should be achieved through future research that incorporates regional analyses, in-depth sectoral studies, social and environmental justice considerations, long-term projections, and dynamic modeling [54]. This will allow for a better understanding of the situation and will effectively address these gaps.

Finally, despite its extensive nature, the existing literature on the linkage between energy, the economy, and the environment frequently suffers from several constraints. Nuanced analyses of energy portfolios are frequently impeded by the overemphasis of fossil fuel dependence and aggregate energy sources in studies, which also neglect embodied emissions [55]. In terms of industrial impacts, the emphasis on industry as the primary polluter leads to a frequent failure to account for the intricate determinants of industrial emissions and sectoral interdependencies [56]. In the same vein, the discourse regarding economic growth and CO₂ emissions is frequently polarized, with inadequate consideration given to decoupling strategies and the constraints of GDP as the sole indicator of progress. Therefore, the key areas for future research are identified through a critical review of this literature. It is imperative to conduct more detailed analyses of energy mixtures that consider embodied emissions and concentrate on the obstacles to the adoption of renewable energy.

3. Methodology

3.1. The Tapio-Z Decoupling (T-ZDP) Method and Energy Sources

In the present investigation, we make use of the T-ZDP model, which is an effective instrument for evaluating the connection between economic expansion and the influence that CO₂ emissions have on the environment. This is especially true when considering the relationship between energy input and output and the impact that they have on CO₂ emissions. These variables are connected to one another and co-integrated across a variety of industries, which are the factors that lead to economic growth [57,58]. The groups are arranged in the F-LGM according to environmental criteria, including CO₂ emissions and GDP, and we investigate technology by decoupling [59]. The purpose of this model is to provide an understanding of the degree to which a region or country is decoupling its economic growth from its environmental impact. This is accomplished by conducting an analysis of the decoupling status between economic growth and a variety of environmental indicators. For the T-ZDP calculation, this information (data) goes through adjustments based on covariance and variance. The decoupling process reveals individual value variations in CO₂ emissions based on energy input and utilization. It illustrates how a change of one percent can have an influence on energy sources, as well as how the introduction of new technologies can have an effect on the utilization of energy sources in the USA and China [16,60,61]. After ensuring that all the requirements of the group are met, the T-ZDP model was selected for the groups in the F-LGM (

Table 1. Variables’ definition and codes.

Variables	Code	F-LGM	Description
CO2 emissions	CO2	Environment factors	Based on utilization, per capita CO2 emissions.
Gross domestic product	GDP		Purchasing power parity (PPP) is used to calculate the per capita GDP. The gross domestic product is converted to international dollars and divided by the total population.
Hydrocarbon extraction (TWh)	HDP	Energy source and utilization	The quantity of energy that is emitted during various combustion processes.
Hydrocarbon utilization (EJ)	HDC
Natural gas extraction (TWh)	NGE		A long-term transformation in the extraction and utilization of gas. It illustrates the rapidity with which countries increase the extraction level through various processes.
Natural gas utilization (EJ)	NGU
Coal extraction (TWh)	CPR		Utilized in the iron and steel industries to generate electricity and is a highly significant element.
Coal utilization (EJ)	CCS

Note: TWh (terawatt hour) and EJ (exajoules) are the units of measurement for the extraction and utilization of energy, including oil, gas, and coal.

). The Tapio-Z decoupling method is an effective instrument for determining the nature of the connection between economic expansion and environmental impact, particularly the emission of CO₂. In this study, it offers essential insights into how various energy decisions influence decoupling outcomes when applied to energy sources. Economic growth is frequently accompanied by rising carbon emissions in economies that are dependent on fossil fuels. This type of coupling is known as weak or expansion decoupling [42].

Within the scope of this analysis, T-ZDP can be incorporated with the energy source indicators to better understand the components that are responsible for decoupling. In this study, we identify areas where changes are required in order to guide policy decisions by analyzing the decoupling status of various fossil fuel energy sources. On the other hand, transitioning to renewable energy sources has the potential to dramatically improve decoupling, which could result in relative or even strong decoupling. Reducing the energy intensity of economic activity is one of the most important factors in attaining decoupling, and improving energy efficiency across all sectors is a key component in this process. Through this analysis, we can determine which regions require improvement. With the decoupling of economic growth and CO₂ emissions from the consumption of fossil fuels, governments will be free to target certain sectors for energy efficiency improvements or investments in renewable energy technology. This is demonstrated by the great growth demonstrated by the USA and China [62]. The success of policies that promote the adoption of clean energy may also be evaluated by policymakers through analysis of the decoupling between economic growth and the consumption of renewable energy.

3.2. Data Estimation

Table 1 shows the definitions of the variables and how they have been used in the analysis. The dependent variables are GDP and CO₂ emissions. As indicated in Table 1, it has been concluded that the indicator definitions containing symbols have been categorized. The World Bank’s online database was used to gather the information [63].

The exact combination of energy source indicators (Table 1) that are utilized in an economy, technological improvements in energy production and utilization, and regulations that are implemented by the government are all factors that have a considerable impact on the efficiency of decoupling techniques. It is possible for policymakers and researchers to obtain significant insights into the effectiveness of various energy policies and strategies in reaching sustainable development goals by conducting an analysis of decoupling states for a variety of energy sources.

3.3. Fuzzy Logic Models

Fuzzy logic models offer a method that is both rigorous and effective for assessing complicated energy systems [64]. This is especially true in large economies such as the USA and China. The inherent uncertainty and imprecision that are present in energy systems can be effectively managed by these models, which are particularly talented in this regard. Through the incorporation of a wide range of elements, such as economic growth, technology advancements, and policy changes, fuzzy logic models have the potential to provide important insights into patterns of energy use, production trends, and environmental repercussions [65]. Utilizing a fuzzy logic model and the Tapio-Z decoupling technique, this study employs a combined approach to further investigate the intricate relationships between energy sources and their impact on GDP per capita and CO₂ emissions. The fuzzy logic model enables us to capture the non-linear and complex interactions between the variables of interest, while the Tapio-Z method enables us to categorize the decoupling status of economic growth from CO₂ emissions. Specifically, we consider the decoupling status identified by the Tapio-Z analysis when modeling CO₂ and GDP per capita as functions of various energy sources, i.e., HDP, HDC, NGE, NGU, CPR, and CCS. The core of our econometric model is represented by the following equations:

$$CO{2}_{it}={\beta }_0+{\beta }_{1}HD{P}_{it}+{\beta }_{2}HD{C}_{it}+{\beta }_{3}NG{E}_{it}+{\beta }_{4}NG{U}_{it}+{\beta }_{5}CP{R}_{it}+{\beta }_{6}CC{S}_{it}+{ϵ}_{it}$$

(1)

$$GD{P}_{it}={\alpha }_0+{\alpha }_{1}HD{P}_{it}+{\alpha }_{2}HD{C}_{it}+{\alpha }_{3}NG{E}_{it}+{\alpha }_{4}NG{U}_{it}+{\alpha }_{5}CP{R}_{it}+{\alpha }_{6}CC{S}_{it}+{\mu }_{it}$$

(2)

where $CO{2}_{it}$ and $GD{P}_{it}$ are the CO₂ emissions and GDP per capita for country i at time t, respectively. Based on the information in Table 1, the independent variables for country i at time t are $HD{P}_{it}, HD{C}_{it}, NG{E}_{it}, NG{U}_{it}, CP{R}_{it}, \mathrm{a}\mathrm{n}\mathrm{d} CC{S}_{it}$. The intercepts in these equations are ${\beta }_0$ and ${\alpha }_0$. Additionally, ${\beta }_1 \mathrm{t}\mathrm{o} {\beta }_6 \mathrm{a}\mathrm{n}\mathrm{d} {\alpha }_1 \mathrm{t}\mathrm{o} {\alpha }_6$ are coefficients, and ${ϵ}_{it}$ and ${\mu }_{it}$ are error terms. We calculated the effect of each independent variable on CO₂ and GPD. The phases of the Tapio-Z decoupling technique were deconstructed and compared to the equations of the variables. The decoupling techniques were implemented following the data preparation process to approximate the individual change in the response variable following a 1% change in the explanatory variables. Initially, the Tapio-Z method involved the calculation of CO₂ emissions in relation to GDP per capita, followed by the estimation of explanatory variables for each response variable. This metric quantifies the percentage increase in CO₂ emissions corresponding to a 1% increase in GDP per capita. Additionally, the response variable was based on GDP, and the initial stage percentage change was calculated solely on GDP. Subsequently, a 1% change was calculated for CO₂ emissions in HDP, HDC, NGE, NGU, CPR, and CCS. Then, we assigned each period for each country to one of the Tapio-Z decoupling types based on the decoupling calculation. Although the original Tapio method employs thresholds, the Z-score approach is frequently chosen due to its reduced sensitivity to outliers and its ability to modulate the decoupling factor based on its standard deviation. Subsequently, we established thresholds that are typically derived from the standard normal distribution in order to classify decoupling states. Next, we classified the variables based on the response and explanatory variables based on the fuzzy logic model. The variables were distributed into two categories: environmental factors and energy input and output.

In this study, we employed fuzzy logic models to map inputs to outputs by operating on a set of rules and membership functions. The process is concisely described, with an emphasis on the input and output of energy. First, we converted the fuzzy sets using energy input (energy input and output) and relevant environmental factors (e.g., CO₂ emissions) converted into fuzzy sets. Secondly, based on decoupling, the functions assigned degrees of membership (between 0 and 1) to each input value, indicating its level of association with fuzzy sets as low, medium, or high. Furthermore, we employed a decoupling technique to compute the data. It serves as an illustration of the economic growth, population, energy input, and CO₂ emissions in the USA and China [66], as well as the correlation between energy input and output utilization. The uncomfortable reality that policymakers must confront is that economic expansion is ecologically unsustainable. The primary objective of this study is, therefore, to investigate the decoupling of CO₂ emissions using T-ZDP with the F-LGM. Additionally, the study examines the GDP change and the decoupling factor exerted by the F-LGM. The variables’ definitions and their application in the analysis are illustrated in Table 1. The datasets from the USA and China were analyzed using panel data [67].

The T-ZDP modeling technique was used to compute the decoupling, as shown in Section 4, which correlated a 1% change in CO₂ emissions to a 1% change in GDP. There are six divisions in total, distributed between 1994 and 2023. Two technical steps were used to depict the decoupling computation. Covariance and variance ratios with years (n − 1) were used to calculate the first decoupling every five years. A decoupling value was calculated every five years by comparing the average change of the dependent variable to a beta value. Additionally, the second step was to classify the decoupling distribution into three levels: decoupling, negative decoupling, and coupling. The critical decoupling aspects were verified by the positive (+1 to +2) and negative (−1 to −2) decoupling aspects.

Based on the percentage change over a period of five years, we computed the T-ZDP decoupling attitude. In addition, the beta findings were computed, which include the average change in CO₂ emissions by explanatory factors as well as the covariance/variance based on five divided by four. Based on the findings of previous studies, the most important contribution made by this study is the alpha analysis that decouples attitudes from other factors. A more accurate representation of the percentage change in CO₂ emissions is presented, broken down by GDP, population, energy input, and utilization [68]. The decoupling values in the T-ZDP model indicated that zero and its subdivisions maintain the characteristic attitude towards decoupling. Meanwhile, if there is a change in the catch-up growth value and it is greater than zero, this demonstrates that the variable has a decoupling effect. According to the findings of previous research, the decoupling technique includes negative decoupling, strong coupling, and expensive coupling [69]. There was a percentage change in CO₂ emissions that was influenced by the percentage change in energy input and utilization between the highest and lowest decoupling levels, as stated in the T-ZDP. The positive and negative attitudes associated with decoupling represent different scenarios, including strong, weak, recessive, or expanding negative situations.

The challenges include the necessity of maintaining a balance between environmental preservation and rapid economic development, as well as addressing the ongoing reliance on coal and air pollution. Fuzzy logic models have been employed to address a variety of energy-related issues in both the USA and China. They may also be implemented to enhance energy efficiency in the transportation, industrial, and building sectors, among other sectors. By analyzing a variety of aspects, including energy pricing, occupancy patterns, and weather conditions, fuzzy logic models are able to provide recommendations for efficient energy use. In this manner, the energy input (HDP, NGE, CPR) and utilization (HDC, NGU, CCS) of the USA and China are taken into consideration separately with T-ZDP attitudes. Based on the individual change in decoupling, an analysis was performed to determine the actual percentage change in CO₂ emission caused by the utilization of environmental sources in each country. Furthermore, the incorporation of renewable energy sources into the grid can also be facilitated by these models, which take into consideration a variety of aspects, including grid stability, energy storage, and fluctuations in the weather. As the complexity and interconnectedness of energy systems continues to increase, it is anticipated that fuzzy logic models will become increasingly indispensable [70]. The incorporation of fuzzy logic with other advanced methodologies, such as artificial intelligence and machine learning, can help researchers and policymakers improve their capacities in the areas of energy analysis, planning, and decision-making. However, if the decoupling value in energy input and utilization is smaller than −1, then the situation is different.

The effects of CO₂ emissions are reduced by the use of various technologies. Capabilities, and new strategic policies for the utilization of energy sources are adjusted accordingly. GDP was utilized in this study to investigate the impact of energy input and utilization on CO₂ emissions. Lastly, we will be able to determine the future of energy systems based on our ability to harness the potential of breakthrough technologies such as fuzzy logic to overcome the challenges of cost, security, and sustainability.

4. Results and Discussion

The T-ZDP link between CO₂ emissions and GDP is employed as the basis for the decoupling estimation in this work. The GDP, population, energy input and utilization, and population data in China and the USA were used. Each piece of information was gathered from Our World in Data between the years 1994 and 2023. The results demonstrate that the decoupling condition exhibits elasticity within the low, medium, and high decoupling ranges. The F-LGM evaluated the covariance, variance, alpha, and beta of each cohort every five years. The research analyzed the predictor variables, which are energy sources and utilization, in relation to the response variables, which are environmental issues, as well as the one percent change in CO₂ emissions that were recorded in the USA and China and the impact that these outcomes have on environmental policy. Furthermore, the USA, which has a long history of being the dominant producer of hydrocarbons, has witnessed a rebound in the production of oil and gas within its borders because of technical breakthroughs such as fracking. This has resulted in the USA moving closer to achieving energy independence, but it also creates difficulties in striking a balance between energy security and environmental concerns [71]. The continuous reliance on fossil fuels poses enormous threats to climate change, even though natural gas has been an essential component in the process of coal’s transformation into energy. In contrast, China’s energy generation is significantly reliant on coal, resulting in significant CO₂ emissions. Although efforts are being made to diversify its energy balance by incorporating renewable sources and nuclear power, coal continues to be the primary source of energy. China is confronted with the challenge of reconciling environmental sustainability with accelerated economic expansion [72]. The transition from coal dependence remains a substantial obstacle, even though the country is actively investing in renewable energy technologies and pursuing energy efficiency measures. The critical challenge of decoupling economic development from carbon emissions is shared by both the USA and China. Although technological advancements and the transition to natural gas have made progress in the USA, a substantial departure from fossil fuels is necessary to achieve a genuinely sustainable energy future. China is confronted with an even greater obstacle due to its substantial dependence on coal and its accelerated economic expansion.

In addition, the USA has demonstrated some progress in the decoupling of economic growth from CO₂ emissions, despite its longstanding reliance on fossil fuels and high per capita CO₂ emissions. Increased energy efficiency, the development of renewable energy sources, and the transition toward natural gas are all indicative of this progress. Nevertheless, a substantial obstacle stands in the way of attaining robust decoupling, which involves a simultaneous reduction in CO₂ emissions and economic growth. Political polarization on climate issues, a large and energy-intensive transportation sector, and a strong reliance on fossil fuels are all obstacles that the USA continues to encounter [47]. Conversely, coal-fired power plants and heavy industry have been the primary contributors to the significant increase in CO₂ emissions that China has experienced because of its accelerated industrialization. Nevertheless, China has made significant progress in the decoupling of economic growth from carbon emissions. This is primarily due to the transition to renewable energy sources, the enhancement of energy efficiency, and the implementation of government policies that are designed to decrease carbon intensity. Nevertheless, the process of achieving robust decoupling remains complex.

China’s most recent investments in energy efficiency and renewable energy initiatives provide a glimmer of optimism for a more sustainable future. The interpretation of the analysis is based on the individual change in year and groupings. For instance, in the initial phase, we examined the percentage change in CO₂ emissions based on predictor variables, while in the subsequent phase, we examined the change in individual groups.

4.1. Economic Growth in Environmental Factor

In the T-ZDP computation, the estimated results of economic growth in the USA and China indicated completely different perspectives regarding the percentage change in CO₂ emissions. China routinely demonstrates significantly better rates of GDP growth than the USA does across most categories. As an illustration, in Figure 1, the growth rate of China in Group B is 0.240, whereas the growth rate of the USA is 0.022.

Table 2. T-ZDP decoupling (part 1).

T-ZDP Decoupling
No. of Groups	No	Years		GDP			One Percent Change in CO2 Emissions of USA			Percentage Change in GDP of USA		One Percent Change in CO2 Emissions of China			Percentage Change in GDP of China
				USA	China		GDP	HDP	HDC	HDP	HDC	GDP	HDC	NGU	HDC	NGU
Group A	1	1994	Environmental Factors			Energy Source and Utilization
	2	1995		0.014	−0.009		0.014	0.016	0.012	0.892	1.279	−0.009	−0.075	0.014	0.117	−5.534
	3	1996		0.011	0.061		0.011	0.008	0.003	1.399	2.633	0.061	0.035	0.093	1.759	0.376
	4	1997		0.030	−0.026		0.030	0.003	0.016	8.624	0.219	−0.026	−0.012	0.047	2.290	−0.248
	5	1998		0.011	0.009		0.011	−0.004	0.006	−2.603	−0.705	0.009	−0.040	−0.011	−0.226	3.652
Group B	6	1999		0.022	0.038		0.022	0.007	0.013	3.074	0.571	0.038	−0.021	−0.005	−1.827	4.404
	7	2000		0.023	0.240		0.023	0.008	0.013	2.929	0.611	0.240	0.012	0.057	20.338	0.209
	8	2001		−0.020	0.150		−0.020	0.013	0.011	−1.550	1.151	0.150	0.027	0.055	5.541	0.494
	9	2002		−0.002	0.084		−0.002	−0.020	−0.014	0.107	1.396	0.084	0.058	0.024	1.466	2.385
	10	2003		0.022	0.436		0.022	0.009	0.010	2.364	0.985	0.436	0.076	0.080	5.720	0.956
Group C	11	2004		0.017	0.410		0.017	0.004	0.005	4.500	0.783	0.410	0.101	0.113	4.056	0.896
	12	2005		0.038	0.484		0.038	0.021	0.020	1.790	1.072	0.484	0.130	0.105	3.721	1.242
	13	2006		0.011	0.183		0.011	−0.003	0.003	−3.856	−1.052	0.183	0.026	0.033	6.943	0.800
	14	2007		−0.006	−0.119		−0.006	−0.017	−0.008	0.378	1.976	−0.119	−0.017	−0.007	6.851	2.554
	15	2008		0.015	−0.145		0.015	−0.005	−0.003	−3.136	1.699	−0.145	−0.003	0.010	54.343	−0.268
Group D	16	2009		−0.022	−0.085		−0.022	−0.031	−0.044	0.713	0.704	−0.085	0.014	0.011	−5.941	1.321
	17	2010		−0.058	−0.046		−0.058	−0.052	−0.079	1.123	0.656	−0.046	0.022	0.007	−2.138	2.945
	18	2011		0.051	−0.076		0.051	0.040	0.022	1.260	1.861	−0.076	−0.009	−0.012	8.669	0.699
	19	2012		0.004	−0.042		0.004	−0.002	−0.019	−1.763	0.117	−0.042	−0.001	−0.002	66.166	0.329
	20	2013		−0.012	0.125		−0.012	−0.016	−0.039	0.726	0.421	0.125	−0.054	−0.051	−2.329	1.063
Group E	21	2014		0.037	0.176		0.037	0.020	0.012	1.859	1.674	0.176	−0.049	−0.042	−3.561	1.168
	22	2015		0.022	0.169		0.022	−0.009	0.004	−2.441	−2.459	0.169	−0.032	−0.019	−5.233	1.677
	23	2016		−0.029	0.264		−0.029	0.000	−0.010	57.739	0.011	0.264	−0.058	−0.128	−4.572	0.451
	24	2017		−0.017	0.173		−0.017	0.000	−0.003	88.303	0.055	0.173	−0.008	−0.010	−20.756	0.799
	25	2018		−0.004	0.100		−0.004	0.012	0.000	−0.328	−51.549	0.100	0.008	0.001	12.415	12.302
Group F	26	2019		0.072	−0.112		0.072	0.045	0.043	1.595	1.035	−0.112	0.016	0.004	−7.124	3.709
	27	2020		−0.108	0.306		−0.108	−0.076	−0.034	1.430	2.202	0.306	0.371	0.560	0.825	0.662
	28	2021		0.007	−0.259		0.007	0.033	0.072	0.225	0.453	−0.259	−0.302	0.518	0.858	−0.583
	29	2022		0.001	−0.262		0.001	0.060	0.073	0.025	0.826	−0.262	−0.315	1.868	0.832	−0.169
	30	2023		0.004	−0.359		0.004	0.239	0.073	0.019	3.268	−0.359	−0.302	1.174	1.189	−0.257

Note: Variable definitions are stated in Table 1.

and

Table 3. T-ZDP decoupling (part 2).

T-ZDP Decoupling
No. of Groups	No	Years		GDP			One Percent Change in CO2 Emissions of USA			Percentage Change in GDP of USA		One Percent Change in CO2 Emissions of China			Percentage Change in GDP of China		One Percent Change in CO2 Emissions of USA			Percentage Change in GDP of USA		One Percent Change in CO2 Emissions of China			Percentage Change in GDP of China
				USA	China		GDP	NGE	NGU	NGE	NGU	GDP	NGE	NGU	NGE	NGU	GDP	CPR	CCS	CPR	CCS	GDP	CPR	CCS	CPR	CCS
Group A	1	1994	Environmental Factors			Energy Source and Utilization
	2	1995		0.014	−0.009		0.014	0.043	0.009	0.327	4.990	−0.009	0.009	−0.055	−1.015	−0.158	0.014	0.006	0.009	2.453	0.660	−0.009	−0.055	−0.088	0.160	0.623
	3	1996		0.011	0.061		0.011	0.003	0.001	3.044	2.691	0.061	0.001	0.038	47.522	0.034	0.011	−0.002	0.001	−4.676	−2.452	0.061	0.040	−0.013	1.550	−3.105
	4	1997		0.030	−0.026		0.030	0.004	0.009	7.729	0.444	−0.026	0.009	−0.010	−3.066	−0.868	0.030	0.008	0.007	3.799	1.058	−0.026	−0.011	−0.055	2.479	0.194
	5	1998		0.011	0.009		0.011	−0.004	0.001	−3.166	−6.815	0.009	0.001	−0.028	17.164	−0.018	0.011	0.000	0.003	168.922	0.019	0.009	−0.028	−0.041	−0.317	0.689
Group B	6	1999		0.022	0.038		0.022	0.003	0.006	6.533	0.538	0.038	0.006	−0.019	5.958	−0.330	0.022	0.007	0.010	3.012	0.760	0.038	−0.024	−0.035	−1.590	0.677
	7	2000		0.023	0.240		0.023	0.005	0.005	5.106	0.917	0.240	0.005	0.031	48.147	0.161	0.023	0.005	0.006	4.715	0.774	0.240	0.013	0.008	18.338	1.721
	8	2001		−0.020	0.150		−0.020	0.014	0.011	−1.418	1.277	0.150	0.011	0.066	13.650	0.167	−0.020	0.012	0.017	−1.716	0.671	0.150	0.019	0.025	7.687	0.784
	9	2002		−0.002	0.084		−0.002	−0.026	−0.029	0.084	0.879	0.084	−0.029	0.101	−2.897	−0.288	−0.002	−0.033	−0.025	0.066	1.323	0.084	0.051	0.053	1.656	0.964
	10	2003		0.022	0.436		0.022	0.000	−0.001	−90.880	0.195	0.436	−0.001	0.117	−349.732	−0.011	0.022	0.001	0.003	19.675	0.434	0.436	0.072	0.080	6.072	0.900
Group C	11	2004		0.017	0.410		0.017	−0.004	−0.004	−4.909	0.879	0.410	−0.004	0.126	−102.268	−0.032	0.017	0.005	0.000	3.734	−60.388	0.410	0.105	0.102	3.918	1.027
	12	2005		0.038	0.484		0.038	0.010	0.011	3.678	0.919	0.484	0.011	0.126	43.510	0.088	0.038	0.012	0.016	3.136	0.744	0.484	0.109	0.105	4.428	1.040
	13	2006		0.011	0.183		0.011	−0.009	−0.003	−1.342	2.859	0.183	−0.003	0.075	−61.263	−0.040	0.011	−0.005	−0.003	−2.341	1.496	0.183	0.066	0.069	2.784	0.954
	14	2007		−0.006	−0.119		−0.006	−0.015	−0.012	0.415	1.221	−0.119	−0.012	0.043	9.577	−0.290	−0.006	−0.013	−0.011	0.503	1.104	−0.119	0.025	0.043	−4.702	0.586
	15	2008		0.015	−0.145		0.015	−0.007	−0.006	−2.202	1.062	−0.145	−0.006	0.077	22.947	−0.082	0.015	−0.006	−0.005	−2.581	1.169	−0.145	0.046	0.049	−3.172	0.933
Group D	16	2009		−0.022	−0.085		−0.022	−0.038	−0.035	0.580	1.095	−0.085	−0.035	0.061	2.429	−0.576	−0.022	−0.033	−0.038	0.678	0.874	−0.085	0.029	0.016	−2.890	1.802
	17	2010		−0.058	−0.046		−0.058	−0.046	−0.050	1.281	0.911	−0.046	−0.050	0.002	0.925	−32.911	−0.058	−0.058	−0.067	1.003	0.872	−0.046	0.018	0.023	−2.555	0.774
	18	2011		0.051	−0.076		0.051	0.073	0.059	0.698	1.228	−0.076	0.059	−0.097	−1.274	−0.610	0.051	0.042	0.039	1.200	1.096	−0.076	−0.034	−0.020	2.222	1.739
	19	2012		0.004	−0.042		0.004	0.055	0.025	0.071	2.239	−0.042	0.025	−0.025	−1.689	−0.971	0.004	0.001	−0.004	4.820	−0.217	−0.042	−0.006	0.005	6.572	−1.155
	20	2013		−0.012	0.125		−0.012	0.041	0.003	−0.287	14.761	0.125	0.003	0.000	44.634	−10.412	−0.012	−0.021	−0.030	0.557	0.716	0.125	−0.031	−0.023	−4.077	1.321
Group E	21	2014		0.037	0.176		0.037	0.071	0.047	0.512	1.534	0.176	0.047	0.035	3.777	1.316	0.037	0.004	0.011	9.443	0.363	0.176	−0.020	−0.006	−8.737	3.471
	22	2015		0.022	0.169		0.022	0.011	0.018	2.004	0.597	0.169	0.018	0.068	9.218	0.270	0.022	−0.001	−0.001	−18.904	0.999	0.169	−0.014	−0.013	−12.191	1.080
	23	2016		−0.029	0.264		−0.029	−0.067	−0.005	0.430	14.417	0.264	−0.005	0.055	−57.297	−0.084	−0.029	−0.018	−0.023	1.578	0.776	0.264	−0.018	−0.015	−14.791	1.189
	24	2017		−0.017	0.173		−0.017	−0.025	−0.004	0.677	6.543	0.173	−0.004	0.018	−45.525	−0.212	−0.017	−0.020	−0.022	0.860	0.870	0.173	−0.013	−0.009	−13.476	1.429
	25	2018		−0.004	0.100		−0.004	0.005	0.003	−0.843	1.483	0.100	0.003	0.024	30.978	0.133	−0.004	−0.003	−0.007	1.228	0.476	0.100	0.006	0.006	17.283	0.975
Group F	26	2019		0.072	−0.112		0.072	0.046	0.034	1.542	1.382	−0.112	0.034	0.033	−3.329	1.016	0.072	0.024	0.016	2.924	1.533	−0.112	0.013	0.009	−8.450	1.549
	27	2020		−0.108	0.306		−0.108	−0.060	−0.075	1.806	0.803	0.306	−0.075	0.641	−4.109	−0.116	−0.108	−0.088	−0.140	1.228	0.627	0.306	0.444	0.430	0.689	1.033
	28	2021		0.007	−0.259		0.007	0.048	0.035	0.153	1.393	−0.259	0.035	0.056	−7.479	0.616	0.007	0.022	−0.039	0.336	−0.570	−0.259	−0.125	−0.077	2.067	1.633
	29	2022		0.001	−0.262		0.001	0.060	0.054	0.025	1.106	−0.262	0.054	0.924	−4.848	0.058	0.001	0.027	−0.028	0.055	−0.974	−0.262	0.138	0.055	−1.896	2.532
	30	2023		0.004	−0.359		0.004	0.162	0.148	0.028	1.100	−0.359	0.148	−0.583	−2.432	−0.253	0.004	−0.023	−0.031	−0.193	0.739	−0.359	−0.762	0.124	0.471	−6.149

Note: Variable definitions are stated in Table 1.

show that China’s growth rate reaches its highest point in Group C at 0.484, whereas the growth rate of the USA is 0.037 over the same period. Except for the first four numbers in Group A, China consistently displays better growth rates in all of the categories. In addition to this, it exhibits the highest growth rate (0.484 in Group C) and the lowest growth rate (−0.359 in Group F) among all the observations, which highlights the fact that its growth trajectory is highly unpredictable. In contrast, the USA shows negative growth in several instances, particularly in Groups D, E, and F. Its continued rapid expansion might be attributable, in large part, to the economic changes and policies that have encouraged investments in areas such as manufacturing, infrastructure, and technological innovation [73]. Meanwhile, the fast industrialization of China and the enormous scale of its market might have played a role in the country’s impressive economic performance [74]. It is possible that the two nations’ growth paths have been affected differently by global economic conditions, trade relations, and technology advancements. As an illustration, the growth rate of the USA in Group D is −0.058, but the growth rate of China is −0.046.

There is a striking disparity in the economic performances of the USA and China over various time periods, which is most likely indicated by the differences between the groupings. A more dynamic and robust economic trajectory for China is indicated by the fact that its GDP growth has continuously surpassed that of the USA. On the other hand, this rapid economic growth in China, which has been fueled by industrialization and energy consumption, has most likely come at a major cost to the environment, including an increase in CO₂ emissions [75]. Even though China has had amazing economic success, the country’s fast industrialization has also resulted in a significant increase in energy consumption. China is mostly dependent on fossil fuels such as coal for its energy needs. Massive CO₂ emissions caused by this heavy use of fossil fuels have accelerated global warming. On the other hand, the USA has been working to switch to cleaner energy sources, which might reduce CO₂ emissions relative to GDP, even while the economy is slowing down [76]. Across various time periods, the table shows that the USA and China’s GDP growth trajectories could not be more different. Repeatedly, China outpaces the USA in terms of growth rate.

According to Figure 1, while the USA experienced negative growth in Group D (−0.058 and −0.075), China maintained growth (0.041 and 0.183). Similarly, in Group F, the USA experienced negative growth (−0.108 and −0.306), whereas China continued to show substantial growth (0.169 and 0.264).

The T-ZDP results were calculated by subtracting the attitude values from the results of a 1% change in CO₂ emissions. The decoupling analysis separately examined the percentage change in CO₂ emissions based on growth, population, energy input, and consumption, as the study’s main contribution [77]. However, we determined the anticipated outcomes for each group (A, B, C, D, E, and F) using the annual decoupling values. In Group A, both countries exhibited growth, with the USA showing a slightly higher growth rate (0.014) compared to China (0.008). A stronger economic performance is suggested by the fact that China’s average GDP growth rate was considerably higher than that of the USA (0.037 vs. −0.004). Additionally, the standard deviations (0.033 for the USA and 0.224 for China) indicate that both nations suffered from fluctuations in growth rates across various categories. Additionally, growth was maintained in most categories during periods of economic decline in the USA, which is indicative of a more robust and resilient economy. The extraordinary volatility of China’s economic trajectory is illustrated by the fact that its growth rate in Group C is 0.484 and that in Group F is −0.359, when compared to all other observations. Thus, it meant that nations should slow their rapid economic expansion and reorganize their policies to be more sustainable. China and the USA, along with showing a percentage change in CO₂ emissions due to the technological revolution, are the countries with the highest decoupling values [78]. The decoupling attitude is higher than −2, indicating a rise in CO₂ emissions. To rein in these environmental impacts, they must revise their sustainability policies. It is also known that China has implemented carbon capture and storage plans or hydrogen-based technologies in preparation for deep decarbonization scenarios that are expected to result in a decrease in costs over the next two decades. Energy-saving technology is a key component in the fight against climate change because of the impact it has on the expansion of the economy. It was found that technical innovation reduces the CO₂ emissions of various sectors by around 89%. It was also proved that the USA was the birthplace of significant decoupling with regard to energy production, which has far-reaching policy consequences for CO₂ mitigation and energy efficiency [79]. Such regulations should be put in place to enhance long-term control of environmental problems. The GDP and population records of the USA and China are the most radically different. Even though China has the highest population in the world, its GDP has increased in proportion to its population since 2015, and there has been minimal change in the total population and GDP per capita. The USA exhibits the most disengaged stance with respect to the detrimental aspects of T-ZDP. Members of Group F, which includes China, advocate for pro-decoupling sentiments. However, in Group F, the alpha decoupling attitude reveals that in five years, the USA will have a positive attitude, and China will have a negative one. Consequently, the USA and China are very active in the growth sector, which is characterized by new and dynamic technologies [80].

4.2. Energy Source and Utilization

The analysis’ interpretation depends on the year and grouping changes. In one phase, we analyzed the percentage change in CO₂ emissions based on predictor variables, whereas in the next, we examined individual groups, as seen in Table 2 and Table 3 above. At the beginning of the process, the first stage involved conducting a study of the percentage changes that have occurred in four variables (HDP, HDC, NGE, and NGU) for the USA and China throughout several time periods or groups. The situation in Group A is relatively balanced, with both countries demonstrating positive development in all variables [80]. Nevertheless, the USA exhibited a marginally superior HDP growth rate in comparison to China (0.015 vs. 0.012). However, this trend underwent a substantial transformation in subsequent cohorts. China consistently demonstrated significantly higher growth rates in “NGU” across all groups, culminating in a considerable growth rate of 1.174 in Group F (Figure 2). In the USA, there was a substantial decrease in “HDC” within the same cohort (−0.302). Conversely, the USA performed better in Group A and Group E for the “HDP” scale. Nevertheless, both countries observed negative growth in specific variables, underscoring the intricate economic and environmental factors that influence these trends and distinguishing the development patterns of the USA and China [81]. There was also a large “NGU” growth rate gap. In some cases, the USA achieved better results in “HDP”, emphasizing trend volatility and complexity. Nevertheless, the analysis has limitations due to gaps in context and variable definitions. The calculation of the decoupling was based on a one percent shift in CO₂ emissions [82]. The alpha and beta attitudes in the T-ZDP procedure were both negatively impacted because of this. As a one percent change in energy input and output, as well as coal mining, immediately led to a change in CO₂ emissions, we anticipated that the decoupling shift in their attitudes would align with our expectations. In order to calculate the decoupling attitude, a five-year period was used as the basis [83]. Each year, the decoupling mindset reflects the impacts that will be felt over the next three years.

HDC represents economic development, while NGU represents factors such as government expenditure or investment. The HDC values, which ranged from −0.075 to 0.371, suggest that the economic performance of the categories is diverse. Similarly, the NGU values demonstrated a significant range of −0.128 to 1.867, which suggests variability. The key observations are as follows: Group C had diverse economic outcomes, with a combination of positive and negative values; Group F faced prospective challenges, with low values for both HDC and NGU; and Group A showed a robust economic performance, characterized by high HDC and NGU values. The NGE values, which ranged from −0.072 to 0.162 (Figure 3), demonstrated substantial variation among the categories. Furthermore, the USA has a broad range of values, spanning from −0.05 to 0.147, which can be used as a reference or comparison point [84]. Key observations include Group A’s robust performance in terms of NGE for the USA, Group F’s prospective challenges with low values in both, and Group C’s diverse economic outcomes with a combination of positive and negative values.

Next, we will consider the CPR and the CCS in the USA. According to Table 1, the significance of CPR and CCS is not entirely obvious; nonetheless, it is possible that these terms could represent a variety of aspects, including economic performance, growth rate, or other pertinent metrics. The CPR values, which ranged from −0.087 to 0.042, and the CCS values, which ranged from −0.072 to 0.038, demonstrated a significant disparity between the groups. The USA provides a comparison or reference point, with a wide range of values from −0.140 to 0.038. Some of the most critical observations are as follows: Group F faced potential challenges, with low values in all three variables, as illustrated in Figure 4; Group C had diverse economic outcomes, with a mix of positive and negative values; and Group A had a robust performance, including a high value for the USA (0.038) and relatively high values for CPR (0.042) and CCS (0.038). CPR and CCS are likely to represent different parts of China’s economic or social situations, even though their precise meanings are not entirely obvious. The CPR and CCS values showed significant variance across the groups, with the CPR values ranging from −0.125 to 0.444 and the CCS values ranging from −0.088 to 0.430. One of the most important observations is that Group A had the highest values for all three variables, which indicates that the economy as a whole is quite strong [85]. When compared to the other two groups, Group F had the lowest numbers across the board, which indicates that there may be difficulties. A variety of economic outcomes are suggested by the fact that other groups exhibited a combination of positive and negative values.

In the second stage, the individual groups were analyzed, as shown in

Table 4. Percentage change in CO₂ emissions in groups (part 1).

No. of Groups	Years	Average Value of GDP		Percentage Change in GDP of USA		Percentage Change in GDP of China		Percentage Change in GDP of USA		Percentage Change in GDP of China		Percentage Change in GDP of USA		Percentage Change in GDP of China
		USA	China	HDP-UG	HDC-UG	HDC-CG	NGU-CG	NGE-UG	NGU-UG	NGE-CG	NGU-CG	CPR-UG	CCS-UG	CPR-CG	CCS-CG
Group A	1994–1998	0.016	0.009	2.078	0.857	0.985	−0.438	1.983	0.327	15.151	−0.253	42.625	−0.179	0.968	−0.400
Group B	1999–2003	0.009	0.19	1.385	0.943	6.248	1.69	−16.115	0.761	−56.975	−0.06	5.15	0.793	6.433	1.009
Group C	2004–2008	0.015	0.163	−0.065	0.896	15.183	1.045	−0.872	1.388	−17.5	−0.071	0.49	−11.175	0.651	0.908
Group D	2009–2013	−0.008	−0.025	0.412	0.752	12.885	1.271	0.469	4.047	9.005	−9.096	1.652	0.668	−0.146	0.896
Group E	2014–2018	0.002	0.176	19.026	−10.454	−4.341	3.28	0.556	4.915	−11.77	0.285	−1.159	0.697	−6.382	1.629
Group F	2019–2023	−0.005	−0.137	0.659	1.557	−0.684	0.673	0.711	1.157	−4.439	0.264	0.87	0.271	−1.424	0.12

Note: The variable symbols for the USA and China are only modified to differentiate between the percentage change in GDP and CO₂ emissions; “GDP-UG” indicates the GDP change in the USA, while “GDP-CG” indicates the GDP valuation in China. Table 1 serves as the foundation for the variables.

and

Table 5. Percentage change of CO₂ emissions in groups (part 2).

No. of Groups	Years	Average Value of GDP		One Percent Change in CO2 Emissions of USA			One Percent Change in CO2 Emissions of China			One Percent Change in CO2 Emissions of USA			One Percent Change in CO2 Emissions of China			One Percent Change in CO2 Emissions of USA			One Percent Change in CO2 Emissions of China
		USA	China	GDP-UC	HDP-UC	HDC-UC	GDP-CC	HDC-CC	NGU-CC	GDP-UC	NGE-UC	NGU-UC	GDP-CC	NGE-CC	NGU-CC	GDP-UC	CPR-UC	CCS-UC	GDP-CC	CPR-CC	CCS-CC
Group A	1994–1998	0.016	0.009	0.016	0.006	0.009	0.009	−0.023	0.036	0.016	0.012	0.005	0.009	0.005	−0.014	0.016	0.003	0.005	0.009	−0.014	−0.049
Group B	1999–2003	0.009	0.19	0.009	0.003	0.006	0.190	0.030	0.042	0.009	−0.001	−0.002	0.190	−0.002	0.059	0.009	−0.002	0.002	0.190	0.026	0.026
Group C	2004–2008	0.015	0.163	0.015	0.000	0.003	0.163	0.048	0.051	0.015	−0.005	−0.003	0.163	−0.003	0.089	0.015	−0.001	−0.001	0.163	0.070	0.074
Group D	2009–2013	−0.008	−0.025	−0.008	−0.012	−0.032	−0.025	−0.005	−0.009	−0.008	0.017	0.000	−0.025	0.000	−0.012	−0.008	−0.014	−0.020	−0.025	−0.005	0.000
Group E	2014–2018	0.002	0.176	0.002	0.005	0.000	0.176	−0.028	−0.040	0.002	−0.001	0.012	0.176	0.012	0.040	0.002	−0.008	−0.009	0.176	−0.012	−0.007
Group F	2019–2023	−0.005	−0.137	−0.005	0.060	0.046	−0.137	−0.106	0.825	−0.005	0.051	0.039	−0.137	0.039	0.214	−0.005	−0.007	−0.044	−0.137	−0.058	0.108

Note: The variable symbols for the USA and China are only modified to differentiate between the percentage change in GDP and CO₂ emissions; “GDP-UC” indicates the CO₂ emissions change in the USA, while “GDP-CC” indicates the CO₂ emissions in China. Table 1 serves as the foundation for the variables.

. Across six groups that each reflect a different historical period, the table displays the percentage changes that occurred in GDP-UC, HDP-UC, HDC-UC, HDP-UG, and HDC-UG following a one percent change in a carbon-related indicator. The slightly high intensity of change in GDP-UC (0.016) and the very high change intensity in HDP-UG (2.077) of Group A imply a substantial initial response to the change in CO₂ emissions. In contrast, Group B exhibited reduced intensities of change for GDP-UC, HDP-UC, and HDC-UC in comparison to Group A. A moderate shift in GDP-UC was observed in Group C, even though the intensities of HDP-UC and HDC-UC were relatively low. Additionally, HDP-UG exhibited a modest decrease (−0.065). During this time period, Group D experienced declines in GDP-UC, HDP-UC, and HDC-UC, all of which suggest a negative statistical correlation between CO₂ emissions and these indicators [86]. It is noteworthy that Group E demonstrated a large decline in HDC-UG (−10.453), which indicates a strong negative statistical link between these variables, and an extraordinarily high intensity of change in HDP-UG (69.026), which suggests a highly active and impactful reaction. Group F demonstrated a decrease in GDP-UC, whereas HDP-UC and HDC-UC demonstrated moderate intensities of change, and HDP-UG had a high intensity of change. The results of this research show that these economic and development indicators demonstrate a wide range of responses to the change in the carbon-related variable over the course of the various time periods. Group E had the most dramatic and statistically significant changes among the groups.

We can infer that there is potential for statistical significance in certain situations. For example, the statistical significance of the exceptional intensity of change in HDP-UG (69.026) in Group E suggests a strong correlation between CO₂ emissions and HDP-UG during that time. The significant decrease in HDC-UG (−10.453) observed in Group E demonstrates a strong negative statistical association [87]. The table presents the percentage changes in GDP-CC, HDC-CC, NGU-CC, GDP-CC, and NGU in response to a one percent change in a carbon-related variable (most likely CO) using six different time periods. The values of GDP-CC for Groups B and C were extremely positive, whereas the values for Groups D and F were negative, indicating a general downward trend. HDC-CC is characterized by a mix of positive and negative changes, with Group C displaying the highest positive value and Group F displaying the lowest positive value seen [88].

Moreover, NGU-CC displays a mix of positive and negative modifications, with Group F displaying the highest positive value and Group D displaying the lowest. This pattern is observed throughout all groups. Exceptionally high values are displayed by Groups B, C, and D, whereas Groups E and F display values that are negative. There is also a wide range of GDP-CC values. According to the results, Group E exhibited the maximum positive value, while Group A exhibited the lowest value with a substantial decline. The quantitative measures of change, GDP-UC (0.016) and NGE-UG (1.983), exhibited a relatively high intensity of change in Group A. The NGE-UG value in Group B dropped by a sizeable amount (−16.112), while the NGE-UC and NGU-UC values also fell. Additionally, unfavorable alterations were observed in NGE-UC and NGU-UC in Group C.

The values of NGE-UC and NGU-UG increased modestly in Group D. It can be observed that Group E had a significant amount of change in NGU-UG (4.914). At the end, Group F exhibited a significant rise in NGE-UC (0.051), while NGU-UC and NGE-UG values showed only minor rises. The values for GDP-CC were significantly positive in Groups B and C but negative in Groups D and F [89]. NGE-CC exhibited a combination of positive and negative alterations, with Group F displaying the highest positive value among the groups investigated. Additionally, NGU-CC exhibited a combination of positive and negative alterations, with Group F displaying the highest positive value. Group A had a very high value, while Groups B and C had very low negative values. NGE-CG displayed a wide range of values, with the highest value being in Group A. NGU-CG exhibited a combination of positive and negative alterations, with Group E displaying the highest positive value and Group D displaying the lowest value, with a considerable decline [82].

Different from the other groups, Group A had a high level of change in CPR-UG (42.625). A modest rise can be seen in the levels of CPR-UG and CCS-UG in Group B, while Group C had a much lower CCS-UG level (−11.175). For Groups D, E, and F, several measures, including GDP-UC, CPR-UC, and CCS-UC, decreased. It is clear that the change in CO₂ levels during those times caused a big rise in GDP-CC for both Group B and Group C, with values of 0.189 and 0.162, respectively. CPR-CC showed both positive and negative changes, while Group C had the best positive score (0.070). CCS-CC also showed a mix of positive and negative changes, as shown by Group F’s highest positive score of 0.108. CPR-CG displayed a wide range of values, with a very high value in Group B (6.432) and extremely low negative values in Groups E (−6.382) and F (−1.424). However, the value in Group B is the highest of the three. Group E demonstrated the highest positive value (1.629), while Group A demonstrated the lowest value with a considerable reduction (−0.399). For CCS-CG, there was a combination of positive and negative changes [83]. According to the findings of this analysis, the reactions of these economic and development indicators to the change in the carbon-related variable across the various historical periods are diverse and complex. Furthermore, certain groups demonstrated considerable gains in certain variables, while others demonstrated losses in the same variable.

In addition, the aggregated decoupling effects demonstrated that China has a considerable impact on the amount of CO₂ emissions. A one percent shift in CO₂ emissions will result from changes in energy input in both the USA and China. China and the USA have undergone a technological revolution, allowing them to manage their energy input and causes of the percentage change in CO₂ emissions. They have also used alternative energy sources. It has been estimated that the NGE decoupling attitude demonstrated a positive attitude in both the USA and China [84]. A positive decoupling attitude was also demonstrated for the CPR in China. For a period of five years, these estimated results demonstrate a decoupling attitude of ±. If it is greater than −2, then the CO₂ emissions should grow. It was also shown and advised that the annual carbon footprint can be reduced by removing routine flaring, reducing methane leaks, and utilizing modern technology. The utilization of energy sources in China is expected to reach its peak in 2035, with a value of 705 (mote). The country’s reliance on oil imports is anticipated to fluctuate between 70 and 60 percent between 2050 and 2030. The results that were previously mentioned also illustrate the implications of energy output, and a one percent change in the indicators illustrates the repercussions that T-ZDP will have over the next three years. The utilization of petroleum in the USA is expected to decrease by approximately 13% in 2020 compared to the level in 2021 to 2022. This research was expected to produce results that highlight the significant influence of coal and gas utilization on CO₂ emissions through catch-up growth [90]. Further, the energy level has provided an indication of the overall amount of electricity that has been utilized. It accounts for 98% of the company’s own consumption, with the remaining 2% coming from other countries [91]. While the T-ZDP model is a formidable instrument, it is essential to consider its limits. The model is dependent on data that are both accurate and reliable, which can be difficult to gather, particularly for countries that are still in the process of developing their economies [85]. In addition, the model assumes that the growth of the economy is directly proportionate to the influence that it has on the environment. This is a scenario that may not be totally accurate in the real world. For the purpose of overcoming these constraints, researchers can combine the T-ZDP technique with additional analytical methods, such as input–output analysis and life cycle evaluation [86]. More thorough knowledge of the intricate relationships that occur between energy systems, economic growth, and the environment may be obtained using several complimentary techniques, which have the potential to deliver such insights.

5. Conclusions and Recommendation

In this study, we employed the T-ZDP technique to examine various decoupling attitudes in computing CO₂ emissions relative to the GDP, energy input (HDP, NGE, and CPR), and energy output (HDC, NGU, and CCS) of the USA and China. Using T-ZDP decoupling, we conducted an analysis of the economic growth as well as the relationship between CO₂ emissions and GDP, population, energy input, and energy production in Groups A to F. The results suggest that the energy input and utilization from eventual total ± decoupling effects in the USA and China are the same. Furthermore, we were able to accomplish a viable decoupling methodology that is dependent on energy vitality and renewable sources. From a technological standpoint, China and the USA have a multitude of capabilities that allow them to guarantee environmental security. This approach of decoupling is utilized to estimate energy sources and utilization. The energy input and energy output are of particular concern. In every group, the volume of CO₂ emissions increased. The overall energy production can be managed through energy conservation, which is the process of reducing the amount of energy used to cut expenses and reduce the impact of CO₂ emissions on the environment.

The integrated results of this analysis, which compare the hydrocarbon extraction and utilization and CO₂ emissions of the USA and China, can be substantially improved by incorporating the findings of previous studies that have employed the Tapio-Z decoupling model and fuzzy logic. Fuzzy logic is capable of accurately capturing the intricate relationships between energy sources, economic growth, and environmental impacts due to its capacity to effectively manage uncertainty and imprecision. By integrating fuzzy logic into the Tapio-Z framework, researchers can more accurately evaluate the decoupling states of various energy sources, including hydrocarbons, coal, and natural gas. They can also detect minute changes in these associations over time. This can uncover non-linear correlations or unexpected aspects that traditional statistical methods have missed.

The generation of clean energy from sources such as biomass, the Earth, water, wind, and other sources is of utmost importance. Additionally, newly redesigned HVAC (heating, ventilation, and air conditioning) systems will help reduce the amount of electricity used. Within the context of well-modified infrastructure, they illustrate the milestones of building mechanical systems that provide thermal comfort for people in addition to indoor air quality. Furthermore, the implementation of carbon capture and storage (CCS) technology in a variety of megawatt power plants has the potential to eliminate enough CO₂ emissions to compensate for GHG emissions that are created annually by millions of automobiles. In addition, oil and gas companies in the USA and China have introduced a new and improved CCS technology that has the potential to generate additional power while simultaneously relieving emissions of CO₂. It is also important to determine the amount of energy that is being consumed and take consistent actions by imposing stringent government regulations, reducing expenses, and increasing the demand for the utilization of renewable energy sources. This should allow us to exercise control over climate change, which can otherwise lead to an increase in food insecurity, changes in ecosystems, rising sea levels, and an increase in extreme weather events such as storms, droughts, and flooding. Using new technology, it is possible to regulate industrial pollution, which includes both direct and indirect emissions, as well as eliminate leaks in the production process and chemical reactions that occur during the manufacturing process. Roughly twenty-four percent of GHG emissions in the USA are attributed to the industrial sector. Some of the largest contributors necessitate the management of facilities and the modification of standards in the manufacturing extraction process in order to limit the amount of CO₂ emissions produced by enterprises. As a result, we should reduce the amount of energy that is produced by applying new regulations and technologies. CO₂ emissions are slightly less effective in terms of energy input in groups, according to the results that were displayed. This research provides pertinent recommendations, as indicated by the data presented above.

To transition to sustainable energy systems, the USA and China must surmount a variety of challenges. China’s primary source of energy is coal, while the USA, which possesses a plethora of fossil fuel resources, is heavily reliant on oil and natural gas. Despite the fact that China has made more substantial progress than the USA, both nations are investing in renewable energy sources. The USA has a more diverse mix of energy sources, whereas China relies primarily on coal. Both countries also face energy security concerns, with the USA focusing on independence and China focusing on securing reliable supplies. Moreover, they must also address environmental impacts, with China facing severe air pollution and the USA grappling with extraction-related issues. These are the central differences between the two countries. Adopting renewable energy sources, improving energy efficiency, and addressing environmental issues are all things that both countries need to work on moving forward. This can be accomplished by both nations making significant investments into the research and development of innovative renewable energy technologies, expanding grid infrastructure, implementing higher emission limits, promoting energy efficiency, fostering international collaboration, and placing an emphasis on taking measures to safeguard the environment. To combat climate change and make progress towards a future with sustainable energy, it is essential for the USA and China to work together on energy technology and regulations. The valuable insights that this work provides will be beneficial to policymakers and researchers who are interested in promoting sustainable energy transitions and mitigating the effects of climate change. By including the specific energy sources of hydrocarbons, coal, and natural gas, this study expands upon prior research, enabling a more detailed examination of decoupling trends and their implications for each energy source.

Nevertheless, this analysis is subject to certain constraints. This conclusion offers a broad perspective and may not completely encompass the intricacies and subtleties of energy policies and practices in both nations. It is also crucial to recognize that the energy landscape is in a state of perpetual evolution, and new technologies and policies are being developed at a rapid pace. This analysis may not accurately represent the most recent advancements and future trends in the energy sector. In the future, one possible research approach could be to conduct an in-depth investigation into the effectiveness of energy policies in both countries involved. Both the USA and China have been the subject of studies that compare the implementation of renewable energy and the integration of grids. Several different energy transition strategies have been evaluated regarding their economic and societal ramifications. The public’s view and adoption of renewable energy technology in both countries will be investigated in a future study. Within the context of the acceleration of the energy transition, this study will examine the role that technology transfer and innovation play. Addressing these research questions is necessary to obtain a more profound understanding of the challenges and opportunities that both countries are facing in their transition to sustainable energy systems. This understanding is necessary to inform the development of energy policies that are more effective and equitable. Additionally, we recommend that both nations improve their economic sustainability and development structure, as well as adjust their strategic policies to align with the regulations of environmental protection agencies.