Analyzing Resource and Environment Carrying Capacity of Kunming City Based on Fuzzy Matter–Element Model

Abstract

The determination of the sustainable development of a region requires estimating its carrying capacity in terms of resources and environment. It is essential to investigate the carrying capacity of Kunming City to comprehend its rapid development and create a resource and environment-friendly society. This research involved the selection of a set of 35 evaluation indicators from three categories: resources, environment, and social economy. These indicators were chosen based on statistical data obtained from Kunming City between 2011 and 2020. An evaluation system was established using the entropy weight method to determine the weight of these indicators. Subsequently, the fuzzy matter–element analysis method was utilized to construct the European closeness model of Kunming’s resource and environmental carrying capacity. The correlation between the carrying capacity of resources and environment and sub-carrying capacities was analyzed using Pearson’s correlation coefficient to determine the degree of influence of different aspects on the carrying capacity of resources and environment in Kunming. The results show a consistent upward trend in the carrying capacity of resources and environment in Kunming City from 2011 to 2019. However, in 2020, due to national policy adjustments and the impact of COVID-19 on the social economy, the resource and environment carrying capacity index in Kunming City slightly decreased.

1. Introduction

The 21st century has experienced a swift pace of social and economic advancement, which has brought about enhanced living conditions. However, it has also resulted in a multitude of environmental and resource-related challenges. The outbreak of the recent pandemic has had a significant detrimental effect on human social activities and the economic progress of nations. Thus, in the post-epidemic era, mitigating the pressure on resources and the environment is crucial and balancing the contradiction between the uneven distribution of resources and excessive consumption. According to the Annual Report of China Green Development Index–Regional Comparison, Kunming, also known as the “Spring City” in China, experienced a decline in its resource and environment, carrying a potential score from 0.546 in 2011 to 0.2838 in 2019. The swift urbanization and economic growth have generated a greater need for natural resources, particularly land resources, posing ongoing constraints on the urban development of Kunming. Therefore, how to achieve a balance between the carrying capacity of resources and the environment and economic development, alleviate the contradiction between man and land, and establish a resource and environment-friendly society has become a pressing research frontier in the field of resource and environment carrying capacity [1]. The study of carrying capacity dates back to Malthus’s era in 1789, and provides the theoretical basis for extending the concept of carrying capacity. Over time, foreign scholars have proposed a series of qualitative and quantitative methods to study carrying capacity. Foreign scholars’ studies on carrying capacity include tourism carrying capacity [2], ecological carrying capacity [3], urban carrying capacity [4,5], resource carrying capacity [6,7], and environmental carrying capacity [8], etc. A series of different research methods based on computer technology have been proposed, such as GIS technology, energy analysis method, artificial neural network and fuzzy inference system model based on adaptive networks, and so on. Walsh et al. employed the ecological footprint method to evaluate Limerick and Belfast in Ireland, where resource flow was converted into the land area, and carbon footprint was confirmed as one of the measures of sustainable development [9]. The PSR model, or the pressure–state–response model, was initially introduced by the Organization for International Economic Cooperation and Development (OECD) to assess the global environmental state. Salemi et al. utilized the PSR model to create the ecotourism carrying capacity model of the Karkheh protected area [10]. Laheab A. Jasem Al-Maliki et al. [4] processed the raw data using an Excel program. Then, they represented the data in a geographic information system (GIS) program using the reverse distance weighting (IDW) tool to create the permissible load maps of soils at 0–2 m depth. The urban carrying capacity of An-Najaf and Kufa was evaluated. By adopting the energy analysis method, Chanhoon Jung et al. [11] evaluated the environmental carrying capacity of sustainable development of Jeju Island in 2005, 2015, and 2030. They proved that for tourism-intensive areas, taking Jeju Island as an example, development strategies should be proposed according to regional environmental carrying capacity. In their study, Karimi et al. [12] employed the concept of carrying capacity to develop a spatial urban density model. To determine the necessary parameters for the model, they utilized the analytic hierarchy process (AHP) and the Delphi method. The sample data from a medium-sized city in Isfahan Province, Iran, was used to demonstrate the application of 3D visualization technology within a GIS environment to visually validate the obtained results. The developed model effectively maintains the balance between building height and density. Comparing the predicted bearing capacity values, it was evident that the artificial neural networks and fuzzy inference system models based on adaptive networks outperformed the simple linear regression and multiple linear regression models. In 2021, Tugrul Varol et al. [7] proposed a fuzzy reasoning system based on an adaptive network to evaluate and predict the soil carrying capacity of forest highways. Few current studies of environmental carrying capacity consider predictions based on future conditions. Following this, numerous Chinese scholars have explored the concept of resource and environmental carrying capacity from different perspectives and to varying degrees. He et al. [1] posited that resource and environmental carrying capacity is a comprehensive concept closely related to both resource and environmental carrying capacity. It signifies the capacity of a regional resource and environment system to withstand human activity within a specific timeframe under the condition that sustainable development requirements are met, and ecological effectiveness is not destroyed. Zhang et al. [13] investigated the spatial pattern differentiation features of the resource and environmental carrying capacity in Hebi City from ecological, farming, and urban construction viewpoints. Li et al. [14] assessed the resource and environmental carrying capacity of Ningyuan County in Hunan Province from three functions, namely ecology, agriculture, and construction, by adhering to the principle of “double evaluation” of territorial spatial planning. Therefore, drawing upon the knowledge gained from previous studies, the concept of resource and environmental carrying capacity can be defined as “the ability of a particular region to sustain its total population and accommodate human social and economic activities within a designatedtimeframe and spatial scope, while simultaneously ensuring ecological equilibrium and rational utilization of regional resources.” Numerous evaluation systems and methods have been developed to assess resource and environmental carrying capacity. The domestic evaluation system primarily constructs a multi-level index evaluation system encompassing resources, environment, ecology, economy, society, and policies [15,16,17,18]. Commonly utilized evaluation methods include system dynamics [19], the ecological footprint method [20], the comprehensive index method [21], the fuzzy evaluation method [22], the state space method [23], the analytic hierarchy process [24], principal component analysis [25], and the pressure–state–response (PSR) model [26,27]. Currently, the construction of the index system in the evaluation of resource and environmental carrying capacity encompasses a broad spectrum, and the evaluation methods are diverse. The PSR model is widely employed to establish the resource and environment evaluation index system as it reveals the interrelationship between human and economic society, resources, and environment. However, some methods still have limitations, such as weak index selection, complicated evaluation procedures, and subjective factors. To determine the index evaluation system of resource and environmental carrying capacity, all factors, including their mutual influence, must be considered, and the system should be comprehensively evaluated.

In the 1980s, Professor CAI Wen introduced the theory of matter–element analysis, which is commonly used to address contradictions and compatibility issues in research. This theory involves converting practical problems in systematic research into formal problem models and models that describe the problem-solving process [27]. In the case of multi-index evaluation problems, the problem-solving process is formalized to establish the corresponding matter–element. Research has shown that the concept of fuzzy sets [28] can be effectively applied to summarize index functions in various fields where information is incomplete or imprecise. Fuzzy matter–element theory has been widely applied in water quality assessment [29,30], urban ecosystem health assessment [31,32,33] regional environmental quality assessment [34], cultivated land quality assessment [35], early warning analysis [36,37], and other fields. Compared to traditional methods, the organic combination of fuzzy mathematics and matter–element analysis theory can facilitate practical evaluations of systems or entire entities while reducing complex analysis steps. This approach enhances convenience and feasibility, and simultaneously effectively mitigates the impact brought about by the uncertainty of evaluation standards, enabling a more comprehensive and objective assessment of Kunming City’s resource and environmental carrying capacity. In this research, the evaluation system for Kunming City’s resource and environmental carrying capacity was developed using the principles of fuzzy matter–element theory and the entropy weight method. Additionally, a European proximity model was constructed to analyze the extent of resources and environmental carrying capacity.

2. Evaluation Model to Determine Resource and Environment Carrying Capacity Based on Fuzzy Matter–Element

2.1. Fuzzy Matter–Element and Compound Fuzzy Matter–Element

The object $M$ described in the matter–element analysis, its feature vector $C$ (evaluation index), and a characteristic value $x$(evaluation index present value) collectively constitute the matter–element $R=\left(M, C, x\right)$of resource and environment carrying capacity. If the magnitude value$x$ is fuzzy, it is called the fuzzy matter–element. The object $M$has n eigenvectors $C_1,C_2,···,C_n$ and their corresponding values are $x_1,x_2,···,x_n$, so $R$is considered as the n-dimensional fuzzy matter–element. m objects$\left(X=1,2,\dots ,m\right)$ N-dimensional matter–elements together make N-dimensional complex fuzzy matter–elements$R_{mn}$ of m objects, namely:

$$R_{mn}=\left[\begin{array}{ccccc} & M_1& M_2& \cdots & M_m\\ C_1& x_{11}& x_{21}& \cdots & x_{m1}\\ C_2& x_{12}& x_{22}& \cdots & x_{m2}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ C_n& x_{1n}& x_{2n}& \cdots & x_{mn}\end{array}\right]$$

(1)

In the Equation, $R_{mn}$represents the n-dimensional complex fuzzy matter–element of m things, $M_j \left(j=1,2,···,m\right)$ is the JTH thing, $C_i\left(i=1,2, ···, n\right)$ is the ith feature, $x_{ij}$ is the fuzzy quantity value corresponding to its feature of the JTH thing. This study considered the state of the evaluated object’s resource and environmental carrying capacity as the matter–element and constructed the compound fuzzy matter–element by pairing each evaluation index with its corresponding fuzzy value.

2.2. Suboptimal Membership

The fuzzy value corresponding to each evaluation index represents the membership degree of the corresponding index in the standard scheme, which is referred to as the subordinate membership degree. The principle formulated on this basis is known as the principle of subordination. The subordinate membership degree can be calculated using Equations (2) and (3):

$$\mathrm{The}\mathrm{bigger},\mathrm{the}\mathrm{better}:u_{ij}=\frac{x_{ij}}{max{x}_{ij}}$$

(2)

$$\mathrm{The}\mathrm{smaller},\mathrm{the}\mathrm{better}:u_{ij}=\frac{min{x}_{ij}}{x_{ij}}$$

(3)

where $u_{ij }$ is the degree of subordinate membership; $max{x}_{ij }$ and $min{x}_{ij }$ are, respectively, the maximum and minimum values of each evaluation index in each scheme. On this, a membership degree of fuzzy matter–element $\overline{R_{mn}}$, can be built as:

$$R_{mn}=\left[\begin{array}{ccccc} & M_1& M_2& \cdots & M_m\\ C_1& u_{11}& u_{21}& \cdots & u_{m1}\\ C_2& u_{12}& u_{22}& \cdots & u_{m2}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ C_n& u_{1n}& u_{2n}& \cdots & u_{mn}\end{array}\right]$$

(4)

2.3. Standard Fuzzy Matter–Element and Differential Square Fuzzy Matter–Element

(1) Standard fuzzy matter–element. The standard fuzzy matter–element $R_{0n }$ is determined by the maximum and minimum values of the subordinate membership degree of each evaluation index in the subordinate membership degree fuzzy matter–element $R_{mn}$. In this study, the maximum value was taken for optimality. Hence, the ideal membership degree for each index should be 1, and the standard representation of the fuzzy matter–element can be expressed as follows:

$$R_{0n}=\left[\begin{array}{cc} & M_0\\ C_1& 1\\ C_2& 1\\ \cdots & \cdots \\ C_n& 1\end{array}\right]$$

(5)

(2) Differential square fuzzy matter–element. If ${\Delta }_{ij}={\left(u_{0j}-u_{ij}\right)}^2\left(i=1,2,···,n;j=1,2,···,m\right)$ according to the standard fuzzy matter–element $R_{0n }$ systemic and membership degree of fuzzy matter–element $\overline{R_{mn}}$ corresponding to the square of the difference is of poor square fuzzy matter–element $R_{\Delta }$:

$$R_{\Delta }=\left[\begin{array}{ccccc} & M_1& M_2& \cdots & M_m\\ C_1& {\Delta }_{11}& {\Delta }_{21}& \cdots & {\Delta }_{m1}\\ C_2& {\Delta }_{12}& {\Delta }_{22}& \cdots & {\Delta }_{m2}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ C_n& {\Delta }_{1n}& {\Delta }_{2n}& \cdots & {\Delta }_{mn}\end{array}\right]$$

(6)

2.4. Determination of Entropy Weight

Different evaluation indices contribute differently to the evaluation units during the comprehensive evaluation process. Hence, it is essential to assign weights to the indicators based on their respective significance. Information entropy serves as a metric for assessing the level of information disorder in an information system, with smaller entropy indicating a higher degree of system order. Thus, the degree of order and usefulness of the system information can be evaluated by information entropy. Specifically, the judgment matrix comprising evaluation index values can be used to determine their weights. This approach can somewhat reduce human interference in index weight calculation, making the evaluation results more objective and practical. The following steps outline the calculation process:

(1) Construction of a judgment matrix of $m$ objects and $n$ evaluation indexes $R={(x_{ij})}_{mn}\left(i=1,2,···,n; j=1,2,···,m\right).$

(2) The judgment matrix is normalized to obtain the normalized judgment matrix $B$.

$$b_{ij}=\frac{x_{ij}-x_{min}}{x_{max}-x_{min}}$$

(7)

In the Equation, $x_{max}$ are $x_{min}$ the most or least satisfied among different things under the same index (the smaller value, the more satisfied, or the bigger the value, the more satisfied).

(3) According to the definition of entropy, there are $m$ evaluation objects and $n$ evaluation indexes, and the entropy of evaluation indexes can be determined as:

$$H_i=-\frac{1}{lnm}\left[{{\displaystyle \sum }}_{j=1}^m\left(f_{ij}ln{f}_{ij}\right)\right]$$

(8)

In Equation (8), $i=1,2,···,n;j=1,2,···,m;f_{ij}=\raisebox{1ex}{$b_{ij}$}\!\left/ \!\raisebox{-1ex}{${{\displaystyle \sum }}_{j=1}^m{b}_{ij}$}\right.$. Obviously, when $f_{ij}=0$, $ln{f}_{ij}$ is meaningless, defining $\lim f_{ij}ln{f}_{ij}=0$.

(4) The entropy weight $w_i$ and weight $W$ of the evaluation index were calculated.

$$W={\left(w_i\right)}_{1\times n}$$

(9)

$$w_i=\frac{1-H_i}{n-{{\displaystyle \sum }}_{i=1}^n{H}_i}$$

(10)

In Equations (9) and (10), ${\displaystyle \sum }_{i=1}^n{w}_i=1$.

2.5. Calculation of Euclidean closeness

The correlation degree refers to a measure of the relationship between two variables, and it is represented by the correlation function. This study used the Euclidean distance as the correlation function to measure the degree of proximity between a matter–element and an ideal matter–element, which is referred to as the Euclidean closeness $\rho H_j$. Euclidean closeness represents the degree of proximity between the evaluated sample and the standard sample. A larger value indicates a greater degree of proximity, whereas a smaller value indicates the opposite. Therefore, the resource and environmental carrying capacity’s strengths and weaknesses can be analyzed based on the magnitude of the Euclidean closeness degree. This article uses the (°, +) algorithm, namely first by following the European degree calculation $\rho H_j$.

$$\rho H_j=1-\sqrt{{{\displaystyle \sum }}_{i=1}^n{w}_i{\Delta }_{ij}}\left(j=1,2,···,m\right)$$

(11)

Based on this, a meta-model of the European proximity complex for resource and environmental carrying capacity evaluation is constructed $R_{\rho H}$, as:

$$R_{\rho H}=\left[\begin{array}{ccccc} & M_1& M_2& \cdots & M_m\\ \rho H_j& \rho H_1& \rho H_2& \cdots & \rho H_m\end{array}\right]$$

(12)

3. Resources and Environmental Carrying Capacity of Kunming

3.1. General Situation of Kunming City

Kunming City is situated in the central part of Yunnan Province, covering an area of about 21,012.54 km² with coordinates 102°10′~103°40′ east longitude and 24°23′~26°22′ north latitude. Its terrain is high in the north and low in the south, with a stepped slope from north to south. As depicted in Figure 1, it belongs to the subtropical monsoon climate. Being the capital of Yunnan Province, Kunming is a significant hub city facing Southeast Asia and South Asia. While Kunming City faces a relative scarcity of natural resources such as water and cultivated land, it boasts abundant tourism resources. However, the increasing population and economic development exert significant pressure on the resources and environment of Kunming City, making ecological restoration a challenging endeavor. Therefore, a comprehensive evaluation of the resources and environment carrying capacity of Kunming City is crucial for its sustainable development and ecological civilization construction.

3.2. Selection of Evaluation Index

The concept of resource and environment carrying capacity focuses on the capacity of a certain area to support resources, environment, and social and economic conditions over a specific time scale [1]. Based on prior studies [17,24], resources encompass agricultural resources, forestry resources, and living resources, while the environment encompasses the impact of regional water, atmospheric, solid waste, and soil environments on carrying capacity. Moreover, social and economic conditions pertain to the influence of population, economic level, and infrastructure on carrying capacity. To assess the carrying capacity of resources and the environment in Kunming City between 2011 and 2020, a total of 35 evaluation indices were chosen from the three subsystems of resources, environment, and social economy. Data sources included the Kunming National Economic Statistical Yearbook from 2012 to 2021, the National Economic and Social Development Statistical Bulletin from 2011 to 2020, the Water Resources Bulletin, the Air Quality Bulletin, and other data.

Table 1. Evaluation index system of resources and environment carrying capacity in Kunming City.

Target Layer A	Criterion Layer B	Element Layer C	Index Layer D	Index Property
Resources and environment carrying capacity of Kunming City	Resources (B1)	Agricultural Resources (C1)	Per capita available farmland area/mu (D1)	Positive Indicator
			Total annual grain crop output/ton (D2)	Positive Indicator
			Agricultural fertilizer application amount (converted)/ton (D3)	Negative Indicator
		Forest Resources (C2)	The green area of the garden/hectare (D4)	Positive Indicator
		Living Resources (C3)	Per capita domestic water consumption/ton (D5)	Negative Indicator
			Total water supply/ten thousand tons (D6)	Negative Indicator
			Per capita urban road area/square meter (D7)	Positive Indicator
			Per capita household consumption of liquefied gas/ton (D8)	Positive Indicator
	Environment (B2)	Water Environment (C4)	Sewage treatment plant centralized treatment rate/% (D9)	Positive Indicator
			Industrial wastewater COD discharge/ton (D10)	Negative Indicator
			COD discharge of domestic sewage/ton (D11)	Negative Indicator
			Discharge of ammonia nitrogen from industrial wastewater/ton (D12)	Negative Indicator
			Ammonia nitrogen discharge from domestic sewage/ton (D13)	Negative Indicator
			County-level drinking water quality standard/% (D14)	Positive Indicator
			Municipal drinking water quality up to standard rate/% (D15)	Positive Indicator
		Atmospheric Environment (C5)	Days of air quality in the main city/day (D16)	Positive Indicator
			RMB 100 million GDP industrial SO2 emissions/ton (D17)	Negative Indicator
			RMB 100 million GDP industrial smoke dust emissions/ton (D18)	Negative Indicator
			Average area ambient noise/decibels (D19)	Negative Indicator
		Solid Waste Environment (C6)	Harmless treatment rate of household garbage/% (D20)	Positive Indicator
			The utilization rate of Industrial solid waste disposal/% (D21)	Positive Indicator
			Industrial Hazardous waste disposal utilization rate/% (D22)	Positive Indicator
	Social Economy (B3)	Population (C7)	Natural population growth rate/‰ (D23)	Positive Indicator
			Urbanization rate/% (D24)	Positive Indicator
			Total employed persons/ten thousand people (D25)	Positive Indicator
		Economic Level (C8)	Per capita GDP/CNY/person (D26)	Positive Indicator
			Per capita disposable income of permanent urban residents/CNY (D27)	Positive Indicator
			Per capita disposable income of rural permanent residents/CNY (D28)	Positive Indicator
			Per capita retail sales of consumer goods/CNY (D29)	Positive Indicator
		Infrastructure (C9)	Per capita freight volume/ton (D30)	Positive Indicator
			Per capita passenger volume/person (D31)	Positive Indicator
			Motor vehicle ownership per 10,000 people/vehicle (D32)	Positive Indicator
			Number of R&D personnel/person (D33)	Positive Indicator
			Number of health institutions/units (D34)	Positive Indicator
			Number of high school graduates/person (D35)	Positive Indicator

shows the evaluation index system of resources and environment carrying capacity of Kunming City.

3.3. Construction of Evaluation Model

(1) The composite fuzzy matter–element model is constructed.

To evaluate the resources and environment carrying capacity of Kunming City during the period of 2011–2020, a total of 35 evaluation indexes and a 10-year time series data were chosen, from sources, including the Kunming National Economic Statistical Yearbook, National Economic and Social Development Statistical Bulletin, and the water resources and air quality bulletins. Using the available data, an evaluation index system was created, and a composite fuzzy matter–element model was constructed to analyze the carrying capacity of resources and the environment. The fuzzy matter–element method was employed for this purpose and the details of the model can be found in

Table 2. Compound fuzzy matter–element model of resource and environment carrying capacity in Kunming City.

Index Layer	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
D1	0.79	0.77	0.84	0.84	0.85	0.85	0.85	0.75	0.76	0.64
D2	1,198,428	1,206,700	1,230,074	1,236,000	1,235,700	1,248,400	1,217,600	997,100	1,022,000	1,036,500
D3	176,248	178,587	181,875	170,306	198,597	205,244	197,170	187,300	178,471	170,155
D4	16,449	19,377	18,847	18,926	19,153	21,029	20,962	21,129	21,207	22,905
D5	36.97	32.39	36.68	39.31	39.89	42.22	37.83	37.88	40.89	50.03
D6	40,249.48	30,578.49	42,158.21	44,091.73	44,476.72	50,020.29	50,186.60	54,971.40	56,783.74	55,945.34
D7	11.10	9.75	9.68	18.81	13.07	15.22	9.32	9.69	11.23	13.48
D8	0.04	0.04	0.04	0.04	0.03	0.02	0.05	0.08	0.08	0.07
D9	131.95	92.53	92.35	90.15	91.83	91.53	92.37	94.84	94.97	96.83
D10	8148	8261	8114	7000	7597	8837	3962	3599	3327	2969
D11	8526	2340	4840	14,154	11,411	12,742	7754	5980	8048	27,230
D12	260	258	266	201	221	356	289	251	304	128
D13	4980	4828	4543	4971	4845	5050	2215	1231	2051	3734
D14	90	95	92	97	100	100	100	100	96	100
D15	96	71	87	98	96	100	100	100	100	100
D16	117	117	101	100	161	146	154	188	184	203
D17	41.57	37.62	29.77	18.64	18.65	18.62	10.47	9.24	4.33	4.86
D18	24.37	19.37	15.91	7.94	6.18	5.86	7.41	7.45	7.29	6.38
D19	53	53	54	54	54	54	53	54	53	54
D20	97	82	84	87	87	95	100	100	100	100
D21	72	96	98	98	99	99	95	100	91	76
D22	100	100	100	100	100	100	99	99	98	100
D23	5.66	5.61	5.59	5.71	5.98	6.21	6.68	6.96	6.74	3.48
D24	66.00	67.05	68.05	69.05	70.05	71.05	72.05	72.85	73.60	79.67
D25	400.66	401.88	403.51	405.29	412.78	420.37	432.14	448.01	453.78	502.43
D26	38,690	46,256	52,094	56,236	59,656	64,156	71,906	76,387	93,853	80,584
D27	21,966	25,240	28,354	31,295	33,955	36,739	39,788	42,988	46,289	48,018
D28	6985	8040	9273	10,366	11,444	12,555	13,698	14,895	16,356	17,719
D29	19,606	22,865	25,875	27,070	30,877	34,335	38,198	40,692	45,852	36,281
D30	24.34	25.60	28.25	41.77	42.67	42.37	41.68	47.65	50.63	44.30
D31	17	18	19	17	17	16	13	13	13	9
D32	2323	2586	2768	2959	3221	3371	3684	3867	4064	3510
D33	8237	7891	8903	8592	13,134	14,390	13,224	13,765	13,853	12,857
D34	3103	3163	4552	4492	4490	4755	4823	4892	5068	5526
D35	26,994	27,743	28,771	32,606	32,343	32,606	31,310	33,288	35,969	38,607

.

(2) The optimal membership degree fuzzy matter–element is constructed.

According to the suboptimal membership principle and index property given in Equations (2) and (3), the suboptimal membership compound fuzzy matter–element $\overline{R_{mn}}$ is constructed. The fuzzy matrix of subordinate membership degree is shown in

Table 3. Suboptimal membership fuzzy matrix.

Index Layer	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
D1	0.9240	0.9026	0.9866	0.9854	0.9910	1.0000	0.9976	0.8785	0.8889	0.7560
D2	0.9600	0.9666	0.9853	0.9901	0.9898	1.0000	0.9753	0.7987	0.8186	0.8303
D3	0.9654	0.9528	0.9356	0.9991	0.8568	0.8290	0.8630	0.9085	0.9534	1.0000
D4	0.7181	0.8460	0.8228	0.8263	0.8362	0.9181	0.9152	0.9225	0.9259	1.0000
D5	0.8761	0.9999	0.8830	0.8239	0.8120	0.7672	0.8561	0.8550	0.7921	0.6475
D6	0.7597	1.0000	0.7253	0.6935	0.6875	0.6113	0.6093	0.5563	0.5385	0.5466
D7	0.5901	0.5183	0.5146	1.0000	0.6948	0.8091	0.4955	0.5152	0.5970	0.7166
D8	0.5394	0.5107	0.5901	0.4957	0.6971	1.0000	0.4187	0.2751	0.2859	0.3146
D9	1.0000	0.7013	0.6999	0.6832	0.6959	0.6937	0.7000	0.7188	0.7197	0.7338
D10	0.3643	0.3593	0.3659	0.4241	0.3908	0.3359	0.7493	0.8249	0.8923	1.0000
D11	0.2744	1.0000	0.4835	0.1653	0.2051	0.1836	0.3018	0.3913	0.2908	0.0859
D12	0.4916	0.4959	0.4810	0.6365	0.5789	0.3594	0.4429	0.5100	0.4207	1.0000
D13	0.2471	0.2549	0.2709	0.2475	0.2540	0.2437	0.5556	1.0000	0.5999	0.3296
D14	0.9032	0.9466	0.9232	0.9740	0.9983	1.0000	1.0000	1.0000	0.9550	1.0000
D15	0.9577	0.7113	0.8732	0.9829	0.9608	1.0000	1.0000	1.0000	1.0000	1.0000
D16	0.5764	0.5764	0.4975	0.4926	0.7931	0.7192	0.7586	0.9261	0.9064	1.0000
D17	0.1042	0.1151	0.1455	0.2323	0.2321	0.2325	0.4134	0.4685	1.0000	0.8917
D18	0.2405	0.3025	0.3683	0.7384	0.9478	1.0000	0.7903	0.7868	0.8043	0.9180
D19	1.0000	1.0000	0.9870	0.9851	0.9907	0.9907	0.9962	0.9743	0.9981d	0.9833
D20	0.9680	0.8236	0.8447	0.8655	0.8658	0.9493	1.0000	0.9968	1.0000	1.0000
D21	0.7236	0.9634	0.9786	0.9834	0.9918	0.9954	0.9552	1.0000	0.9083	0.7620
D22	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	0.9947	0.9882	0.9750	1.0000
D23	0.8132	0.8060	0.8032	0.8204	0.8592	0.8922	0.9598	1.0000	0.9684	0.5000
D24	0.8284	0.8416	0.8541	0.8667	0.8793	0.8918	0.9044	0.9144	0.9238	1.0000
D25	0.7974	0.7999	0.8031	0.8067	0.8216	0.8367	0.8601	0.8917	0.9032	1.0000
D26	0.4801	0.5740	0.6465	0.6979	0.7403	0.7961	0.8923	0.9479	1.1647	1.0000
D27	0.4575	0.5256	0.5905	0.6517	0.7071	0.7651	0.8286	0.8952	0.9640	1.0000
D28	0.3942	0.4538	0.5233	0.5850	0.6459	0.7086	0.7731	0.8406	0.9231	1.0000
D29	0.4818	0.5619	0.6359	0.6652	0.7588	0.8438	0.9387	1.0000	1.0000	0.8916
D30	0.4807	0.5056	0.5579	0.8250	0.8428	0.8368	0.8232	0.9412	1.0000	0.8749
D31	0.8767	0.9460	1.0000	0.8832	0.8821	0.8218	0.7100	0.6657	0.7078	0.4502
D32	0.5716	0.6364	0.6812	0.7281	0.7926	0.8295	0.9066	0.9515	1.0000	0.8636
D33	0.5724	0.5484	0.6187	0.5971	0.9127	1.0000	0.9190	0.9566	0.9627	0.8935
D34	0.5615	0.5724	0.8237	0.8129	0.8125	0.8605	0.8728	0.8853	0.9171	1.0000
D35	0.6992	0.7186	0.7452	0.8446	0.8377	0.8446	0.8110	0.8622	0.9317	1.0000

.

(3) The differential square fuzzy matter–element is constructed.

The maximum value of each index in the optimal membership fuzzy matter–element matrix in 10 years is taken as the standard fuzzy matter–element, that is, $u_{0j}=1 \left(j=1, 2\dots n\right)$.

Table 4. Differential square fuzzy matter–element matrix.

Index Layer	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
D1	0.0058	0.0095	0.0002	0.0002	0.0001	0.0000	0.0000	0.0148	0.0123	0.0596
D2	0.0016	0.0011	0.0002	0.0001	0.0001	0.0000	0.0006	0.0405	0.0329	0.0288
D3	0.0012	0.0022	0.0042	0.0000	0.0205	0.0292	0.0188	0.0084	0.0022	0.0000
D4	0.0794	0.0237	0.0314	0.0302	0.0268	0.0067	0.0072	0.0060	0.0055	0.0000
D5	0.0154	0.0000	0.0137	0.0310	0.0354	0.0542	0.0207	0.0210	0.0432	0.1243
D6	0.0577	0.0000	0.0754	0.0939	0.0976	0.1511	0.1526	0.1969	0.2130	0.2056
D7	0.1680	0.2320	0.2356	0.0000	0.0931	0.0364	0.2545	0.2351	0.1624	0.0803
D8	0.2121	0.2394	0.1680	0.2543	0.0917	0.0000	0.3379	0.5255	0.5099	0.4698
D9	0.0000	0.0893	0.0901	0.1004	0.0924	0.0938	0.0900	0.0791	0.0785	0.0708
D10	0.4041	0.4104	0.4021	0.3317	0.3712	0.4410	0.0629	0.0307	0.0116	0.0000
D11	0.5264	0.0000	0.2668	0.6967	0.6319	0.6664	0.4875	0.3705	0.5030	0.8355
D12	0.2584	0.2541	0.2694	0.1321	0.1773	0.4104	0.3104	0.2401	0.3356	0.0000
D13	0.5668	0.5552	0.5316	0.5662	0.5565	0.5720	0.1975	0.0000	0.1601	0.4495
D14	0.0094	0.0029	0.0059	0.0007	0.0000	0.0000	0.0000	0.0000	0.0020	0.0000
D15	0.0018	0.0833	0.0161	0.0003	0.0015	0.0000	0.0000	0.0000	0.0000	0.0000
D16	0.1795	0.1795	0.2525	0.2574	0.0428	0.0788	0.0583	0.0055	0.0088	0.0000
D17	0.8025	0.7830	0.7302	0.5894	0.5896	0.5891	0.3441	0.2824	0.0000	0.0117
D18	0.5769	0.4865	0.3990	0.0684	0.0027	0.0000	0.0440	0.0455	0.0383	0.0067
D19	0.0000	0.0000	0.0002	0.0002	0.0001	0.0001	0.0000	0.0007	0.0000	0.0003
D20	0.0010	0.0311	0.0241	0.0181	0.0180	0.0026	0.0000	0.0000	0.0000	0.0000
D21	0.0764	0.0013	0.0005	0.0003	0.0001	0.0000	0.0020	0.0000	0.0084	0.0567
D22	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0001	0.0006	0.0000
D23	0.0349	0.0376	0.0387	0.0323	0.0198	0.0116	0.0016	0.0000	0.0010	0.2500
D24	0.0294	0.0251	0.0213	0.0178	0.0146	0.0117	0.0091	0.0073	0.0058	0.0000
D25	0.0410	0.0401	0.0388	0.0374	0.0318	0.0267	0.0196	0.0117	0.0094	0.0000
D26	0.2703	0.1815	0.1250	0.0913	0.0674	0.0416	0.0116	0.0027	0.0271	0.0000
D27	0.2944	0.2250	0.1677	0.1213	0.0858	0.0552	0.0294	0.0110	0.0013	0.0000
D28	0.3670	0.2984	0.2272	0.1722	0.1254	0.0849	0.0515	0.0254	0.0059	0.0000
D29	0.2685	0.1919	0.1326	0.1121	0.0582	0.0244	0.0038	0.0000	0.0000	0.0118
D30	0.2697	0.2444	0.1955	0.0306	0.0247	0.0266	0.0313	0.0035	0.0000	0.0156
D31	0.0152	0.0029	0.0000	0.0136	0.0139	0.0318	0.0841	0.1118	0.0854	0.3023
D32	0.1835	0.1322	0.1016	0.0740	0.0430	0.0291	0.0087	0.0023	0.0000	0.0186
D33	0.1828	0.2040	0.1454	0.1623	0.0076	0.0000	0.0066	0.0019	0.0014	0.0113
D34	0.1923	0.1829	0.0311	0.0350	0.0351	0.0195	0.0162	0.0132	0.0069	0.0000
D35	0.0905	0.0792	0.0649	0.0242	0.0263	0.0242	0.0357	0.0190	0.0047	0.0000

presents the matrix of the difference square fuzzy matter–element, which is obtained using Equations (5) and (6) to calculate the difference between square fuzzy matter–elements.

(4) Entropy method to determine the weight.

According to Equation (7), normalized judgment matrix $B$ is obtained, and the entropy value $H_i$ is obtained from Equation (8), weight $w_i$ is obtained from Equation (9), the entropy of each index and the weight coefficient of each index in each layer are shown in

Table 5. Entropy of each index and weight coefficient of each index in each layer.

Index Layer	$\mathbf{Entropy} {\mathit{H}}_{\mathit{i}}$	Weight Coefficient of Index Layer (D Layer) to Criterion Layer (B Layer)	Weight Coefficient of Index Layer (D Layer) to Factor Layer (C Layer)	Weight Coefficient of Index Layer (D Layer) to Target Layer (A Layer)
D1	0.9404	0.0676	0.2318	0.0143
D2	0.8937	0.1204	0.4132	0.0255
D3	0.9087	0.1035	0.3550	0.0219
D4	0.9306	0.0786	1.0000	0.0167
D5	0.9432	0.0643	0.1021	0.0136
D6	0.8422	0.1789	0.2840	0.0379
D7	0.7725	0.2578	0.4092	0.0547
D8	0.8863	0.1289	0.2047	0.0273
D9	0.6126	0.2198	0.3440	0.0931
D10	0.8230	0.1004	0.1571	0.0425
D11	0.9462	0.0305	0.0478	0.0129
D12	0.9158	0.0478	0.0748	0.0202
D13	0.7086	0.1653	0.2587	0.0700
D14	0.9187	0.0461	0.0721	0.0195
D15	0.9488	0.0290	0.0454	0.0123
D16	0.8453	0.0878	0.3965	0.0372
D17	0.9053	0.0537	0.2427	0.0228
D18	0.9298	0.0398	0.1799	0.0169
D19	0.9294	0.0401	0.1809	0.0170
D20	0.8827	0.0665	0.4766	0.0282
D21	0.9239	0.0432	0.3093	0.0183
D22	0.9473	0.0299	0.2141	0.0127
D23	0.9463	0.0765	0.3265	0.0129
D24	0.8678	0.0777	0.3315	0.0318
D25	0.7405	0.0802	0.3421	0.0624
D26	0.8962	0.0776	0.2507	0.0249
D27	0.8945	0.0773	0.2497	0.0253
D28	0.8859	0.0774	0.2501	0.0274
D29	0.8936	0.0773	0.2495	0.0256
D30	0.8852	0.0756	0.1658	0.0276
D31	0.9359	0.0756	0.1658	0.0154
D32	0.9025	0.0768	0.1684	0.0234
D33	0.8524	0.0749	0.1642	0.0355
D34	0.9038	0.0767	0.1682	0.0231
D35	0.8796	0.0764	0.1676	0.0289

.

(5) Calculation of Euclidean proximity complex fuzzy matter–element.

Using the results obtained from the calculations mentioned above and Equation (11), the Euclidean proximity degrees of A, B, C, and D, representing Kunming City’s resource and environmental carrying capacity between 2011 and 2020, are presented in

Table 6. Euclidean proximity matrix at each level.

	Index Layer	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020
Target layer	Resources and environment carrying capacity (A)	0.5702	0.5816	0.5967	0.6296	0.6555	0.6525	0.7066	0.7411	0.7365	0.7032
Criterion layer	Resources (B1)	0.7018	0.6942	0.6843	0.7677	0.7554	0.7916	0.6253	0.5851	0.6077	0.6346
	Environment (B2)	0.5016	0.5034	0.5012	0.5154	0.5372	0.5119	0.6625	0.7535	0.7188	0.6554
	Social Economy (B3)	0.5851	0.6236	0.6853	0.7335	0.7932	0.8271	0.8460	0.8734	0.8933	0.7847
Element layer	Agricultural Resources (C1)	0.9507	0.9412	0.9599	0.9905	0.9143	0.8981	0.9168	0.8479	0.8688	0.8397
	Forest Resources (C2)	0.7181	0.8460	0.8228	0.8263	0.8362	0.9181	0.9152	0.9225	0.9259	1.0000
	Living Resources (C3)	0.6393	0.6206	0.6081	0.7138	0.7030	0.7483	0.5323	0.4883	0.5145	0.5527
	Water Environment (C4)	0.4946	0.4883	0.4845	0.4743	0.4731	0.4413	0.6279	0.7398	0.6542	0.5750
	Atmospheric Environment (C5)	0.3920	0.4095	0.4091	0.4926	0.5993	0.5826	0.6616	0.7189	0.8982	0.9359
	Solid waste environment (C6)	0.8447	0.8765	0.8921	0.9067	0.9072	0.9649	0.9750	0.9941	0.9477	0.8676
	Population (C7)	0.8124	0.8148	0.8185	0.8291	0.8510	0.8704	0.8987	0.9197	0.9261	0.7143
	Economic level (C8)	0.4522	0.5265	0.5961	0.6476	0.7098	0.7730	0.8449	0.9011	0.9073	0.9458
	Infrastructure (C9)	0.6055	0.6248	0.7008	0.7626	0.8412	0.8520	0.8257	0.8412	0.8723	0.7598

. A higher Euclidean closeness value signifies closer proximity of the resource and environmental carrying capacity to the optimal level. A proximity degree of 1 indicates the highest level of carrying capacity, whereas a proximity degree of 0 indicates the lowest level of carrying capacity. In this study, the proximity degree is used to measure the resource and environmental carrying capacity, and the dynamic changes in Kunming City’s carrying capacity are quantitatively analyzed by observing the changes in time series data of the Euclidean proximity degree. The annual proximity degree can be used to determine the level of the carrying capacity of resources and the environment and to identify strengths and weaknesses [15].

3.4. Evaluation Result Analysis

Figure 2, Figure 3, Figure 4, Figure 5 depict the analysis of the comprehensive evaluation index for the resource and environment carrying capacity and its subsystems (resource, environment, economic, and social) of Kunming City from 2011 to 2020.

Pearson’s correlation coefficient was computed using SPSS 26.0 software to determine the correlation between the comprehensive carrying capacity and sub-carrying capacity of resources and environment in the time series. The results are presented in

Table 7. Time series correlation coefficients of resources and environment carrying capacity and sub-carrying capacity in Kunming City.

Target Layer	Resources	Environment	Social Economy
Resource and environmental carrying capacity (Pearson’s correlation)	−0.615	0.928 **	0.938 **

Note: ** in Table 7 indicates that the correlation between the two indicators is statistically significant at the p < 0.01 level.

,

Table 8. Time series correlation coefficients between resource carrying capacity and sub-carrying capacity of Kunming City.

Criterion Layer	Living Resources	Agricultural Resources	Forest Resources
Resource subsystem (Pearson’s correlation)	0.999 **	0.602	−0.444

Note: ** in Table 8 indicates that the correlation between the two indicators is statistically significant at the p < 0.01 level.

,

Table 9. Time series correlation coefficients between environmental carrying capacity and sub-carrying capacity of Kunming City.

Criterion Layer	Water Environment	Atmospheric Environment	Solid Waste Environment
Environmental subsystem (Pearson’s correlation)	0.962 **	0.825 **	0.601

Note: ** in Table 9 indicates that the correlation between the two indicators is statistically significant at the p < 0.01 level.

,

Table 10. Time series correlation coefficients between the Kunming socioeconomic carrying capacity and sub-carrying capacity.

Criterion Layer	Population	Economic Level	Infrastructure
Socioeconomic subsystem (Pearson’s correlation)	0.583	0.916 **	0.967 **

Note: ** in Table 10 indicates that the correlation between the two indicators is statistically significant at the p < 0.01 level.

.

(1) The resource and environmental carrying capacity of Kunming City demonstrated a general upward trend between 2011 and 2020, with two minor fluctuations. Specifically, the carrying capacity index remained stable at 0.65 in both 2015 and 2016, followed by a continuous increase. It reached a peak of nearly 0.75 in 2018, marking a 10-year high, and then slightly declined to 0.7 in 2020 (Figure 2). During this period, the carrying capacity index of the environmental and socioeconomic subsystems increased while that of the resource subsystem decreased. Based on Pearson’s correlation coefficient calculation results presented in Table 7, a significant positive correlation was observed between the environmental and socioeconomic subsystems and the resources and environment carrying capacity, with correlation coefficients of 0.928 and 0.938, respectively. However, the resource subsystem had a moderate negative correlation with the resources and environment carrying capacity. This suggests that the level of resource carrying capacity is lagging behind that of the environmental and socioeconomic carrying capacity, and resources are becoming a bottleneck and restriction factor in the development of resource and environmental carrying capacity in Kunming City.

In recent years, the rapid development of industrialization and urbanization in Kunming City has resulted in increased pressure on resources and the environment. The urbanization rate has approached 80%, and the utilization rate of land has reached 82.55%, leading to insufficient land resources for development and utilization. Although the ecological environment quality is satisfactory and the water quality of centralized drinking water sources is 100%, the availability of water resources remains extremely limited. In the Dianchi Lake Basin, the annual per capita water resource utilization is merely 271 m³, which is only 1/8th of the national average. Despite the improvement in the environmental condition of the Dianchi Lake basin, the protection task of Dianchi Lake still requires a significant amount of work. Furthermore, ecological degradation, rocky desertification of land, soil pollution, and invasion of alien species still exist in certain areas. In 2020, the average equivalent sound level of environmental noise (daytime) in the main urban areas of Kunming was 53.9 decibels, and the overall equivalent sound level of daytime environmental noise in the counties was at level 2. Overall, while the environmental quality in the city is good, there are still resource constraints and environmental challenges that need to be addressed.

(2) The trend analysis in Figure 3 reveals that the resource subsystem’s carrying capacity level exhibits unstable fluctuations, with the carrying capacity index decreasing from 0.70 in 2011 to 0.63 in 2020. The living resources and resource subsystems demonstrate similar, changing patterns, characterized by a decline, followed by an increase, then another decline, and finally another rise. Factors such as total water supply, per capita urban road area, per capita household consumption of liquefied gas, and per capita living water consumption exhibit an overall upward trend with minor fluctuations observed over the course of the decade. Meanwhile, the carrying capacity index of agricultural resources decreased from 0.95 in 2011 to 0.84 in 2020 due to the declining crop yield and agricultural fertilizer amount. However, the forestry resources’ carrying capacity is increasing rapidly and has little impact on the decline of the resource carrying capacity. The rise in forestry resources is closely related to Kunming City’s investment and development in landscaping. According to Table 8, the Pearson Pearson’s correlation coefficient between the resource carrying capacity and sub-carrying capacity of Kunming City shows that living resources and agricultural resources have a significant positive correlation with the resource subsystem, with a correlation coefficient of 0.999 and 0.602, Conversely. In contrast, forestry resources exhibit a negative correlation with the resource subsystem, implying that lower consumption of forestry resources leads to a higher carrying capacity for the resource subsystem. To summarize, the level of carrying capacity for living resources has a more significant influence and constraint on the carrying capacity level of the resource subsystem compared to agricultural and forestry resources, with forestry resources having the least impact.

During the “13th Five-Year Plan” period, the government implemented measures to ensure the safety of agricultural production environments by managing agricultural land and formulating a soil protection plan. Despite an increase in population, the carrying capacity of agricultural resources showed a downward trend, while cultivated land area and grain output remained stable. The government has also taken steps to protect the local ecology in Kunming by implementing forest land construction projects, such as returning farmland to forest and grassland, protecting natural forests, and establishing a shelterbelt system. As of 2020, the forest coverage rate in Kunming reached 52.62%. However, due to the expanding population, the supply and demand of basic living resources are insufficient, and living resources have a greater impact on the carrying capacity of resources.

(3) Figure 4 depicts that the environmental carrying capacity index of the environmental subsystem remained stable around 0.50, within a small range between 2011 and 2016. Subsequently, it exhibited a rapid increase from 2016 to 2018, reaching its peak value in a decade at 0.75 before declining to 0.65 in 2020. The trend observed in the water environmental carrying capacity index aligns with the curve of the carrying capacity index in the environmental subsystem. The improvements in the environment and the alteration in environmental carrying capacity can be attributed to notable reductions in the discharge of chemical oxygen demand (COD) and ammonia nitrogen from industrial wastewater and domestic sewage. Additionally, the increased implementation of centralized sewage treatment and compliance with drinking water standards have played a significant role in enhancing the environment and influencing the change in environmental carrying capacity. The atmospheric carrying capacity index has been consistently on the rise in the past decade, especially from 2016 to 2020, due to the reduction in industrial SO₂ and smoke and dust emissions, which has significantly improved air quality. The environmental carrying capacity index of solid waste increased by 17.86% from 0.84 in 2011 to 0.99 in 2018 and then slightly decreased to 0.87 in 2020. The harmless treatment of household waste contributed to the improvement of the environmental carrying capacity index of solid waste. The fluctuation of the utilization rate of solid waste and hazardous waste also affects the carrying capacity index. According to Table 9, by calculating Pearson’s correlation coefficient between Kunming’s environmental carrying capacity and its sub-carrying capacity, it is apparent that the water environment and atmospheric environment are significantly positively correlated with the environmental subsystem, with a correlation coefficient of 0.962 and 0.825, respectively. The correlation coefficient between the solid waste environment and the environmental subsystem is slightly weaker compared to the correlation between the water environment and atmospheric environment, with a coefficient of 0.601. Since the 18th CPC National Congress, the pursuit of ecological progress has been incorporated into the comprehensive plan for the cause of socialism with Chinese characteristics, encompassing five key areas. This has reversed the situation of ecological and environmental damage and contributed to the continuous improvement of ecological and environmental quality, including in Kunming City. In conclusion, the water environment and atmospheric environment significantly impact the environmental subsystem, while the solid waste environment has a minor effect.

In accordance with the “13th Five-Year Plan,” Kunming City was required to meet the national secondary standards for environmental air quality by the end of 2020, with more than 92% of days in urban areas meeting this standard. Moreover, the remediation of Dianchi Lake remains a key objective in the development of water ecological civilization. It is imperative to continuously enhance the urban sewage treatment system, bolster the protection of rivers and their tributaries, preserve and safeguard water resources, and optimize their utilization rate. The comprehensive utilization of solid waste as a resource has been significantly improved, with the establishment of a complete solid waste pollution prevention and control facility and management system and the achievement of 100% harmless treatment of urban household waste.

(5) From Figure 5, it can be observed that the socioeconomic subsystem’s carrying capacity index increased steadily, peaking at 0.89 in 2019. However, in 2020, due to the impact of the COVID-19 pandemic, the carrying capacity index decreased significantly to 0.78, with a decline rate of 12.36%. The trend of the infrastructure curve also followed that of the socioeconomic subsystem, peaking at 0.87 in 2019. The carrying capacity of the socioeconomic subsystem is significantly influenced by four key aspects: transportation, scientific research, medical care, and education which cater to the fundamental needs of human survival. Factors such as per capita passenger traffic, per capita freight traffic, vehicle count, number of scientific researchers, number of healthcare institutions, and number of high school graduates exert substantial impacts on the carrying capacity. The population decreased significantly in 2020 due to the national fertility policy and the pandemic but steadily increased in the remaining nine years with minimal fluctuations. The economic level has been steadily increasing, but the growth rate was lower in 2020 than in previous years due to the pandemic. According to Table 10, the economic level and infrastructure are significantly and positively correlated with the socioeconomic subsystem, with correlation coefficients of 0.916 and 0.967, respectively. However, the correlation coefficient for population size is relatively small at 0.583. To summarize the carrying capacity of the socioeconomic subsystem is primarily influenced by the economic level and infrastructure, whereas the population exerts a relatively lesser impact.

4. Conclusions and Discussion

In this research paper, an evaluation system for the carrying capacity of resources and the environment in Kunming City was constructed using three subsystems: resources, environment, and social economy. The application of the fuzzy matter–element model facilitated an analysis of the carrying capacity of resources and the environment in Kunming City between 2011 and 2020. The primary objective was to establish a harmonious relationship among resources, the environment, and socioeconomic development, ensuring sustainable development and ecological preservation. The findings indicate that the level of resource and environment carrying capacity in Kunming is gradually increasing, with the environmental subsystem and the socioeconomic subsystem showing steady growth, while the resource subsystem is exhibiting a downward trend. The results also suggest that the level of resource carrying capacity lags behind that of the environment and socio-economy. These findings are significant for guiding the steady and high-quality development of Kunming’s economy in a sustainable and ecologically friendly manner.

(1) The carrying capacity of resources is greatly affected by the high consumption of living and agricultural resources, leading to a reduction in their carrying capacity. On the other hand, the consumption of forestry resources has a smaller impact and is beneficial for the improvement of resource carrying capacity. As of the end of 2020, Kunming City has achieved significant progress in environmental protection and resource management, including an increase in urban green space by 1559.15 hm², a forest coverage rate of 52.62%, and soil erosion control in an area of 1691 km². This demonstrates China’s substantial investment in protecting forestry resources and improving environmental quality.

(2) The environmental subsystem in Kunming City has witnessed significant improvements in recent years, thanks to the implementation of ecological governance. Consequently, significant improvements have been observed in both the water and atmospheric environments. Furthermore, the implementation of garbage classification methods and awareness-raising campaigns has played a key role in enhancing the solid waste environment. At the end of 2020, the overall water quality of Dianchi Lake showed marked improvements, while the main city’s air quality remained above 98%. Furthermore, the municipal household garbage treatment facilities’ coverage rate and the effective treatment rate of household garbage in villages have both reached 100%. Notably, Kunming City is a national demonstration city for the treatment of black and smelly water bodies.

(3) The improvement in the economic level and infrastructure has resulted in an increase in population, thereby significantly enhancing the socioeconomic carrying capacity. By 2020, Kunming’s gross regional product had increased to CNY 673.379 billion, marking a cumulative growth of 40.6% from CNY 434.238 billion in 2015. Additionally, the urbanization rate grew by 13.7%, from 70.05% in 2015 to 79.67% in 2020. Furthermore, the city invested a total of CNY 51 billion in research and development, with an average annual growth rate of 11.6%. Education, medical care, science, and technology have also progressed, significantly improving people’s livelihood.

The analysis indicates that the carrying capacity of resources and the environment in Kunming City has been steadily increasing over the years, which is a positive trend. The enhancement of the carrying capacity in the environmental subsystem can be attributed to Kunming’s decade-long endeavors in energy conservation, emission reduction, and afforestation. Likewise, there has been an improvement in the carrying capacity of the socioeconomic subsystem, reflecting the fundamental support that rapid economic development offers to social activities. However, the decline in carrying capacity within the resource subsystem underscores the challenges posed by population growth in Kunming City, leading to a conflict between human needs and land availability, and unequal distribution of resources. To achieve the objectives set forth in the “13th Five-Year Plan,” Kunming City must increase its gross regional product by more than 9%, achieve a gross enrollment rate of 98.36% for senior high schools, increase the forest coverage rate, and meet provincial targets for water consumption, environmental air quality, and the reduction of major pollutants such as chemical oxygen demand, ammonia nitrogen, sulfur dioxide, and nitrogen oxide emissions. Nonetheless, the city has failed to meet its 2020 target for the number of hectares of arable land. In the 14th Five-Year Plan, the state has called for the strengthening of the strategy to enhance China’s human resources, optimize the spatial layout of the territory, and construct a robust ecological security barrier.

Considering the population growth trends and available resources, it is necessary to propose effective and feasible recommendations for the rational planning of the ecological economy’s spatial layout in Kunming City in the future.

(1) In light of the resource issues faced by Kunming City, it is essential to prioritize the optimization of the resource utilization rate for living facilities. To accomplish this, it is important to enhance the efficiency of resource utilization in household liquefied gas equipment. Furthermore, the promotion of water conservation and domestic water reuse concepts is crucial to increase public awareness and ensure the sustainable utilization of water resources. It is also crucial to rationalize the allocation of cultivated land area in conjunction with the rural population’s size to enhance the cultivated land output to meet the needs of people’s lives and support the economic development of society. Furthermore, increasing the forestry acreage and green coverage should remain a top priority, and efforts should be directed toward constructing green villages and cities.

(2) In light of the environmental challenges in Kunming City, it is crucial to remain vigilant toward “black, evil, and smelly” water bodies. To improve water quality and the water environment quality, the treatment of Dianchi Lake must continue. Despite some improvements in the atmospheric environment, efforts to reduce the emission of industrial harmful gases and CO₂ emissions should be intensified to enhance air quality. Additionally, it is vital to improve the street environment, rationally optimize the urban spatial layout, and mitigate environmental noise pollution. The implementation of garbage classification should involve improving publicity and raising public awareness of garbage classification, increasing the standard rate of garbage classification, and reducing environmental pollution caused by improper garbage disposal.

(3) Considering the social and economic challenges faced by Kunming City, the city has witnessed continuous growth in economic development. However, the rise in population has also exerted pressure on the city’s infrastructure resources and allocation of urban space. Therefore, the next step is to rationally optimize urban space, enhance the infrastructure utilization rate, control the population growth, alleviate the pressure on Kunming’s social and economic environment, improve the carrying capacity, and overcome the current state of population expansion and resource scarcity in Kunming.