Evaluation of Urban Public Building Renovation Potential Based on Combination Weight Cloud Model—Case Study in China

Abstract

Currently, urban renovation activities in China are booming. And promoting the renovation of public buildings is a key feature of urban renovation due to its large scale, high cost, and significant impact to the natural and social environment. To reduce the ambiguity and uncertainty in evaluating the potential for the renovation of existing public buildings, a renovation potential evaluation model integrating a game theory-based combination weighting method and cloud model theory is proposed. This paper constructs a comprehensive evaluation index system based on relevant standards and the literature. Game theory is used to optimize the weights obtained by AHP and entropy weight methods to obtain a combined weight. MATLAB programming is used to calculate the comprehensive cloud parameters of the evaluation index for the potential renovation of existing public buildings and therefore generate cloud Graphs. Through a case study in Nanjing, China, it was demonstrated that the combination weight cloud model can objectively reflect the relationship between the fuzziness and randomness of evaluation indicators for public building renovation potential. The visual expression of cloud Graphs can intuitively reflect the magnitude of renovation and renovation potential and the degree of uncertainty in evaluation results. The research result provides useful references for the sustainable utilization of building resources in the era of building.

1. Introduction

Urban renovation refers to a series of actions aimed at demolishing, rebuilding, and comprehensively improving areas that have experienced physical, functional, or social decline, as well as built environments that no longer meet current housing or future development needs [1]. As China shifts towards high-quality urbanization, urban renovation has transitioned from large-scale incremental development to smaller-scale, quality-focused improvements [2]. In 2020, the Fifth Plenary Session of the 19th Central Committee of the Communist Party of China approved the “Recommendations for Formulating the 14th Five-Year Plan for National Economic and Social Development and the Long-Range Objectives Through the Year 2035”, explicitly proposing the implementation of urban renovation actions. Subsequently, the report of the 20th National Congress further emphasized the need to “enhance the Grades of urban planning, construction, and accelerate the transformation of development patterns in large cities, as well as implement urban renovation actions”. This report has elevated urban renovation to an unprecedented national strategic priority [3].

According to the “Implementation Plan for Promoting the Renovation of Building and Municipal Infrastructure Equipment” [4] and the “Five-Year Action Plan for the In-Depth Implementation of a People-Centered New Urbanization Strategy” [5], which were issued by the Ministry of Housing and Urban-Rural Development and the State Council in 2024, public building renovation content encompasses several aspects: infrastructure and equipment upgrades, improvements of safety and building energy efficiency, environmental facility upgrades, functional space modifications and the integration of intelligent and information systems, as well as cultural and historical preservation. As a critical component of urban renovation, public building renovation is characterized by large areas, low design standards, and significant energy and environmental burdens [6]. Current research on public building renovation has made substantial progress in areas such as research of renovation implementation pathways, stakeholder rights, and funding sources analysis during the renovation process [7,8,9]. However, there remains a gap between theory and practice, especially a lack in research about the potential evaluation of public building renovation.

The potential for retrofitting public buildings is based on the current situation of existing public buildings, such as cultural history, geographical location, structural safety, and comfortable use. It is a practical activity that transforms potential utility into actual utility through external conditions [10]. The evaluation of the potential for renovation of existing buildings is the basis for determining renovation plans (demolition, repair and renovation, preservation and renovation). At present, scholars at home and abroad mainly focus on the evaluation of urban planning, evaluation of renovation plans, and performance evaluation after renovation [11]. Urban planning evaluation mainly evaluates the potential for urban regional renovation from a medium perspective, including land use renovation and regional environmental efficiency. Haghighi Fard and Doratli [12] and Foroughi and Rasol [13] used a method combining GIS and AHP to determine the retrofit sequence of urban areas; Martí et al. [14] evaluated the activity level in urban areas based on user data from social networks (LBSN); and Yao et al. [15] established a land application potential evaluation system based on multiple perspectives such as geology, architecture, agglomeration, public facilities, and social factors to optimize land resources from the perspective of urban renovation. They also developed an AET (AHP-EWM-TOPSIS) model to evaluate the potential for renovation and transformation in corresponding areas. Wang [16] evaluated the renovation potential of Shenzhen’s administrative regions based on Internet data; Han [17] proposed the concept model of spatial renovation and reproduction in Yaohai Old Industrial Zone, Hefei City; and Wang [18] explored the direction and implementation path of urban historical street and alley space renovation from the perspective of block memory.

The evaluation of the retrofit plan is based on the theories of energy conservation, emission reduction, and sustainable development, aiming to improve the functionality of existing buildings and enhance user satisfaction. Kim [19] defines sustainability as three categories: physical, cultural, and ecological. Specific renovation plans are compared from three dimensions: social and economic environmental benefits, and the optimal renovation plan is selected; Jun [20] analyzed the relationship between the green renovation effect of existing buildings and energy consumption with the goal of improving user comfort; and Liu [21] proposed the TOPSIS decision-making method based on cloud models for evaluating green renovation plans for existing public buildings.

The performance evaluation after renovation is an assessment of the effectiveness of the renovation. Zhu [22] used the Analytic Hierarchy Process and TOPSIS method to construct a comprehensive evaluation model, evaluating the renovation performance from four aspects: building performance, economic performance, environmental performance, and social performance; Pan [23] constructed a multidimensional evaluation index system for the renovation of existing residential areas from the perspective of residents’ welfare level. Based on a multi-source data analysis and combined with a cloud model calculation of the numerical characteristics of the indicators, the welfare level of the renovation was evaluated and suggestions were made. Li et al. [24] evaluated the transformation performance from the perspectives of input and output and constructed an evaluation model using principal component analysis (PCA) and data envelopment analysis (DEA) methods.

From the perspective of evaluation methods, the evaluation methods for retrofitting potential can be summarized into two categories. The most common is the multi-objective and multi-attribute decision-making method based on fuzzy theory, which focuses on the establishment of evaluation indicators, calculation of indicator weights, and membership degrees. Another method is to convert multiple objectives into a single objective and calculate the retrofit potential value by establishing an evaluation model to calculate the utility function, such as the ARP (Adaptive Reuse Potential) model [25], AdaptSTAR model [26], etc.

In summary, there are two prominent issues in the evaluation of urban public building renovation and renovation: first, the evaluation of public building renovation potential belongs to the planning evaluation category, and existing research mainly focuses on urban and regional renovation evaluation, with relatively little research on the evaluation of specific public building renovation potential. The existing literature mainly focuses on scheme evaluation and performance evaluation after renovation, and the indicator systems constructed by different studies have significant differences; second, the evaluation indicators are mainly qualitative and subjective. In addition, the multi-objective and multi-attribute evaluation method based on fuzzy decision theory cannot reflect the degree of uncertainty of evaluation indicators and evaluation results; although the utility function evaluation method represented by ARP is expressed simply and intuitively, the calculation of relevant parameters and the acquisition of data are relatively difficult and cannot clearly reflect the inherent relationship between evaluation results and evaluation indicators.

Therefore, this article takes the Nanjing Military Club urban renovation project as an example to establish an existing public building renovation potential index system and renovation potential evaluation cloud model. The game theory-based combination weighting method is used to calculate the index weights, and MATLAB R2023b is used for programming and computing a cloud model potential index membership degree and a comprehensive analysis of evaluation results, providing decision-making recommendations for existing building renovation.

2. Materials and Methods

2.1. Evaluation Index System for Public Building Renovation Potential

The establishment of a comprehensive evaluation index system should adhere to principles of systematic, scientific, and a combination of qualitative and quantitative approaches. Typically, methods such as a literature review and expert consultation are employed to develop the index system. The factors influencing the renovation potential of existing public buildings are complex and can be categorized from different dimensions depending on the evaluation method. Langston [27] categorized the influencing factors of urban building renovation potential into seven types of obsolescence such as “physical, economic, functional, technological, social, legal and political and so on”. Wu [10] divided the influencing indicators for evaluating the renovation potential of public buildings into five categories, such as “building integrity, energy optimization, historical continuity, future profitability, and environment revenue”.

Given the dynamic nature of urban renovation activity across time and space dimensions, the renovation plan needs to follow the principle of “one city, one strategy; one district, one policy” [28]. The evaluation indicators for the renovation of existing public buildings should reflect both the project’s generality and the individuality that captures the uniqueness of each project. Based on previous studies [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] and industry standards such as GB/T 33171-2016 [29,30], GB/T 18507-2014 [31], and GB 50292-2015 [32], an initial index system was established. Subsequently, after gathering opinions from functional departments responsible for construction management, scholars of universities, and facility management experts, the final determination of a comprehensive evaluation system for public building renovation potential was developed. This system includes one target index, four criteria indices, and twenty-nine observational indices, as illustrated in

Table 1. Comprehensive evaluation index system for the renovation potential of existing public buildings.

Target	Criteria Layer		Indicator Layer		Reference
Renovation Potential of Existing Public Buildings	A	Land Spatial Value	A1	Node Accessibility Coefficient	[10,11,21]
			A2	Land Price Grade	[6,10,12]
			A3	Building Density Ratio	[11,12,13,15]
			A4	Density of Adjacent Buildings	[12,17,18]
			A5	Proportion of Nearby Low-Rise Buildings	[10,11,12,15]
			A6	Continuity Length of Block Facades	[11,12,23]
			A7	Accessibility to the CBD	[13,15,16,22]
			A8	Green Coverage Ratio	[13,14,16,24]
			A9	Commercial and Service Vibrancy	[10,13,16]
	B	Surrounding Traffic Operation Status	B1	Average Travel Speed	[18,23,24]
			B2	Delay Time Ratio	[12,22,23]
			B3	Travel Time Ratio	[23,24,25]
			B4	Traffic Saturation	[22,23,24]
			B5	Roadway Width	[19,22,24]
			B6	Road Function Index	[23,24]
	C	Conditions of Building Itself	C1	Degree of Vacancy	[23,24]
			C2	Spatial Layout Flexibility	[12,13,22]
			C3	Condition of Maintenance	[14,18,22]
			C4	Property Rights Clarity	[19,23]
			C5	Building Age	[10,11,13]
			C6	CO2 Emissions	[11,16,18,20,21]
			C7	Indoor natural light illuminance	[12,13,18]
			C8	Energy consumption	[11,16,18,20,21]
			C9	Component damage parameters	[10,19]
	D	Future Development	D1	Degree of functional obsolescence	[15,16,19]
			D2	Public willingness for renovation	[22,24]
			D3	Compliance of the planned land use	[23,24]
			D4	Historical and cultural heritage value	[10,13,16,22,26]
			D5	Safety resilience degree	[13,21]

.

The four criteria indices comprehensively consider the current state (C) and future development (D) of public buildings over a time dimension. It also covers the land value (A) on which public buildings rely, the current state of the buildings themselves (C), and the surrounding environmental conditions associated with the public buildings (B) from the space dimension. Criterion A represents the attachment of the building to its site, as the value of any building is inherently linked to the value of the land it occupies. This criterion can be viewed as a latent variable, measured using observational indices (A1–A9). Criterion B reflects the impact of the external surrounding environment on the renovation potential of public buildings. Given the “public” nature of public buildings, the surrounding traffic conditions, among various environmental factors, most effectively reflect the potential value of public buildings, which can be measured using observational indices B1–B5. Criterion C represents the function, comfort, and safety of the existing building itself, which is the most important influential criterion on renovation potential. According to relevant standards for the renovation of existing buildings, this criterion is measured using observational indices C1–C9. Criterion C primarily reflects the physical state of the building. Considering the actual situation in China, an additional indicator, C4 (property rights clarity), is added, as clear property ownership helps to reduce legal disputes and obstacles during the renovation process. Criterion D reflects the future value of existing public buildings from a time dimension. Observational indices D1–D5 indicate the subjective willingness for renovation (D2) and the objective expectations of the building’s functional, safety, and historical value (D1, D3–D5).

2.2. Classification of Evaluation Standards

Based on the multi-criteria and multi-Grade evaluation system established in Table 1, the observational indicator layer employs a combination of qualitative and quantitative methods to obtain the basic data. Referring to the relevant literature [10], the evaluation results of public building renovation potential are categorized into five semantic Grades: low potential, relatively low potential, moderate potential, relatively high potential, and high potential, corresponding to the evaluation set U = {I, II, III, IV, V}, which is divided into five equal intervals within [0, 1]. Following similar principles, qualitative observational indicators are formed through the ratings provided by 12 experts in the fields of urban planning, land economics, and urban renovation. Based on relevant evaluation standards and statistical data, different experts, depending on their experience and knowledge, assign scores following the rule of 10-point scale and five equal intervals. For example, in order to obtain the indicator “Land Price Grade A2”, we should first obtain the latest land transaction price of the adjacent plot (P1) and the average land price of the main urban area where the public building located (P0). When P1/P0 < 50%, the corresponding score is within the interval [0, 2), with a rating of “significantly low”; when 25% < P1/P0 < 50%, the corresponding score is within the interval [2, 4), with a rating of “relatively low”; when 25% < P1/P0 < 1.25, the corresponding score is within the interval [4, 6), with a rating of “average”; when 1.25 < P1/P0 < 1.5, the corresponding score is within the interval [6, 8), with a rating of “relatively high”; and when P1/P0 > 1.5, the corresponding score is within the interval [8, 10), with a rating of “significantly high”. For other observational indicators that cannot obtain quantitative evaluation data, the evaluation data can only be obtained based on expert subjective opinions. To eliminate the differences in expert evaluations, the expert linguistic assessments can be converted into triangular fuzzy numbers, and the mean area method can be employed to convert expert opinions into definite values. Furthermore, quantitative observation indicators follow the threshold divisions according to the industry standards outlined in Section 2.1, as detailed in

Table 2. Classification standards for comprehensive evaluation indicators.

Observation Indicators	If Positive	Grades of Potential Evaluation
		Grade I [0, 0.2)	Grade II [0.2, 0.4)	Grade III [0.4, 0.6)	Grade IV [0.6, 0.8)	Grade V [0.8, 1)
A1	-	(1.6, 2]	(1.0, 1.6]	(0.6, 1.0]	(0.4, 0.6]	(0, 0.4]
A2	+	Low	Lower	Moderate	Higher	High
A3	-	[5.4, 6.0)	[4.5, 5.4)	[4.0, 4.5)	[2.5, 4.0)	[2.0, 2.5)
A4	-	(80%, 100%]	(60%, 80%]	(40%, 60%]	(20%, 40%]	(0, 20%]
A5	+	(0, 20%]	(20%, 40%]	(40%, 60%]	(60%, 80%]	(80%, 100%]
A6 (km)	-	(0.6, 1]	(0.4, 0.6]	(0.3, 0.4]	(0.1, 0.3]	(0, 0.1]
A7 (km)	-	(20, 30]	(17, 20]	(10, 17]	(000, 10]	(0, 5]
A8	-	(35%, 60%]	(34%, 35%]	(33%, 34%]	(32%, 33%]	(25%, 33%]
A9	+	(0, 0.10)	[0.10, 0.20)	[0.20, 0.40)	[0.40, 0.50)	[0.50, 0.70)
B1 (km/h)	+	[0, 20)	[20, 30)	[30, 40)	[40, 50)	[50, 60)
B2	-	[0.70, 1.00)	[0.60, 0.70)	[0.50, 0.60)	[0.30, 0.50)	[0, 0.30)
B3	-	[2.20, 7.00)	[1.90, 2.20)	[1.60, 1.90)	[1.30, 1.60)	[1.00, 1.30)
B4	-	[0.90, 1.00)	[0.75, 0.90)	[0.60, 0.75)	[0.40, 0.60)	[0, 0.40)
B5 (m)	+	[12, 20]	[25, 35]	[25, 50]	[35, 50]	[50, 80]
B6	+	(0, 0.40]	(0.40, 0.55]	(0.55, 0.75]	(0.60, 0.80]	(0.80, 1.00]
C1	+	Low	Lower	Moderate	Higher	High
C2	+	Narrow	Relatively Narrow	Adequate	Relatively Spacious	Spacious
C3	-	High	Higher	Moderate	Lower	Low
C4	+	Complex	Relatively Complex	Moderate	Relatively Clear	Clear
C5 (years)	+	(0, 15)	[15, 25)	[25, 30)	[30, 40)	[40, 50)
C6 (kg/m2)	+	(0, 20]	(20, 40]	(40, 60]	(60, 100]	(100, 150]
C7	-	[600, 750)	[450, 600)	[300, 450)	[150, 300)	[100, 150)
C8 kWh/(m2·a)	-	[130,150)	[100, 130)	[50, 100)	[30, 50)	[0, 30)
C9	+	(0, 0.2]	(0.2, 0.4]	(0.4, 0.6]	(0.6, 0.8]	(0.8, 1)
D1	+	Low	Lower	Moderate	Higher	High
D2	+	Negative	Relatively Negative	Moderate	Relatively Positive	Positive
D3	+	Unreasonable	Relatively Unreasonable	Moderate	Relatively Reasonable	Reasonable
D4	+	Low	Lower	Moderate	Higher	High
D5	-	Strong	Relatively strong	Moderate	Relatively low	Low

.

3. Building a Cloud Evaluation Model

Combining probability and fuzzy set theory, the cloud model facilitates the transformation between qualitative and quantitative assessments through forward and backward cloud generators. The model describes linguistic values using three characteristic parameters: Expectation (Ex), Entropy (En), and Hyper Entropy (He). ‘Ex’ represents the central point of the concept. ‘En’ reflects the degree of uncertainty of the concept, and ‘He’ measures the uncertainty of the entropy [33]. The evaluation index system for public building renovation potential is complex, with significant fuzziness and randomness inherent in various indicators. The cloud model not only considers the randomness of the membership degrees of each evaluation indicator but also accounts for the intrinsic relationship between randomness and fuzziness [34], making it well suited for evaluating the renovation potential of existing public buildings.

After establishing the classification standards for the indicators as shown in Table 2, the evaluation based on the cloud model primarily involves two tasks: “determination of weights” and “cloud model evaluation”. The specific process is illustrated in Figure 1.

3.1. Game Theory-Based Combination Weight and Cloud Model Parameters Calculation

Scientifically determining the weights of evaluation indicators is a prerequisite for cloud model evaluation. Existing weighting methods can be categorized into two types of subjective and objective approaches. Subjective weighting methods, such as the Analytic Hierarchy Process (AHP), can leverage the professional experience of decision-makers. However, due to differences in professional knowledge and background among respondents, these methods may lead to instability in the results. On the other hand, objective weighting methods, such as the entropy weight method, are based on sample data but often struggle to reveal the relative relationships between indicators. Considering the strengths and weaknesses of both AHP and the entropy weight method, the combination weighting method based on game theory facilitates the acquisition of comprehensive, balanced, and accurate integrated weights [35].

3.1.1. Analytic Hierarchy Process (AHP)

The 9-point scale method is used to invite experts to assign scores and construct a judgment matrix A_n×n. The square root method is then employed to combine and calculate the experts’ judgment matrices to obtain the indicator weights, followed by a consistency check. The specific process is detailed in Equations (1)–(3).

$$\overline{\mathrm{A}}={({\displaystyle \prod _{k=1}^m{a}_{ij}^k})}^{{\displaystyle \frac{1}{\mathrm{n}}}}$$

(1)

$${\mathrm{W}}_i={\displaystyle \frac{\overline{\mathrm{A}}}{{\displaystyle \sum _{i=1}^n\overline{\mathrm{A}}}}}$$

(2)

$$CR={\displaystyle \frac{CI}{RI}}={\displaystyle \frac{{\lambda }_{max}-n}{(n-1)RI}}<0.1$$

(3)

3.1.2. Entropy Weight Method

This method evaluates the importance of each factor based on the degree of variation of the indicators and information entropy. It calculates the entropy weights after data standardization, as detailed in Equations (4)–(6).

$$p_{ij}={\displaystyle \frac{x_{ij}}{{\displaystyle \sum _{i=1}^n{X}_{ij}}}}$$

(4)

$$e_j=-{\displaystyle \frac{1}{ln\left(n\right)}}{\displaystyle \sum _{i=1}^n{p}_{ij}}ln\left(p_{ij}\right)$$

(5)

$$w_j={\displaystyle \frac{1-e_j}{{\displaystyle \sum _{j=1}^m(1-e_j)}}}(j=1,2,\cdots ,m)$$

(6)

3.1.3. Game Theory-Based Combination Weight

The essence of game theory-based combined weighting lies in aiming for Nash equilibrium, where the goal is to find the weight combination that minimizes the differences between the weight vectors of various indicators. The steps are as follows:

(1) The weight vectors of the subjective and objective indicators are linearly combined to obtain the comprehensive weight vector (In the formula, α₁ and α₂ respectively represent the subjective and objective weight coefficients.):

$$W={\alpha }_1{w}_1^T+{\alpha }_2{w_2}^T$$

(7)

(2) By minimizing the deviation as the objective, the two linear combination coefficients are optimized, resulting in the optimal weights:

$$\min {‖W-w_k‖}_2,k=1,2$$

(8)

(3) According to the properties of matrix differentiation, Equation (8) can be equivalently transformed into a system of linear equations based on the first-order optimality conditions:

$$\left(\begin{array}{cc}{w}_1{w}_1^T& w_1{w}_2^T\\ w_2{w}_1^T& w_2{w}_2^T\end{array}\right)\left[\begin{array}{c}{\alpha }_1\\ {\alpha }_2\end{array}\right]=\left[\begin{array}{c}{w}_1{w}_1^T\\ w_2{w}_2^T\end{array}\right]$$

(9)

(4) By normalizing the subjective and objective weight coefficients, the comprehensive weight ω is determined:

$$\omega ={\alpha }_k/{\displaystyle \sum _{k=1}^2{\alpha }_k}$$

(10)

3.2. Cloud Model Parameters and Membership Degree Calculation

Following the steps outlined above, after calculating the combined weights for each evaluation indicator, the calculation sequence for the cloud model’s relevant parameters and membership degrees corresponds to Equation (11) through (14).

(1) Construct the Evaluation Standard Cloud.

$$\left\{\begin{array}{l}Ex={\displaystyle \frac{U_{\max }+U_{\min }}{2}}\hfill \\ En={\displaystyle \frac{U_{\max }-U_{\min }}{6}}\hfill \\ H{e}_0=k\hfill \end{array}\right.$$

(11)

(2) Calculate the cloud parameters for each evaluation indicator.

$$\left\{\begin{array}{l}\overline{X}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{x}_i}\hfill \\ S^2={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{i=1}^n{(x_i-\overline{X})}^2}\hfill \\ E_x=\overline{X}\hfill \\ E_n=\sqrt{{\displaystyle \frac{\pi }{2}}}\cdot {\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}|x_i-E_x|\hfill \\ H_e=\sqrt{|S^2-E_n^2|}\hfill \end{array}\right.$$

(12)

(3) Calculate the comprehensive cloud parameters for the evaluation object.

$$\left\{\begin{array}{l}Ex={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\omega }_i}E{x}_i}{{\displaystyle \sum _{i=1}^n{\omega }_i}}}\hfill \\ En={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\omega }_i^2}E{n}_i}{{\displaystyle \sum _{i=1}^n{\omega }_i^2}}}\hfill \\ He={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\omega }_i^2}H{e}_i}{{\displaystyle \sum _{i=1}^n{\omega }_i^2}}}\hfill \end{array}\right.$$

(13)

(4) Calculate the membership degree of the evaluation object for each potential Grade.

$$\mu (x_i)=\exp (-{\displaystyle \frac{{(x_i-Ex)}^2}{2y_i^2}})$$

(14)

(5) Generate the evaluation cloud Graph: By combining the evaluation cloud Graph with the standard cloud Graph, the area with the highest overlap between the two cloud Graphs indicates the evaluation Grade.

In Equation (11), ‘k’ is a constant, typically set between 0.005 and 0.01, adjusted according to the degree of fuzziness of the indicators. In Equation (13), ω_i represents the weight. In Equation (14), y_i~N(En,He²) and x_i~N(Ex,y_i²).

4. Case Study

4.1. Case Overview

The Nanjing Military Club is located at 105 Zhongshan North Road, Gulou District. It was founded in 1935, with a land area of approximately 29,070.7 m² and a total construction area of approximately 43,749.22 m², including 14 buildings (as shown in Figure 2). Among them, Building 1 is listed as a cultural relic protection unit in Jiangsu Province in 2006. It used to be the largest book market in East China, with various entertainment facilities such as cinemas and specialty restaurants, making it a popular place for youth leisure and entertainment in Nanjing. On 1 January 2018, the entire store ceased operations, and it remained idle. The Military Club was included in the “2024 Nanjing Urban Renovation Project Implementation Plan” as a key renovation project, aiming to become a combination of historical culture and urban commerce, covering functions such as retail, entertainment, and catering. The renovation project includes cultural relic restoration, exterior facade renovation, site landscape enhancement, optimization of traffic organization, and enhancement of project vitality. The renovation activity started in September 2024.

4.2. Data Sources

In this case, the qualitative indicator data were collected through scores provided by 10 experts, while the “D2 Public Willingness to Retrofit” data were gathered through questionnaire surveys of residents living near the building. Quantitative indicators were obtained in two ways: first, through measurements and calculations based on professional standards such as the General Code for Building Environment GB 55016-2021 [36], Acoustic Environment Quality Standards GB 3096-2008 [37], and so on; and second, by querying relevant departments of Nanjing’s urban construction management, specialized websites, and platforms like the Baidu map. After standardizing the collected qualitative and quantitative indicator data, MATLAB R2023b software was used to develop programs for calculating indicator weights, cloud model parameters, and membership degrees.

4.3. Model Implementation

4.3.1. Establishment of the Evaluation Standard Cloud

The rating intervals were divided based on five semantic Grades of building renovation potential. Setting the hyper-entropy (He) value to 0.005, the standard cloud parameters derived from Equation (11) are presented in

Table 3. Scoring intervals and standard cloud parameters for potential grades.

Interval Division	Semantic Division	Potential Grade	Standard Cloud Parameters (Ex, En, He)
[0, 0.2)	low potential	Grade I	(0.1000, 0.0333, 0.0050)
[0.2, 0.4)	relatively low potential	Grade II	(0.3000, 0.0333, 0.0050)
[0.4, 0.6)	moderate potential	Grade III	(0.5000, 0.0333, 0.0050)
[0.6, 0.8)	relatively high potential	Grade IV	(0.7000, 0.0333, 0.0050)
[0.8, 1)	high potential	Grade V	(0.9000, 0.0333, 0.0050)

. Using the cloud model code in MATLAB, 2000 cloud droplets were generated to plot the evaluation standard cloud Graph.

4.3.2. Calculation of Indicator Combination Weights and Cloud Parameters

Weight Calculation Using the AHP Method: Based on the importance comparisons of indicator weights made by 10 experts, a judgment matrix was constructed. The subjective weights for the evaluation indicators of public building renovation potential were calculated using Equations (1)–(3). The results for the criterion layer are shown in

Table 4. Combination weights and cloud parameters for evaluation indicators.

Criterion Layer							Indicator Layer
Code	ω11 1	ω12 2	ω 3	Ex	En	He	Code	ω21 1	ω22 2	ω0 3	Ex	En	He
	(1)	(2)	(3)	(4)	(5)	(6)		(7)	(8)	(9)	(10)	(11)	(12)
A	0.2914	0.3283	0.2987	0.6263	0.1124	0.0382	A1	0.1964	0.0654	0.2495	0.5700	0.2478	0.0166
							A2	0.1486	0.1063	0.1658	0.7200	0.0426	0.0071
							A3	0.0330	0.0727	0.0169	0.8010	0.0000	0.0000
							A4	0.0687	0.0677	0.0691	0.7000	0.0000	0.0000
							A5	0.1011	0.1326	0.0883	0.8000	0.0000	0.0000
							A6	0.0202	0.0654	0.0019	0.6200	0.0000	0.0000
							A7	0.0426	0.1009	0.0190	0.6143	0.3760	0.1157
							A8	0.0120	0.1308	0.0181	0.8300	0.0000	0.0000
							A9	0.3774	0.2582	0.3715	0.5500	0.0752	0.0323
B	0.1990	0.1641	0.1920	0.6884	0.1604	0.0237	B1	0.1086	0.1301	0.1119	0.5900	0.0978	0.0232
							B2	0.0481	0.1741	0.0675	0.5059	0.3981	0.0515
							B3	0.0337	0.1435	0.0506	0.7040	0.3499	0.1123
							B4	0.2875	0.1887	0.2723	0.6478	0.3553	0.1172
							B5	0.1272	0.2345	0.1437	0.7333	0.0000	0.0000
							B6	0.3950	0.1291	0.3540	0.7650	0.0652	0.0279
C	0.4310	0.3725	0.4195	0.6480	0.2182	0.0292	C1	0.2892	0.0519	0.1875	0.9050	0.0589	0.0259
							C2	0.1508	0.0681	0.1153	0.8000	0.0627	0.0227
							C3	0.0339	0.1414	0.0800	0.5100	0.0677	0.0176
							C4	0.0751	0.0504	0.0645	0.9800	0.0401	0.0130
							C5	0.1115	0.2373	0.1654	0.6200	0.6200	0.0000
							C6	0.0141	0.1254	0.0618	0.4000	0.3008	0.0854
							C7	0.0462	0.1928	0.1090	0.5250	0.3509	0.0900
							C8	0.0186	0.0823	0.0459	0.5631	0.3855	0.0583
							C9	0.2606	0.0504	0.1705	0.4200	0.0852	0.0344
D	0.0786	0.1351	0.0898	0.7883	0.0643	0.0542	D1	0.4175	0.1754	0.4122	0.8050	0.0589	0.0259
							D2	0.0952	0.1992	0.0975	0.8750	0.0501	0.0000
							D3	0.1459	0.1890	0.1469	0.8650	0.0689	0.0085
							D4	0.0447	0.1890	0.0479	0.8400	0.0652	0.0050
							D5	0.2966	0.2473	0.2955	0.6900	0.0752	0.0280

¹ ω₁₁, ω₂₁ represents the criteria layer weight derived from the AHP method. ² ω₁₂, ω₂₂ represents the criteria layer weight derived from the entropy method. ³ ω, ω₀ represents the combination weight derived from the game theory method.

-(1), and the indicator layer results are in Table 4-(7).

Weight Calculation Using the Entropy Method: Data from six public building renovation projects similar to the Military Club building in Nanjing (including Xinjiekou Art Building, Nanjing Normal University Xuanwu Science Park, Hanzhongmen Bus Station, etc.) were collected. Using Equations (4)–(6), the objective weights for the indicators were calculated. The results for the criterion layer and indicator layer are shown in Table 4-(2) and Table 4-(8), respectively.

Combination Weight Calculation: Based on Equations (7)–(10), a MATLAB code was written to calculate the game theory-based combination weight distribution coefficients for the criterion layer, resulting in α1 = 0.802 and α2 = 0.198. The final combination weights for the criterion layer ω are shown in Table 4-(3). Similarly, the combination weights for the indicator layer ω₀ were calculated, with results shown in Table 4-(9).

Cloud Parameter Calculation: The measured data from the case studies were substituted into Equation (12) to calculate the cloud parameters for the indicator layer, with results shown in Table 4-(10), (11), and (12). The criteria layer cloud parameters were then obtained by combining ω₀ and Equation (13), as shown in Table 4-(4), (5), and (6). Finally, Equation (13) was used again to calculate the comprehensive ·evaluation cloud parameters for the renovation potential at the target layer, resulting in (Ex, En, He) = (0.6551, 0.1900, 0.0320).

4.4. Membership Degree Calculation and Evaluation Cloud Graph Generation

Membership Degree Calculation: Based on the cloud parameters for the criteria layer and indicator layer in Table 4, the membership degrees for the target layer and criteria layer can be calculated using Equation (14). The results are shown in

Table 5. Evaluation results of renovation potential grades.

Evaluation Subject	Membership Degree of Each Potential Grade					Evaluation Results
	Grade I	Grade II	Grade III	Grade IV	Grade V
Target layer	0.0000	0.0076	0.1592	0.2490	0.0191	IV
Land Spatial Value	0.0015	0.0133	0.0852	0.2155	0.0877	IV
Surrounding Traffic Operation Status	0.0073	0.0428	0.1350	0.1419	0.0811	IV
Conditions of Building Itself	0.0000	0.0000	0.0024	0.1973	0.1274	IV
Future Development	0.0047	0.0248	0.1149	0.1815	0.0652	IV

.

Cloud Graph Generation: By integrating the standard cloud parameters and evaluation cloud parameters, the comprehensive evaluation cloud Graph for renovation potential and the cloud Graphs for the criteria layer are plotted, as shown in Figure 3. The five pure color cloud graphs represent the level of renovation potential. On the far left, blue graph indicates the scope of lowest renovation potential, red indicates higher, and others increase in sequence until to the far-right graph which shows the highest renovation potential level. The mixed color graph represents the renovation potential grade is located.

4.5. Results, Analysis, and Discussion

According to Figure 3a, the comprehensive evaluation cloud Graph is primarily distributed between the Grade III and Grade IV standard cloud Graphs, closely aligning with the Grade IV standard cloud. Combined with the membership degree value in the target layer from the second row of Table 5 and following the principle of maximum membership degree, it is determined that the renovation potential of the Military Club building is Grade IV, indicating a high potential. This result aligns with the planning status of Nanjing’s second batch of urban renovation projects.

From Table 5, it can be seen that the membership degree evaluation results for criterion layers A, B, C, and D are all at Grade IV. Based on the relative positions of the criterion layer evaluation cloud Graphs compared to the evaluation standard clouds, only “D Future Benefits” (Figure 3e) is located to the right of the Grade IV standard cloud, indicating that the future benefits after the building renovation will increase significantly. It can also be observed that the cloud droplets for “B Surrounding Traffic Conditions” (Figure 3c) and “D Future Benefits” (Figure 3e) are relatively dispersed, indicating a higher degree of uncertainty in the evaluation results. The reason for this uncertainty could be that the former’s indicators were affected by factors such as holidays and weather during data collection, leading to significant data fluctuations, while the latter’s indicator layer consists of qualitative indicators that are highly influenced by the subjective judgments of respondents. The indicators under “A Land Space Value” (Figure 3b) and “C Building Condition” (Figure 3d) mainly reflect static data about the building, resulting in more stable data and higher certainty, leading to more convergent evaluation cloud Graphs.

The Ex values of the indicator layer cloud parameters in Table 4-(10) reflect the sensitivity of each indicator to the criterion layer. For positive indicators, higher Ex values are more beneficial for project renovation. Conversely, for negative indicators, higher Ex values indicate worse current conditions, highlighting the urgency for renovation. For example, in criterion layer C, the Ex value for “C1 Vacancy Grade” is 0.9050, the highest among all indicators, suggesting that this indicator has the highest potential and expectation for renovation. The reason for this high potential is due to the fact that the Military Club was previously used as the Yangtze River Delta Publication Market, but due to outdated functionality and reduced social demand, the market closed in 2018, leaving most of the building vacant, thus leading to strong public demand for its renovation. The Ex value for “C2 Flexibility of Spatial Layout” is 0.8, indicating the second-highest renovation potential, as the project was constructed a long time ago, and its design standards and function no longer meet contemporary needs, making it particularly urgent to optimize the spatial layout of the building.

The Ex values of the indicator layer reflect the building’s current conditions and renovation potential, but a higher Ex value does not necessarily imply prioritizing that aspect for renovation. For instance, the indicators under criteria layers A and B are more constrained by urban planning and traffic planning, meaning that individual public building renovations should adhere to the overall urban development layout. In summary, the suggested priority order for the renovation work of the Military Club is: C1, D4, A8, D1, A3, C2, D5, C8, C7, C9, C6. The renovation practice should first focus on transforming building functions and improving utilization rates while ensuring the protection and use of cultural heritage and historic buildings. Subsequently, the work should be carried out in the order of optimizing internal spatial layout, enhancing safety resilience, improving natural lighting, upgrading worn physical components, and improving sound insulation performance.

4.6. Comparative Verification

To further verify the applicability of the evaluation index system and evaluation methods, two additional projects (

Table 6. Overview of comparing the actual projects.

Case	Project Name	Location	Abstract
1	National fitness center	Xuanwu district Nanjing, China	The first high-rise sports and fitness center in China. Since 2005, it has been in operation for 19 years, facing problems such as aging hardware facilities and outdated functional formats. The operation has been completely suspended since 1 April 2024.
2	Suojie Bus Station	Jianye district, Nanjing, China	The traditional station mode has a single function, resulting in inefficient use of land resources and a mismatch with the image of surrounding cities. It is now a key case of inefficient land redevelopment in Jianye District.

) were selected for renovation potential evaluation. The evaluation results are shown in

Table 7. The results of the project renovation evaluation and the actual situation.

Case	Project Name	Evaluation Grade	Evaluation Cloud Parameters	Actual Situation
1	National fitness center	Ⅳ	(0.6318, 0.1810, 0.0310)	Listed in the Implementation Plan for Nanjing Urban Renovation Projects in 2024 (starting in April 2024 and expected to be completed during the National Day holiday)
2	Suojie Bus Station	Ⅴ	(0.8031, 0.1270, 0.0218)	The second batch of urban renovation production pilot projects in Nanjing (starting in March 2023 and completed within the year)

and are consistent with the actual situation of the projects. Among them, the corresponding evaluation result of the street bus station is level V, and it was first included in the pilot project with the earliest actual construction schedule. The corresponding evaluation result of the National Fitness Center is level IV, which was included in the government’s planning retrofit later.

5. Conclusions and Outlook

(1) The application of the cloud model for evaluating the renovation potential of public buildings effectively captures the relationship between indicator fuzziness and randomness. The cloud Graph-based representation allows for a clear visualization of the renovation potential and the degree of uncertainty in the evaluation results. Additionally, the sensitivity of indicators is determined based on the expectation (Ex) parameter at the indicator Grade, providing insights that support the implementation and optimization of renovation plans. The combination weighting method based on game theory yields more balanced and accurate comprehensive weights, significantly influencing the calculation of cloud model parameters and the generation of backward clouds.

(2) In this study, qualitative indicators were assessed using the expert judgment method. The arithmetic mean was used to obtain the average values, without accounting for the influence of expert experience and biases. Quantitative indicators were derived from the literature or project inspection reports, with limited on-site measured data. Although a cloud model calculation program was developed based on MATLAB, the calculation process remains relatively complex, and user-friendliness is limited. In the future, two aspects of research will be conducted. First, based on the subdivision of public building types, the author will construct universal criteria and alternative observation indicators that will be selected by the planner. Second, research on the intelligent evaluation of renovation potential, automation of data acquisition, and visualization of evaluation results will be the focus.