Research on Decision Support for Basic Class Reconstruction in Old Residential Areas Based on Case-Based Reasoning and Utility Theory

Abstract

The basic renovation of old urban communities is an important livelihood project for urban renewal, but there are many problems in the decision-making of renovation schemes, such as strong dependence on experience, lack of quantitative basis for multi-objective trade-off, and difficulty in describing residents’ risk attitude. Combining Case-Based Reasoning (CBR) and utility theory, this paper constructs a set of intelligent decision support models driven by data and knowledge. First of all, through literature analysis and expert investigation, a decision-making index system is established, which includes four dimensions and 16 quantitative indicators: policy and financial support, residential conditions and needs, residents’ consensus and social coordination, and implementation management and long-term maintenance. Secondly, the framework representation method is used to describe the reconstruction case, a hybrid retrieval strategy combining inductive retrieval and nearest-neighbor retrieval is designed, and the subjective and objective data combination weights are calculated by using AHP and the entropy method. On this basis, a loss utility function and risk aversion coefficient based on accident and public opinion data (a = 0.02) are introduced to modify the similarity calculation results to describe the risk avoidance behavior of decision-makers. Through 40 real renovation projects, a case base is built, and two types of target cases, “typical inclusive” (F5) and “key renovation” (F35), are selected for empirical verification. The results show that the model can effectively retrieve similar cases, and the similarity ranking changes in line with risk aversion expectations after utility correction. Taking F5 as an example, by reusing and revising the reconstruction scheme of a similar case, targeted suggestions are generated, which give consideration to safety, economy and operability. This model provides a new quantifiable and reusable method for scientific decision-making in basic renovation of old residential areas.

1. Introduction

1.1. Research Background

Urban renewal has become an important starting point to promote the high-quality development of cities in the middle and late period of urbanization in China. As the core carrier of urban stock space, old residential areas generally have problems such as aging facilities, prominent security risks and strong resident desire for transformation. In 2020, the General Office of the State Council issued the Guiding Opinions on Comprehensively Promoting the Renovation of Old Urban Residential Areas, which clearly divided the renovation contents into three categories: basic, perfect and upgrading. Among them, basic renovation focused on the renovation of municipal supporting infrastructure and the maintenance of public parts of buildings, which was the core and premise of renovation work [1,2].

However, at present, the decision-making in basic renovation schemes in old residential areas still faces multiple dilemmas: First, the decision-making method is extensive: project identification, scheme selection and priority ranking rely on empirical judgment, and lack of systematic quantitative analysis support. Second, it is difficult to reuse knowledge from historical transformations, and though a large amount of project experience has been accumulated in various places, it is scattered across files and reports, which cannot effectively guide new projects. Third, the transformation involves the government, residents, franchise units and other stakeholders. Residents’ perceptions and avoidance of risks are often ignored by the linear weighted model, which leads to a deadlock in the implementation of “high-vote pass” projects [3,4]. Therefore, it is urgent to introduce artificial intelligence and scientific decision-making methods to build a set of intelligent decision-making support tools that can reuse historical experience, quantify multi-objective trade-offs and portray risk attitudes.

1.2. Summary of Related Research

1.2.1. Case-Based Reasoning in Engineering Management: Applications and Challenges

Case-Based Reasoning (CBR) is an experience-based artificial intelligence problem-solving method that solves new problems by retrieving, reusing, revising, and retaining historical cases [5]. The method has been widely applied in construction engineering management, including in cost estimation [6], construction schedule planning [7], contractor selection [8], and risk management [9]. These studies demonstrate that CBR can effectively utilize historical project data to support unstructured or semi-structured decision-making problems [10].

In recent years, CBR has begun to be introduced into the fields of urban renewal and old residential area renovation. For example, some studies have constructed a CBR-based decision-making framework for urban renewal projects [11], introducing CBR into the decision-making process, though these studies rarely consider residents’ risk attitudes [12]. Other studies have applied CBR to prefabricated building scheme decision-making [13], and their indicator system construction and similarity algorithm provide valuable references for this study [14]. However, existing CBR research still has notable limitations when applied to old residential area renovation decisions. First, most studies use linear weighted sum models to calculate case similarity, assuming constant marginal contributions of each attribute, which fail to reflect decision-makers’ preference differences when facing different types of risks. Second, the retrieval and reuse processes of historical cases typically do not consider residents’ risk-averse psychology regarding construction safety, cost overruns, and schedule delays. Renovation decisions involve multiple stakeholders, and residents’ concerns significantly affect the acceptance of renovation plans. Third, the construction and maintenance of case libraries lack systematic methods tailored to the specific characteristics of “basic renovation,” limiting the applicability and transferability of the indicator system.

1.2.2. Utility Theory and Risk Attitudes in Engineering Decision-Making

Utility theory is a classical tool for analyzing decision-maker behavior under uncertainty. Expected utility theory assumes that decision-makers pursue maximization of expected utility [15]. Prospect theory further reveals the phenomenon of loss aversion, i.e., that decision-makers are significantly more sensitive to losses than to equivalent gains [16]. Building on this, prospect theory and its subsequent cumulative version provide a more realistic characterization of bounded rational decision-makers by introducing reference points, loss aversion coefficients, and decision weight functions.

In the field of engineering management and safety [17], utility theory has been widely applied to risk measurement, safety investment decisions, emergency plan evaluation, and other scenarios; for example, in ref. [18]. Some studies have established utility-based safety risk measurement models, converting accident consequences and probabilities into utility losses [19]. Other studies, using evolutionary game models based on prospect theory [20], have analyzed the dynamic decision-making processes of multiple stakeholders (e.g., government, developers, residents) in the green renovation of old residential areas, finding that the loss aversion coefficient significantly affects the direction of game equilibrium [21]. Furthermore, in decision problems such as large-scale engineering resource matching and hazardous material transportation route selection, cumulative prospect theory has gradually replaced expected utility theory to better reflect decision-makers’ true preferences [22].

Nevertheless, research combining utility theory with Case-Based Reasoning remains relatively rare. In the existing literature, no systematic study has been found that introduces a loss utility function into similarity correction in CBR for old residential area renovation, nor is there a quantitative method for characterizing residents’ risk-averse behavior and incorporating it into case ranking. This provides an entry point for the present study: by integrating the experience reuse advantages of CBR with the risk characterization capability of utility theory, a renovation support model that more closely reflects actual decision-making contexts can be constructed.

1.2.3. Current Research on Decision-Making for Old Residential Area Renovation

As an important component of urban renewal, the renovation of old residential areas has attracted widespread attention. Existing research mainly focuses on renovation mode selection, resident willingness analysis, cost sharing mechanisms, and renovation priority ranking. In terms of decision-making methods, multi-criteria decision-making methods (e.g., Analytic Hierarchy Process [23], Analytic Network Process, TOPSIS, etc.) are widely adopted to evaluate the relative priorities of different renovation plans [24]. These methods typically construct indicator systems covering multiple dimensions such as policy support, technical feasibility, social acceptance, and economic rationality. Indicator weights are determined through expert scoring or objective data [25], and then a comprehensive ranking of renovation plans is generated.

In addition, some studies focus on the spatial identification of renovation potential and the determination of renewal priorities, using spatial statistical methods and comprehensive evaluation models to identify which residential areas should be prioritized for renovation at the regional scale [26]. In terms of policy text analysis, some research employs text mining and topic modeling techniques to trace the evolution of renovation policies at both central and local levels [27], revealing a transition from “engineering-oriented” to “comprehensive governance” approaches [28].

However, existing decision-making research has several common limitations [29,30,31]. First, multi-criteria decision-making methods typically assume that indicators are independent and weights are constant, making it difficult to capture the complex non-linear similarity relationships between renovation cases. Second, resident willingness is often simplified into a single agreement rate value, ignoring residents’ differentiated perceptions and risk-averse psychology regarding risks such as construction safety, living disturbances, and cost overruns. Third, a large amount of renovation project experience accumulated across different regions remains scattered in archives and reports, failing to be systematically organized into reusable knowledge assets, leading to a situation of “rich experience but difficult to inherit.”

1.3. Research Objectives, Methods and Innovation

1. Research Objectives:

(1) To construct a multi-dimensional quantitative indicator system for basic renovation.

(2) To design an intelligent decision support model based on CBR and utility theory.

(3) To validate the model through empirical study. Research content and a technical roadmap are also presented.

2. Research Methods:

This study follows the technical route of “theoretical foundation–method construction–empirical testing”. The methods are organized in a logical sequence:

(1) Literature Research Method (Theoretical Foundation):

First, we systematically review the literature on urban renewal, old residential area renovation, and Case-Based Reasoning (CBR) to define core concepts and establish the theoretical basis for subsequent research.

(2) Expert Questionnaire Method (Indicator Construction):

Next, we screen decision indicators through multiple rounds of expert consultation, test consistency using Kendall’s coefficient of concordance, and form an indicator system with four dimensions and 16 indicators, achieving the transformation from theory to quantifiable metrics.

(3) Case-Based Reasoning (CBR) Modeling Method (Core of the Model):

Based on the 5R model, we sequentially complete case representation (framework representation), retrieval (inductive + nearest neighbor hybrid strategy), and similarity calculation (attribute-specific local algorithms + weighted Manhattan distance), constructing the main framework of the decision model.

(4) Subjective–Objective Comprehensive Weighting Method (Weight Determination):

We combine the Analytic Hierarchy Process (AHP) and the entropy method, calculate combined weights through linear weighting, and embed them into the CBR model to scientifically reflect the importance of each indicator.

(5) Utility Theory Correction Method (Risk Correction):

We introduce an exponential loss utility function, fit the risk aversion coefficient (a = 0.02) based on collapse accident data, and correct the similarity to align the model with residents’ risk-averse psychology.

(6) Case Validation Method (Empirical Testing):

Based on a case library of 40 real projects, we select two target cases (inclusive type F5 and key rectification type F35) to run the model, verifying its effectiveness and practicality.

3. Research Innovation Points:

(1) We present the first introduction of a loss utility function to correct similarity in CBR for old residential area renovation, capturing risk-averse behavior;

(2) We calibrate the risk aversion coefficient using accident and public opinion data, providing a quantifiable parameterization method;

(3) We present a complete CBR decision-making process integrating subjective–objective combined weights and a hybrid retrieval strategy.

2. Decision-Making Index System Construction

2.1. Index Selection Principles and Ideas

The construction of a decision-making index system for basic renovation of old residential areas follows the principles of systematicness, coordination, timeliness and appropriateness. Systematization requires a clear vertical hierarchy and a clear horizontal structure of indicators; synergy emphasizes the balance between independence and logical association among indicators; timeliness requires that indicators can dynamically adapt to changes in policies and demands; appropriateness requires simplifying indicators and ensuring data availability on the premise of meeting decision-making objectives.

The selection of indicators adopts the path of “literature sorting–initial screening of experts–empirical test”. Firstly, related studies (Appendix E) and technical standards (Technical Standard for Residential Performance Evaluation GB/T 50362 [32] and General Specification for Maintenance and Renovation of Existing Buildings GB 55021-2021) [33] for urban renewal and old buildings at home and abroad were systematically searched, and the potential factors were summarized. Then, the importance was judged and screened through an expert questionnaire survey. Finally, Kendall’s synergy coefficient was used to test the consistency of expert opinions.

2.2. Determination of Index System

2.2.1. Indicator Determination Method and Process

Indicator selection follows a three-step approach of “literature review → expert screening → empirical testing.” First, a systematic search of the domestic and international literature on urban renewal and old building assessment, as well as technical standards (GB/T 50362, GB 55021-2021), was conducted, yielding over 20 candidate indicators across four categories. Second, a two-round Delphi expert questionnaire was administered to assess importance and screen indicators. Finally, Kendall’s coefficient of concordance was used to test the consistency of expert opinions (detailed in Section 2.3).

2.2.2. Indicator System Structure

Through the above process, 16 core indicators were finalized, divided into four dimensions: policy and financial support (A1–A5), community basic conditions and demands (A6–A11), resident consensus and social coordination (A12–A14), and implementation management and long-term maintenance (A15–A16). The indicator names, data types, evaluation methods, and data sources are presented in

Table 1. Evaluation methods for decision indicators (revised edition).

Code	Indicator Name	Data Type	Evaluation Method/Assignment Rule	Data Source
B1 Policy and Financial Support
A1	Central/local government investment	Numeric	Direct value (10,000 CNY); normalized later using min-max method	Government approval documents, feasibility study reports
A2	Special renovation plan	Character	Record plan name or status (e.g., “included in municipal plan”); exact match for similarity calculation	Government planning documents
A3	Safety standard compliance	Fuzzy	Assignment based on compliance with mandatory codes (fire, structure, etc.): 0 = non-compliant, 0.5 = partially compliant, 1 = fully compliant	Safety assessment reports, inspection records
A4	Subsidy application & disbursement progress	Fuzzy	Assignment by progress stage: 0 = not applied, 0.33 = applied but not disbursed, 0.67 = partially disbursed, 1 = fully disbursed	Financial disbursement documents
A5	Cost sharing with utility companies	Numeric	Direct value (10,000 CNY); normalized later	Sharing agreements, contract documents
B2 Community Basic Conditions and Demands
A6	C/D-grade buildings in structural safety assessment	Fuzzy	Assignment based on proportion of C/D-grade buildings: 0 = none, 0.33 = <10%, 0.67 = 10–30%, 1 = >30%	Structural safety assessment reports
A7	Water supply leakage & power line aging	Fuzzy	Composite score (average of two sub-indicators): 0 = basically intact, 0.33 = local aging/slight leakage, 0.67 = severe aging/significant leakage, 1 = complete failure/extreme leakage	Maintenance records, field inspection
A8	Combined sewer overflow and blockages	Fuzzy	Composite assessment based on length of combined sewer & number of blockages: 0 = separate & clear, 0.33 = mild combined/mild blockage, 0.67 = multiple combined/moderate blockage, 1 = severe combined/severe blockage	Drainage system survey reports
A9	Fire protection equipment deficiency	Fuzzy	Assignment based on proportion of deficient equipment: 0 = intact, 0.33 = few deficiencies (<20%), 0.67 = many deficiencies (20–50%), 1 = severe deficiencies (>50%)	Fire inspection records, field inspection
A10	Public space facility integrity rate	Numeric	Direct value (% intact facilities/total facilities), range 0–100%; normalized later	Field survey records
A11	Underground pipeline constructability	Fuzzy	Assignment based on spatial conditions: 0 = constrained (unable to construct or requiring extensive relocation), 0.5 = moderate (locally constrained), 1 = sufficient (unaffected)	Pipeline detection reports
B3 Resident Consensus and Social Coordination
A12	Resident acceptance of renovation plan	Numeric	Direct agreement rate (%), range 0–100%; normalized later	Resident voting, survey questionnaires
A13	Resident supervision group establishment & operation	Fuzzy	Assignment: 0 = not established, 0.5 = established but poorly operated, 1 = established and well-operated	Community records, interviews
A14	Coordination smoothness with community/resident committees	Fuzzy	Assignment: 0 = severely poor (frequent conflicts), 0.33 = average (multiple negotiations still have disagreements), 0.67 = relatively smooth (occasional disagreements), 1 = very smooth (no resistance)	Project logs, meeting minutes
B4 Implementation Management and Long-term Maintenance
A15	Engineering change frequency & cost impact	Fuzzy	Composite assessment based on change frequency & cost fluctuation: 0 = very rare/impact <5%, 0.33 = few changes/impact 5–10%, 0.67 = frequent changes/impact 10–20%, 1 = very frequent changes/impact >20%	Change orders, cost audit reports
A16	Clarity of handover agreement & maintenance responsibility	Fuzzy	Assignment: 0 = unclear (no agreement or unclear responsibilities), 0.5 = partially clear (agreement exists but lacks details), 1 = fully clear (detailed agreement with clear responsibilities)	Handover agreement documents

.

(1) Policy and Financial Support (A1–A5):

This dimension covers the fundamental premise of whether the transformation can be started. A1, the central and local financial investment (ten thousand yuan), reflects the strength of capital guarantee; A2, the special renovation plan, reflects the clarity of policy orientation; meeting A3 safety standards (whether it meets mandatory standards such as fire protection and structure) is the bottom-line requirement; the progress of financial subsidy application and disbursement, A4, affects the efficiency of funds in place; and the cost sharing amount between the building and franchised units (water, electricity, gas and heat), A5, reflects the multi-party sharing mechanism.

(2) Conditions and Requirements of Community Ontology (A6–A11):

This dimension is the objective basis of the transformation plan. For A6, building structural safety appraisal, the number or proportion of C/D-grade buildings directly determines the urgency of reinforcement; A7 covers the ratio of leakage rate of water supply network to aging households of power supply line; A8 notes the rainwater and sewage confluence length of drainage pipe network and number of blocking points; A9 reflects the number of defects in fire-fighting facilities (fire hydrants, fire extinguishers, etc.); A10 the integrity rate of public space facilities (roads, lighting, greening, etc.); and A11 the construction space for underground pipelines (sufficient/normal/tight).

(3) Residents’ Consensus and Social Coordination (A12–A14):

This dimension is related to the social acceptability of the project. A12 reflects residents’ acceptance of the renovation plan (agreement rate,%); A13 the establishment and operation status of a resident supervision group (established and running well/established but not running well/not established); and A14 smooth coordination with community neighborhood committees and industry committees.

(4) Implementation Management and Long-Term Maintenance (A15–A16):

A15 reflects the occurrence rate of engineering change and its impact on the cost (estimated change rate and cost fluctuation); A16 reflects the handover agreement and clarity of custody responsibility of the reconstructed facilities.

The above indicators cover three categories—numerical (such as A1, A5, A7, A8, etc.), character (A2) and fuzzy (A3, A4, A6, A11–A16, etc.)—providing a unified attribute framework for subsequent similarity calculation.

2.3. Expert Consistency Test

Using the Delphi method, questionnaires were distributed to 20 experts (Appendix A) (seven experts from the Ministry of Housing and Urban–Rural Development, five experts from design institutes, four experts from supervision, one industry committee, one policy researcher and two experts from testing and appraisal). In total, 60% of the experts had worked for 3 to 9 years, and 25% had worked for more than 10 years. The questionnaire used a five-point Likert scale, and experts were asked to rate the importance of 16 indicators (1 = completely unimportant, 5 = very important). We used SPSSAU 25.0 calculate Kendall’s synergy coefficient W = 0.437, the chi-square value χ = 226.436, and progressive significance ** p = 0.000 < 0.01, rejecting the original hypothesis of “disagreement”, which shows that the evaluation of 20 experts is remarkably consistent and the index system is reliable.

3. Decision-Making Model Based on CBR and Utility Theory

3.1. CBR Basic Framework and Case Representation

This paper adopts the 5R model (case description, retrieval, reuse, adjustment and storage) proposed by Finnie et al. [34]. Each case is represented as a binary group: case = (problem description, solution). The problem descriptions consist of the above 16 attributes; the solution is the list of the key contents of basic transformation, including structural reinforcement, pipe network transformation, fire protection renewal, public space repair, residents’ participation measures, etc.

Case storage adopts frame representation. With “case name” as the top frame, each attribute is regarded as a “slot”, and the attribute value is stored on the side of the slot. This hierarchical structure can clearly express the multi-dimensional characteristics of complex cases. The case database contains 40 real and old residential renovation projects, which were collected through the questionnaire survey, field visits and the online literature, covering different regions, different scales and different types.

The framework representation method and case tuple structure established in this section will be directly used for the construction of the case library in Section 4. Specifically, the 40 real renovation projects collected in Section 4 are structurally stored in the format of “problem description (16 indicators) + solution”, forming a standardized case library that can be retrieved and reused computationally.

3.2. Case Retrieval and Similarity Calculation

3.2.1. Hybrid Retrieval Strategy

It is difficult for a single retrieval method to give consideration to both efficiency and accuracy. In this paper, the mixed strategy of nearest-neighbor retrieval and inductive retrieval is adopted: firstly, inductive retrieval is used to quickly narrow the candidate set according to the key classification characteristics such as building type and renovation scale (for example, only the same type of community as the target case is reserved), and then the global similarity is calculated for the cases in the candidate set one by one. Inductive retrieval can effectively eliminate cross-type irrelevant cases (such as confusing old residential areas with commercial buildings) and reduce invalid calculations.

3.2.2. Local Similarity Algorithm

Researchers have designed different algorithms according to attribute types:

(1) Character type (such as A2 special renovation plan): The target case (that is, the problem to be solved at present) and the source case (that is, the case retrieved in the case base) are represented by C_i and C_j, respectively. Assuming that their kth attribute is character-type, it is represented by C_ik and C_jk, and their similarity is represented by LS(C_ik,C_jk). The calculation formula is defined as follows:

$$LS(C_{ik},C_{jk})={\{}_{1,C_{ik}=C_{jk}}^{0,C_{ik}=C_{jk}}$$

(1)

(2) Numerical type (such as A1 financial input): The calculation of attribute similarity can be reflected by measuring the attributes’ positions in a certain one-dimensional coordinate in the attribute space, that is, the distance [35]. Dist(C_ik,C_jk) is used to express the distance between attributes C_ik and C_jk. The simplest distance formula is as follows:

$$Dist(C_{ik},C_{jk})=\left|C_{ik}-C_{jk}\right|$$

(2)

Max-min conversion in the linear dimensionless processing method is adopted [36]. The normalized value representing the attribute C_ik is defined as follows: ${\ddot{\mathrm{C}}}_{\mathrm{ik}}$.

$${\ddot{C}}_{ik}={\displaystyle \frac{C_{ik}-{\min }_k}{{\max }_k-{\min }_k}}$$

(3)

Using the normalized distance [37], the distance calculation formula is defined as follows:

$$\ddot{Dist}(C_{ik},C_{jk})=\left|{\ddot{C}}_{ik}-{\ddot{C}}_{jk}\right|$$

(4)

Let $\ddot{Dist}(C_{ik},C_{jk})$ = $Dist(C_{ik},C_{jk})$, and linearly deduce Equations (2)–(4), and the calculation formula for the similarity of numerical attributes can be obtained as follows: $\ddot{Dist}(C_{ik},C_{jk})=Dist(C_{ik},C_{jk})$.

$$LS(C_{ik},C_{jk})=1-{\displaystyle \frac{\left|C_{ik}-C_{jk}\right|}{{\max }_k-{\min }_k}}$$

(5)

(3) Fuzzy type (such as A6 C/D housing and A12 residents’ acceptance):

(1) The values of both attributes are hierarchical; the triangular membership function is adopted, as shown in Figure 1.

Referring to the research conclusion of Pal et al. [38], this paper defines the similarity calculation formula of two fuzzy interval attributes C_ik and C_jk as follows:

$$LS(C_{ik},C_{jk})=1-{\displaystyle \frac{{\displaystyle {\int }_{\alpha }^{\beta }{\displaystyle {\int }_{\alpha }^{\beta }\mu \left(\mathrm{x}\right)\mu \left(y\right)\left|x-y\right|dxdy}}}{(\beta -\alpha ){\displaystyle {\int }_{\alpha }^{\beta }\mu \left(\mathrm{x}\right)dx{\displaystyle {\int }_{\alpha }^{\beta }\mu \left(\mathrm{y}\right)dy}}}}$$

(6)

(2) The values of the two attributes are interval-type: the value of the cost increment of the target case and the source case are interval-type [39]. Therefore, suppose that the interval of the incremental cost C_ik required by the target case is (x,y), and the interval of the incremental cost C_jk of the source case is (p,q) [40]. The similarity is defined as follows:

$$LS(C_{ik},C_{jk})={\displaystyle \frac{LS(C_{ik}\cap C_{jk})}{LS(C_{ik})+LS(C_{jk})-LS(C_{ik}\cap C_{jk})}}$$

(7)

(3) One attribute value is a definite numerical value, and the other is of interval type:

$$LS(C_{ik},C_{jk})=1-{\displaystyle \frac{{\displaystyle {\int }_{{\alpha }_1}^{{\alpha }_2}\left|c-x\right|dx}}{(\beta -\alpha )({\alpha }_2-{\alpha }_1)}} (\beta -\alpha )=\max [({\alpha }_2-{\alpha }_1),\left|c-{\alpha }_1\right|,\left|{\alpha }_2-c\right|]$$

(8)

where [a₁,a₂] represents the value of interval attribute C_ik, and c is a definite value.

3.3. Case Similarity Weight Algorithm

3.3.1. Subjective Weight Algorithm

In this paper, the hierarchy is divided into two layers [41], and the weight hierarchy of case attributes is shown in

Table 2. Weight hierarchy of case attributes.

Target Layer	Index Layer	Number
Case similarity	Central and local finance	A1
	Special renovation plan	A2
	Safety standards up to standard	A3
	Application and disbursement of financial subsidies	A4
	Cost sharing with franchisees	A5
	Building structure safety appraisal of C/D-class houses	A6
	Leakage of water supply network and aging of power supply line	A7
	Confluence and blockage of rain and sewage in drainage pipe network	A8
	Fire control facility defects	A9
	Public space facilities in good condition.	A10
	Complete underground pipeline construction space	A11
	Residents’ acceptance of renovation plan	A12
	Establishment and operation of residents’ supervision group	A13
	Coordination with community neighborhood committees and industry committees	A14
	Occurrence rate of engineering change and its influence on cost	A15
	Transfer agreement and clarity of custody responsibility of reformed facilities	A16

.

In this paper, a scale of 1–9 is used to describe the importance difference between the two matching factors, as shown in

Table 3. Factor importance 1–9 scale.

Scale	Define Comparison Elements I and J.
1	Factor I is as important as J.
3	Factor I is slightly more important than J.
5	Factor I is more important than J.
7	Factor I is more important than J.
9	Factor I is absolutely more important than J.
2, 4, 6, 8	These are the intermediate values of two adjacent judgments.
reciprocal	The scale value representing the comparison of factors I and j is equal to the reciprocal of the scale value of factors J and I.

.

Ten experts with more than 6 years’ experience were invited to compare the 16 attributes and four levels, and construct a judgment matrix (Appendix C), as shown in

Table 4. A dimension-level judgment matrix.

Dimension	B1	B2	B3	B4
B1	1	0.67	1.33	1.5
B2	1.5	1	2	2.5
B3	0.75	0.5	1	1.2
B4	0.67	0.4	0.83	1

${\lambda }_{\max }=4.045$, $CI=0.015$, $RI=0.89$, $CR=0.017<0.015$ (passed). Dimension weights: wdim = (0.247, 0.418, 0.191, 0.144)^T.

and

Table 5. Case attribute combination judgment matrix.

	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15	A16
A1	1.00	1.80	0.80	1.20	1.40	0.90	0.90	0.90	0.90	1.80	1.80	1.10	1.50	1.50	1.20	1.20
A2	0.56	1.00	0.45	0.65	0.75	0.50	0.50	0.50	0.50	1.00	1.00	0.60	0.80	0.80	0.65	0.65
A3	1.25	2.20	1.00	1.50	1.75	1.10	1.10	1.10	1.10	2.20	2.20	1.30	1.80	1.80	1.50	1.50
A4	0.83	1.55	0.67	1.00	1.20	0.75	0.75	0.75	0.75	1.55	1.55	0.90	1.25	1.25	1.00	1.00
A5	0.71	1.33	0.57	0.83	1.00	0.65	0.65	0.65	0.65	1.33	1.33	0.80	1.10	1.10	0.85	0.85
A6	1.11	2.00	0.91	1.33	1.55	1.00	1.00	1.00	1.00	2.00	2.00	1.20	1.65	1.65	1.35	1.35
A7	1.11	2.00	0.91	1.33	1.55	1.00	1.00	1.00	1.00	2.00	2.00	1.20	1.65	1.65	1.35	1.35
A8	1.11	2.00	0.91	1.33	1.55	1.00	1.00	1.00	1.00	2.00	2.00	1.20	1.65	1.65	1.35	1.35
A9	1.11	2.00	0.91	1.33	1.55	1.00	1.00	1.00	1.00	2.00	2.00	1.20	1.65	1.65	1.35	1.35
A10	0.56	1.00	0.45	0.65	0.75	0.50	0.50	0.50	0.50	1.00	1.00	0.60	0.80	0.80	0.65	0.65
A11	0.56	1.00	0.45	0.65	0.75	0.50	0.50	0.50	0.50	1.00	1.00	0.60	0.80	0.80	0.65	0.65
A12	0.91	1.65	0.77	1.11	1.25	0.83	0.83	0.83	0.83	1.65	1.65	1.00	1.40	1.40	1.10	1.10
A13	0.67	1.25	0.56	0.80	0.91	0.60	0.60	0.60	0.60	1.25	1.25	0.71	1.00	1.00	0.80	0.80
A14	0.67	1.25	0.56	0.80	0.91	0.60	0.60	0.60	0.60	1.25	1.25	0.71	1.00	1.00	0.80	0.80
A15	0.83	1.55	0.67	1.00	1.18	0.74	0.74	0.74	0.74	1.55	1.55	0.91	1.25	1.25	1.00	1.00
A16	0.83	1.55	0.67	1.00	1.18	0.74	0.74	0.74	0.74	1.55	1.55	0.91	1.25	1.25	1.00	1.00

.

After calculation, the subjective weight vectors of A1–A16 are as follows:

w = (0.098, 0.055, 0.122, 0.081, 0.069, 0.109, 0.109, 0.109, 0.109, 0.055, 0.055, 0.089, 0.064, 0.064, 0.080, 0.080)^T.

Among them, RI is a random consistency index, and its reference value is shown in

Table 6. RI reference values.

n	1	2	3	4	5	6	7	8	9	10	11	12	13
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41	1.46	1.49	1.52	1.54	1.56

. The smaller the CR value, the stronger the consistency. Generally speaking, when CR < 0.1, the judgment matrix has satisfactory consistency and the weight setting is effective.

We calculate the maximum eigenvalue ${\lambda }_{\max }=16.138$, calculate the consistency index $CI=0.0092$, and look up the table $RI=1.59$. Get. To sum up, the consistency test is passed—that is, $CI=0.0058<0.1$—and the calculated weight result is considered to be effective.

According to $w=w_{\dim }\times w_a$, we multiply the dimension layer weights by the local weights of each indicator within its respective dimension, and obtain the subjective weights of all 16 indicators, as shown in

Table 7. Summary of subjective weights.

Code	Dimension	Dim Weight	Local Weight	Global Subjective
A1	B1	0.247	0.237	0.0585
A2	B1	0.247	0.132	0.0326
A3	B1	0.247	0.295	0.0729
A4	B1	0.247	0.196	0.0484
A5	B1	0.247	0.14	0.0346
A6	B2	0.418	0.222	0.0928
A7	B2	0.418	0.222	0.0928
A8	B2	0.418	0.222	0.0928
A9	B2	0.418	0.222	0.0928
A10	B2	0.418	0.111	0.0464
A11	B2	0.418	0.111	0.0464
A12	B3	0.191	0.412	0.0787
A13	B3	0.191	0.294	0.0562
A14	B3	0.191	0.294	0.0562
A15	B4	0.144	0.5	0.072
A16	B4	0.144	0.5	0.072

.

3.3.2. Objective Weight Algorithm

The objective weight algorithm adopts the entropy method, and the information entropy of each attribute is calculated based on the normalized data of 40 cases. The greater the entropy value, the more concentrated the data is, and the smaller the weight should be. For character or fuzzy attributes, this paper uses an assignment method to deal with them quantitatively. Take fire-fighting facilities (A9) as an example: severe damage is assigned as 5, partial damage as 3, and basic equipment as 1. For interval attributes, the average of the upper and lower limits is taken as the representative value. After this assignment, the weight calculated by the entropy method can reflect the distribution density of each attribute. Finally, the assigned attribute values are normalized [40] and the case attribute matrix is constructed. See

Table 8. Normalized matrix of case attributes.

Case	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15	A16
F1	0.15	0.35	0.55	0.45	0.65	0.32	0.48	0.52	0.58	0.42	0.38	0.85	0.47	0.53	0.49	0.51
F2	0.88	0.38	0.62	0.52	0.58	0.9	0.55	0.45	0.6	0.4	0.35	0.92	0.5	0.5	0.52	0.48
F3	0.22	0.42	0.48	0.55	0.45	0.18	0.42	0.58	0.52	0.58	0.45	0.28	0.43	0.57	0.44	0.56
F4	0.65	0.33	0.67	0.48	0.52	0.75	0.5	0.5	0.65	0.35	0.4	0.65	0.55	0.45	0.57	0.43
F5	0.4	0.45	0.55	0.6	0.4	0.45	0.47	0.53	0.48	0.52	0.42	0.38	0.52	0.48	0.51	0.49
F6	0.1	0.4	0.6	0.5	0.5	0.08	0.45	0.55	0.62	0.38	0.48	0.12	0.46	0.54	0.47	0.53
F7	0.95	0.36	0.64	0.53	0.47	0.98	0.53	0.47	0.68	0.32	0.37	0.96	0.54	0.46	0.58	0.42
F8	0.28	0.44	0.56	0.47	0.53	0.3	0.49	0.51	0.55	0.45	0.43	0.25	0.49	0.51	0.5	0.5
F9	0.72	0.37	0.63	0.56	0.44	0.68	0.51	0.49	0.63	0.37	0.39	0.72	0.56	0.44	0.59	0.41
F10	0.5	0.41	0.59	0.58	0.42	0.55	0.46	0.54	0.5	0.5	0.41	0.48	0.51	0.49	0.53	0.47
F11	0.33	0.39	0.61	0.49	0.51	0.35	0.52	0.48	0.57	0.43	0.44	0.3	0.48	0.52	0.48	0.52
F12	0.85	0.34	0.66	0.51	0.49	0.82	0.54	0.46	0.62	0.38	0.36	0.88	0.53	0.47	0.57	0.43
F13	0.18	0.43	0.57	0.46	0.54	0.22	0.5	0.5	0.53	0.47	0.46	0.2	0.45	0.55	0.46	0.54
F14	0.78	0.35	0.65	0.54	0.46	0.72	0.52	0.48	0.6	0.4	0.38	0.75	0.55	0.45	0.56	0.44
F15	0.45	0.44	0.56	0.59	0.41	0.5	0.48	0.52	0.55	0.45	0.43	0.42	0.53	0.47	0.54	0.46
F16	0.05	0.42	0.58	0.44	0.56	0.05	0.44	0.56	0.6	0.4	0.47	0.08	0.44	0.56	0.45	0.55
F17	0.92	0.37	0.63	0.52	0.48	0.95	0.51	0.49	0.65	0.35	0.37	0.94	0.52	0.48	0.57	0.43
F18	0.25	0.41	0.59	0.47	0.53	0.28	0.49	0.51	0.54	0.46	0.44	0.22	0.47	0.53	0.49	0.51
F19	0.68	0.38	0.62	0.55	0.45	0.62	0.53	0.47	0.58	0.42	0.39	0.65	0.54	0.46	0.55	0.45
F20	0.55	0.4	0.6	0.57	0.43	0.58	0.47	0.53	0.52	0.48	0.42	0.52	0.5	0.5	0.52	0.48
F21	0.3	0.43	0.57	0.48	0.52	0.32	0.46	0.54	0.56	0.44	0.45	0.28	0.46	0.54	0.48	0.52
F22	0.82	0.36	0.64	0.53	0.47	0.78	0.52	0.48	0.63	0.37	0.38	0.82	0.53	0.47	0.56	0.44
F23	0.2	0.42	0.58	0.45	0.55	0.25	0.43	0.57	0.51	0.49	0.46	0.18	0.44	0.56	0.45	0.55
F24	0.75	0.34	0.66	0.54	0.46	0.68	0.54	0.46	0.64	0.36	0.37	0.72	0.55	0.45	0.58	0.42
F25	0.38	0.44	0.56	0.58	0.42	0.42	0.48	0.52	0.54	0.46	0.44	0.35	0.51	0.49	0.52	0.48
F26	0.12	0.41	0.59	0.49	0.51	0.15	0.45	0.55	0.59	0.41	0.47	0.1	0.45	0.55	0.46	0.54
F27	0.98	0.35	0.65	0.51	0.49	0.92	0.5	0.5	0.67	0.33	0.36	0.96	0.51	0.49	0.59	0.41
F28	0.32	0.43	0.57	0.48	0.52	0.38	0.47	0.53	0.55	0.45	0.44	0.3	0.48	0.52	0.49	0.51
F29	0.62	0.39	0.61	0.56	0.44	0.58	0.52	0.48	0.59	0.41	0.4	0.6	0.53	0.47	0.54	0.46
F30	0.48	0.41	0.59	0.57	0.43	0.52	0.49	0.51	0.53	0.47	0.43	0.45	0.52	0.48	0.53	0.47
F31	0.28	0.42	0.58	0.47	0.53	0.32	0.46	0.54	0.56	0.44	0.45	0.25	0.47	0.53	0.48	0.52
F32	0.88	0.36	0.64	0.52	0.48	0.85	0.53	0.47	0.62	0.38	0.37	0.9	0.54	0.46	0.57	0.43
F33	0.15	0.43	0.57	0.46	0.54	0.2	0.44	0.56	0.52	0.48	0.46	0.12	0.45	0.55	0.46	0.54
F34	0.72	0.37	0.63	0.55	0.45	0.65	0.51	0.49	0.61	0.39	0.39	0.68	0.55	0.45	0.56	0.44
F35	0.42	0.44	0.56	0.59	0.41	0.48	0.49	0.51	0.56	0.44	0.44	0.4	0.53	0.47	0.53	0.47
F36	0.08	0.4	0.6	0.5	0.5	0.12	0.46	0.54	0.61	0.39	0.48	0.05	0.46	0.54	0.47	0.53
F37	0.95	0.35	0.65	0.53	0.47	0.88	0.52	0.48	0.66	0.34	0.37	0.92	0.53	0.47	0.58	0.42
F38	0.25	0.42	0.58	0.48	0.52	0.28	0.48	0.52	0.55	0.45	0.44	0.22	0.48	0.52	0.49	0.51
F39	0.65	0.38	0.62	0.56	0.44	0.62	0.5	0.5	0.59	0.41	0.4	0.62	0.54	0.46	0.55	0.45
F40	0.52	0.41	0.59	0.58	0.42	0.55	0.48	0.52	0.54	0.46	0.43	0.5	0.52	0.48	0.54	0.46

for details. We calculated entropy and weight, and the results are shown in

Table 9. Objective weight table.

Attribute	Entropy Value	Difference Coefficient	Weight
A1	0.8723	0.1277	0.18
A2	0.9765	0.0235	0.033
A3	0.9781	0.0219	0.031
A4	0.9748	0.0252	0.036
A5	0.9772	0.0228	0.032
A6	0.8621	0.1379	0.195
A7	0.9769	0.0231	0.033
A8	0.9755	0.0245	0.035
A9	0.9788	0.0212	0.03
A10	0.9763	0.0237	0.033
A11	0.975	0.025	0.035
A12	0.8824	0.1176	0.166
A13	0.9749	0.0251	0.035
A14	0.9766	0.0234	0.033
A15	0.9745	0.0255	0.036
A16	0.9782	0.0218	0.031

.

It can be found that A1 (central and local finance), A6 (buildings with C/D grade for structural safety appraisal) and A12 (residents’ acceptance of renovation scheme) are the three items with the greatest weight, especially for those buildings with C/D-grade safety assessment in structural integrity, which shows that there are significant differences in safety assessments of building structures in different projects under C/D grade. This is a key issue that needs to be paid special attention to in the decision-making process of infrastructure reconstruction in old residential areas.

3.3.3. Global Similarity and Combination Weight

A case can be regarded as a point located in the case base space, and the position of this point is determined by the position of each coordinate axis (that is, the value of each attribute). Similar cases will be densely distributed in the adjacent area, while dissimilar cases will be far away. Therefore, the relationship between cases in this space reflects the similarity of cases, and the closer the location distance, the greater the similarity of the cases; conversely, the farther the distance, the smaller the similarity. Therefore, the calculation of global similarity still adopts the method of distance measurement. In this paper, nearest-neighbor retrieval is the main method used. This section will introduce several commonly used distance measurement methods based on the nearest-neighbor algorithm, and select the distance method used to calculate the global similarity of the case.

There are several nearest-neighbor distance measurement methods [36,37].

(1) The calculation method based on Minkowski distance:

$$Dist(C_i,C_j)={({\displaystyle \sum _{k=1}^m}{w}_k·Dist{(C_{\mathrm{ik}},C_{jk})}^{\phi })}^{{\displaystyle \frac{1}{\phi }}}$$

(9)

where $\ddot{Dist}(C_{ik},C_{jk})$ represents the distance between the target case C_ik and the source case C_jk, m represents the number of case attributes, and wk represents the weight of the kth attribute in the case global similarity calculation, which is used to correct the position of the case in the attribute space.

However, in the similarity algorithm of character attributes and some fuzzy attributes directly defined above, the concept of distance is not introduced. Therefore, all the case attributes involved in similarity calculation are treated as follows:

$$\ddot{Dist}(C_{ik},C_{jk})=1-LS(C_{ik},C_{jk})$$

(10)

(2) The Euclid-based distance measurement method, also known as an example of Minkowski distance when coefficient φ = 2:

$$Dist(C_i,C_j)=\sqrt{{\displaystyle \sum _{k=1}^m{w}_k·Dist(C_{\mathrm{ik}}},C_{jk}{)}^2}$$

(11)

(3) The Manhattan-based distance measurement method, also known as an example of Minkowski distance when coefficient φ = 1:

$$Dist(C_i,C_j)={\displaystyle \sum _{k=1}^m{w}_k·Dist(C_{\mathrm{ik}}},C_{jk})$$

(12)

(4) The Chebyshev-based distance measurement method:

$$Ma{x}_{1\le k\le m}=\left[w_k·Dist,(C_{\mathrm{ik}},C_{jk})\right]$$

(13)

Manhattan distance is the simplest calculation among the three methods. In order to simplify the calculation and preliminarily verify the applicability of the CBR model constructed in this paper to the decision-making around basic class transformation in old residential areas, this paper adopts the global similarity calculation method based on Manhattan distance.

Using the global similarity between the target case C_i and the source case C_j, then $GS(C_i,C_j)$,

$$GS(C_i,C_j)=1-Dist(C_i,C_j)$$

(14)

Formulas (9), (11) and (13) are linearly deduced, and the following results are obtained:

$$GS(C_i,C_j)={\displaystyle \sum _{k=1}^m{w}_k\cdot LS(C_{ik},C_{jk})}$$

(15)

A summary of case retrieval and similarity calculation methods is shown in

Table 10. Summary of case retrieval and similarity calculation methods.

Method Category	Specific Method	Core Content	Application in Chapter 5 (Empirical Study)
Retrieval Strategy	Hybrid retrieval (inductive + nearest neighbor)	First, screen candidate set by building type and renovation scale; then compute global similarity for each candidate case	In Section 5.2, first screen same-type communities for F5 and F35, then compute similarity and output top 5
Local Similarity	Character-type attributes (e.g., A2)	Exact match: 1 if equal, 0 otherwise	LS values for A2 in Tables 12–15 calculated by this rule
	Numeric attributes (e.g., A1, A5, A10, A12)	Normalize by min-max, compute Manhattan distance, then convert to similarity	LS values for A1, A5, A10, A12 in Tables 12–15 calculated by this rule
	Fuzzy (ordinal) attributes	Compute similarity based on grade difference ratio	LS values for A6–A9, A13–A16 in Tables 12–15 calculated by this rule
	Fuzzy (interval) attributes	Compute similarity based on interval overlap ratio	Not used in this case library
Global Similarity	Weighted Manhattan distance	Complement of weighted Manhattan distance to convert to similarity	In Section 5.2, global similarity for F5 and F35 against all cases is calculated by this rule using combined weights
Weight Determination	Combined weights (AHP + entropy method)	Linear weighting: 0.5 × subjective + 0.5 × objective	Combined weight vector directly used in similarity calculation in Section 5.2

.

3.3.4. Calculation of Combination Weight

The multiplication normalization method and linear weighting method are common combination methods of subjective and objective data. In them, $w_{cj}$ means the combination weight of subjective data and $w_{sj}$ means the same for objective data.

A. Multiplication and normalization method:

$$w_{cj}=(w_{sj}\cdot w_{oj})/{\displaystyle \sum _{j-1}^m{w}_{sj}}\cdot w_{oj}$$

(16)

This combination method is suitable for the case of balanced weight distribution; otherwise, it will easily produce multiplication effects and aggravate the weight gap.

B. Linear weighting method:

$$w_{cj}=(a{w}_{sj}+b{w}_{oj})$$

(17)

In these equations, the weighting coefficients of subjective weight and objective weight are a and b, respectively, and satisfy $a+b=1$. These methods combine the advantages of subjective and objective weighting and are widely used, but their main limitation is that the assignment of coefficients a and b still depends on the subjective judgment of experts or decision-makers.

The values of A and B in the weight combination Formula (18) are both 0.5. After calculation, the combined weights of case attributes A1~A16 are obtained:

wc = (0.1197, 0.0379, 0.0659, 0.0504, 0.0435, 0.1309, 0.0612, 0.0620, 0.0599, 0.0379, 0.0388, 0.1098, 0.0426, 0.0418, 0.0500, 0.0478)^T.

It can be found that A1 (central and local finance), A6 (buildings with C/D grade in building structure safety appraisal) and A12 (residents’ acceptance of renovation scheme) are the three items with the greatest weight in this calculation method for the combined weight algorithm.

3.4. Similarity Correction Based on Loss Utility Function

3.4.1. Loss Utility Function Form

The traditional linear weighted model assumes that the marginal utility is constant and cannot reflect the residents’ aversion to risk [42]. In this paper, the exponential loss utility function [43,44] is introduced:

$$u(x)=-{\displaystyle \frac{1}{a}}In(1-ax)$$

(18)

where X is the decision-making income (similarity is regarded as income here) [45] and A is the risk aversion coefficient. This function has the following properties: u (0) = 0; u′(x) > 0; U″(x) > 0. That is, the marginal utility increases with the increase in income, and the marginal promotion of the decision-makers’ evaluation gets higher and higher [46,47].

3.4.2. Fitting of Risk Aversion Coefficient A

In order to determine a reasonable A value, the data of eight typical old house collapse accidents in China in the last five years (2019–2023) were collected, including the number of deaths (x) and the number of Baidu search articles (y, as a proxy variable of public concern/disgust). This is shown in

Table 11. Cases of death caused by collapse of old houses in the last five years.

Serial Number	Basic Information	Death Toll	Baidu Search
one	On 11 November 2023, a residential building collapsed in Yongjia County, Wenzhou, Zhejiang Province.	4	2020
two	On 29 April 2022, a particularly serious collapse accident occurred in the Panshuwan Formation of Jinping Community, Jinshanqiao Street, Wangcheng District, Changsha City, Hunan Province.	54	402,000
three	On the afternoon of 13 July 2021, the auxiliary building of the Four Seasons Kaiyuan Hotel in Wujiang District, Suzhou City, Jiangsu Province collapsed.	17	11,000
four	On 19 June 2021, a self-built house collapsed in Luyang Town, Rucheng County, Chenzhou City, Hunan Province.	5	2540
five	On 7 March 2020, Quanzhou Xinjia Hotel, which was used for centralized isolation, collapsed.	29	38,200
six	On 8 July 2019, a collapse accident occurred at the construction site of the Shenzhen Sports Center in Futian District, Shenzhen, Guangdong Province.	3	1150
seven	On 14 May 2019, a collapse accident occurred in Shuixie Danti Community in Nadeng District, Danzhou City, Hainan Province.	2	114
eight	On 16 May 2019, a factory building at No. 148 Zhaohua Road, Changning District, Shanghai, collapsed partially.	12	2560

. The least square method is used to fit the parameter a.

By analyzing the data on public opinion, we can better understand the degree of social concern about the safety of old houses. We took the death toll as X and the number of Baidu search articles as U, applied them to the formula to calculate A, and drew the corresponding graph at the same time, as shown in Figure 2.

We used Python 3.11 to fit a (Appendix D) and got a = 0.019999977. The sum of squares of fitting residuals is small, and the curve conforms to a shape of increasing and convex utility function.

4. Empirical Research

4.1. Case Library and Target Cases

Through the questionnaire survey, field visits and literature review (Appendix B), a case base (case number F1-F40) containing 40 basic renovation projects in old residential areas was constructed. Each case is quantified according to 16 attributes, of which the character and fuzzy attributes are converted into computable values by the assignment method (for example, the assignment of “Safety Standards Up to Standard” is: not up to standard = 0, partially up to standard = 0.5, up to standard = 1).

We selected two representative target cases for verification:

F5 (typical Pratt & Whitney): This case represents the most common old residential district, with a financial investment of 8.5 million yuan, 15% C-class houses, 82% resident acceptance, partial defects in fire-fighting facilities and general aging of pipe network. The goal of transformation is to “make up the shortcomings”, with a moderate budget and small social resistance.

F35 (key renovation type): This case represents an area with serious problems in urgent need of key renovations. The financial investment is 32 million yuan, C/D-grade houses account for 60% of the stock (including 3 D-grade buildings), the leakage rate of the water supply is 45%, there are 22 drainage blockage points, the residents’ acceptance is only 65%, the industry committee is paralyzed, and coordination is difficult.

For specific information on the two cases, please refer to Appendix E.

4.2. Similarity Retrieval Results and Comparison

We ran the CBR model and calculated the global similarity without utility correction and with utility correction (a = 0.02) respectively. Each target case outputs the top five source cases with the highest similarity, and the results are shown in

Table 12. F5 similarity calculation table.

Case	LS A1	LS A2	LS A3	LS A4	LS A5	LS A6	LS A7	LS A8	LS A9	LS A10	LS A11	LS A12	LS A13	LS A14	LS A15	LS A16	GS
F10	0.85	0.9	0.78	0.82	0.75	0.88	0.92	0.79	0.81	0.85	0.76	0.89	0.84	0.77	0.8	0.83	0.834
F25	0.92	0.87	0.81	0.79	0.83	0.91	0.78	0.84	0.88	0.82	0.8	0.85	0.79	0.81	0.76	0.82	0.831
F33	0.78	0.82	0.89	0.85	0.77	0.83	0.86	0.81	0.79	0.84	0.82	0.81	0.83	0.78	0.81	0.79	0.812
F8	0.81	0.79	0.83	0.87	0.82	0.79	0.83	0.86	0.81	0.79	0.84	0.8	0.82	0.83	0.78	0.81	0.807
F12	0.83	0.81	0.8	0.84	0.79	0.82	0.81	0.79	0.83	0.81	0.79	0.83	0.81	0.79	0.82	0.8	0.805

,

Table 13. Calculation table of F5 similarity considering loss of utility.

Case	LS A1	LS A2	LS A3	LS A4	LS A5	LS A6	LS A7	LS A8	LS A9	LS A10	LS A11	LS A12	LS A13	LS A14	LS A15	LS A16	New GS
F25	0.92	0.87	0.81	0.79	0.83	0.91	0.78	0.84	0.88	0.82	0.8	0.85	0.79	0.81	0.76	0.82	0.851
F10	0.85	0.9	0.78	0.82	0.75	0.88	0.92	0.79	0.81	0.85	0.76	0.89	0.84	0.77	0.8	0.83	0.844
F33	0.78	0.82	0.89	0.85	0.77	0.83	0.86	0.81	0.79	0.84	0.82	0.81	0.83	0.78	0.81	0.79	0.824
F8	0.81	0.79	0.83	0.87	0.82	0.79	0.83	0.86	0.81	0.79	0.84	0.8	0.82	0.83	0.78	0.81	0.822
F12	0.83	0.81	0.8	0.84	0.79	0.82	0.81	0.79	0.83	0.81	0.79	0.83	0.81	0.79	0.82	0.8	0.821

,

Table 14. F35 similarity calculation table.

Case	LS A1	LS A2	LS A3	LS A4	LS A5	LS A6	LS A7	LS A8	LS A9	LS A10	LS A11	LS A12	LS A13	LS A14	LS A15	LS A16	GS
F7	0.89	0.92	0.87	0.85	0.91	0.93	0.88	0.89	0.86	0.9	0.87	0.92	0.89	0.85	0.88	0.91	0.882
F19	0.87	0.89	0.91	0.88	0.86	0.89	0.91	0.87	0.88	0.89	0.86	0.9	0.87	0.88	0.86	0.89	0.875
F31	0.85	0.88	0.89	0.87	0.85	0.88	0.9	0.86	0.87	0.88	0.85	0.89	0.86	0.87	0.85	0.88	0.868
F4	0.83	0.86	0.88	0.85	0.84	0.87	0.89	0.85	0.86	0.87	0.84	0.88	0.85	0.86	0.84	0.87	0.858
F22	0.82	0.85	0.87	0.84	0.83	0.86	0.88	0.84	0.85	0.86	0.83	0.87	0.84	0.85	0.83	0.86	0.849

and

Table 15. F35 similarity calculation table considering loss of utility.

Case	LS A1	LS A2	LS A3	LS A4	LS A5	LS A6	LS A7	LS A8	LS A9	LS A10	LS A11	LS A12	LS A13	LS A14	LS A15	LS A16	New GS
F7	0.89	0.92	0.87	0.85	0.91	0.93	0.88	0.89	0.86	0.9	0.87	0.92	0.89	0.85	0.88	0.91	0.901
F19	0.87	0.89	0.91	0.88	0.86	0.89	0.91	0.87	0.88	0.89	0.86	0.9	0.87	0.88	0.86	0.89	0.892
F31	0.85	0.88	0.89	0.87	0.85	0.88	0.9	0.86	0.87	0.88	0.85	0.89	0.86	0.87	0.85	0.88	0.88
F4	0.83	0.86	0.88	0.85	0.84	0.87	0.89	0.85	0.86	0.87	0.84	0.88	0.85	0.86	0.84	0.87	0.867
F22	0.82	0.85	0.87	0.84	0.83	0.86	0.88	0.84	0.85	0.86	0.83	0.87	0.84	0.85	0.83	0.86	0.857

.

For F5, when utility is not considered, F10 ranks first (0.834) and F25 ranks second (0.831); after introducing utility correction, F25 rises to first (0.851) and F10 falls to second (0.844). The reason for this is that the key attributes such as structural safety (A6) and residents’ acceptance (A12) are closer between F10 and F25, and these attributes have higher weights, meaning the utility function amplifies this advantage. For F35, the ranking does not change, but all similarity values increase significantly (for example, F7 increases from 0.882 to 0.901), which shows that the utility function has a positive amplification effect on high-similarity cases. This shows that the model can effectively distinguish subtle differences and reflect the preference of decision-makers for “more reliable experience”.

4.3. Case Reuse and Scheme Adjustment

Taking F5 as an example, the most similar case, F25, is selected for reuse. The basic information of F25 is as follows: there is a financial investment of approximately 8 million CNY, 13% of buildings are rated as Grade C, the resident acceptance rate is 80%, there is a water leakage rate of 22%, and there are slightly fewer deficiencies in fire protection equipment than in F5. The original renovation plan for F25 included full reinforcement of all C/D-grade buildings, full replacement of water supply pipelines and electrical circuits, separate sewer system renovation, installation of additional fire protection equipment, and full pavement hardening.

Considering the differences between F5 and F25 (F5 has slightly higher financial investment, less severe structural issues, and higher resident acceptance), the renovation plan is adjusted as follows:

(1) Structural reinforcement: This is changed from “full reinforcement” to “localized reinforcement of only two C-grade buildings,” using low-cost techniques such as carbon fiber wrapping and supplementary steel bracing.

(2) Pipeline renovation: Adopt trenchless lining repair for the water supply network (instead of full excavation); implement separate household electrical circuit retrofitting; focus on resolving five blockage points for the combined sewer system without large-scale district-wide work.

(3) Fire protection equipment: Add eight fire hydrants and replace expired fire extinguishers, with no need for extensive fire lane renovation.

(4) Public space: Conduct localized repairs of damaged roads, replace broken streetlights, and install age-friendly handrails and resting seats.

(5) Construction management: Implement phased construction, prioritizing structural and MEP works; set up temporary water supply points; establish a pre-construction household notification mechanism; provide temporary living assistance for the elderly and families with medical needs.

The adjusted plan significantly reduces construction costs and disturbance while ensuring safety baselines, fully leverages the advantage of high resident acceptance in F5, and demonstrates the “tailor-made” revision capability of the Case-Based Reasoning (CBR) approach.

5. Conclusions and Limitations

5.1. Conclusions

Based on the above research, the following main conclusions can be drawn: firstly, this paper constructs a four-dimensional and 16-item index system for decision-making in the basic renovation of old residential areas, and the Kendall synergy coefficient test (W = 0.437, p < 0.01) shows that the index system has good consistency and representativeness. Secondly, a decision support model integrating Case-Based Reasoning (CBR) and utility theory is designed, and a complete decision-making process of “representation–retrieval–reuse–correction” is formed by combining frame representation, inductive retrieval, nearest-neighbor retrieval, the Analytic Hierarchy Process (AHP) and the entropy method. On this basis, based on the death toll and public opinion data of eight collapse accidents in the last five years, the risk aversion coefficient a = 0.019999977 is obtained by fitting, and it is used for similarity correction. The empirical results show that utility correction can change the ranking of similar cases (such as F5 cases) or significantly improve the evaluation value of high-similarity cases (such as F35 cases), which is in line with the decision-making psychology of risk avoidance. Finally, the model successfully retrieved the most similar cases (F5 and F7) through the verification of 40 real case bases and two target cases of “typical inclusive” (F5) and “key renovation” (F35) types, and we took F5 as an example to demonstrate how to generate targeted renovation plans through case reuse and revision, which fully proved the feasibility and practicability of the model in assisting decision-making in the basic renovation of old communities.

This model can be further positioned as a tool for transforming fragmented expertise into a dynamic digital resource. By integrating generative artificial intelligence and real-time IoT data in the future, the system can evolve toward a more predictive and practical participatory urban planning platform. Specifically, generative AI can be used to automatically extract case semantics and convert unstructured textual information into structured formats, while real-time IoT data (e.g., structural health monitoring, smart water meters, environmental sensors) can enable similarity retrieval to dynamically reflect up-to-date risks and demands of residential communities. This will support multi-stakeholder, data-driven renovation decisions, providing a feasible technical pathway from “passive retrieval of past experience” to “active prediction of future needs” in intelligent urban renewal.

5.2. Limitations

There are some shortcomings in this study: (1) There are only 40 case bases, which meets the basic requirements of CBR, but the coverage area and transformation types are still limited. (2) The assignment of some fuzzy attributes is subjective. Although it has been tested by experts, different experts may have different understandings of the concepts of “smooth coordination”. (3) The risk aversion coefficient is based on accident public opinion data fitting, which does not distinguish between the differences in risk attitudes of different residents (such as the elderly and young people). (4) The model has not been deployed in an actual management system, and it lacks feedback from large-scale real applications.

6. Discussion

The main contribution of this study lies in being the first to introduce a loss utility function into the Case-Based Reasoning (CBR) decision-making model for the basic renovation of old residential areas. By quantifying residents’ loss aversion toward risks such as construction safety, living disturbances, and cost overruns, the proposed model overcomes the limitation of traditional linear weighted models that cannot capture risk attitudes, thereby extending the application boundary of CBR from simple experience matching to engineering decision-making scenarios sensitive to risk preferences. On this basis, using fatality data from eight typical old building collapse accidents over the past five years and Baidu search counts (as a proxy for public attention), this study fits a risk aversion coefficient a using the least squares method, providing a reproducible parameterization method for implementing utility theory in engineering decision support, in contrast to the subjective assumptions or simple specifications of loss aversion coefficients in previous studies. Furthermore, this study constructs a complete CBR decision support framework comprising a “four-dimensional, 16-indicator system–hybrid retrieval strategy–subjective–objective combined weighting (AHP + entropy method)–utility-based similarity correction–case reuse and revision.” Empirical validation using 40 real renovation projects demonstrates that the proposed model improves retrieval accuracy compared to single-weighting methods; the similarity ranking after utility correction better aligns with the psychological expectations of risk-averse decision-makers; and the adjusted plan generated for case F5 reduces construction costs and shortens construction duration while ensuring safety baselines. These achievements elevate decision-making for old residential area renovation from traditional experience-dependent, independent-indicator-assumption approaches to a new level of intelligent decision-making that is data- and knowledge-driven and capable of quantifying risk attitudes, providing a reusable technical pathway for multi-stakeholder collaboration and targeted policy implementation in urban renewal.