Contractor Recommendation Model Using Credit Networking and Collaborative Filtering

Abstract

The credit of contractors in the construction market directly affects the cooperative intentions of owners. Although previous scholars have attempted to use credit to select appropriate contractors, they have rarely considered the trust relationship between decision-making and former owners. This work introduces and verifies a credit network recommendation model based on a collaborative filtering algorithm. The contractor’s credit established based on this model serves as a viable method for owners to select efficient contractors. The application of the model includes relevant information collection, neighbor set formation, contractor’s credit evaluation, and recommendation list formation, among which the neighbor set of the owner is used to calculate the comprehensive trust degree of the decision-making owner to the former owner. A time decay function is adopted to correct the difference in the trust relationship between an owner and a contractor introduced over time. To verify the feasibility of this model, an actual scenario was simulated, and the results obtained via simulations were compared and found to be consistent. Thus, a contractor with a high credit can be recommended to the decision-making owner. This approach is crucial for promoting contractors’ credit and conducive to the healthy development of the construction market.

1. Introduction

Owners and contractors are key players in the construction market. Owing to information asymmetry, certain contractors may lack integrity and thus provide buyers with professionally unethical suggestions or guidance [1,2,3]. Occasionally, bid-rigging, collusion, corruption, and other acts occur in the bidding process, wherein some bidders win contracts through dishonesty. Owners are forced to bear the risk of unprofitable outcomes owing to the dishonesty of such contractors. Therefore, the method that the owner adopts to choose the right contractor in the bidding stage is key to the profitability of a project [4,5,6]. With the promulgation of relevant policies, an environment was created to share credit information in the construction industry. Thus, owners can use this credit information to select appropriate contractors. The credit of a contractor spreads through the network among owners. If the decision-making owner does not cooperate with this contractor, an indirect trust score can be obtained from a former owner who has cooperated with the contractor, and the recommendation trust can be accumulated, as shown in Figure 1. If the decision-making owner has cooperated with this contractor, a comprehensive trust will be formed through the last cooperation, and the accumulated recommended trust from other previous owners enables the evaluation of contractor trustworthiness, as depicted in Figure 2.

When choosing a contractor, reference opinions from previous owners often directly affect the judgment of the decision-making owner. If owners who trust each other and have good credit are in the same group, an evaluation previously provided by one of them may have a high reference value. The decision-making owner considers contractors who previously cooperated with other owners in the group to be credible. Thus, the higher the score, the higher the possibility of being a potential cooperative contractor. Contractors with low scores are more likely to be eliminated from the market because owners would consider them to be high-risk contractors; as a result, such contractors are less likely to be placed on the shortlist for cooperation.

Consequently, decision-making owners need to decide how to value the evaluations of previous owners. In this study, a credit network recommendation model was built based on the collaborative filtering algorithm of owners and mutually trusted owners. Moreover, decision-making owners obtain the credit values of contractors through the recommendations and trust evaluations of previous owners. This research complements the trust judgment method at the owner’s level in terms of recommendation trust and helps identify suitable contractors by drawing on algorithms from the computer science field.

For construction with a social investment, bidding is no longer the obligatory means of selecting contractors, and owners can independently decide the method of awarding contracts based on reality. Therefore, owners can choose appropriate contractors by referring to the credit information of the construction market. This study provides a feasible method for owners to select contractors, promotes contractor’s credit improvement, alerts and prompts contractors, and is conducive to improving the organizational and technical levels of contractors and enhancing their competitiveness. To ensure that projects progress in an orderly manner, owners refuse contractors with bad cooperation, which reduces the failure cases across the entire construction market and improves the efficiency of market work. Therefore, this approach is conducive to the healthy development of the construction industry. Notably, this study expands the field of credit in the construction industry and provides new ideas related to methods through which owners can select contractors. Other professionals can also use the findings of the proposed model algorithm to select reliable partners, from the perspective of credit.

2. Literature Review

2.1. Research on Credit

Several previous scholars have focused on the value of credit. Credit is an important component of the socio-economic transaction system, and it is related to the transaction cost and volume of the society. A lack of credit results in chaos in transaction orders and hinders economic development [7,8]. Kreps, Milgrom, Roberts, and Wilson (KMRW) established the KMRW reputation model, which plays a fundamental role in credit research. They showed that, in the course of multiple transactions, operators value long-term expected benefits and provide high-quality labor and services for reputation considerations [9]. Credit is a strategic resource for enterprises to maintain their competitive advantage [10,11]. Friedman and Resnick studied credit under the aforementioned network scenario and rated the credit of online community participants to avoid the dishonest behavior of any community participants who were irresponsible and altered their identities to join the community multiple times [12]. Credit networks are typically applied in computers. Certain scholars have studied the credit mechanism in P2P networks [13,14], whereas others have studied online credit transactions [15,16]. However, few previous studies have focused on the credit networks in the construction industry.

In the field of construction, research on credit has mainly focused on the establishment of a contractor’s credit evaluation index system [17,18] and the development of a constraint and incentive mechanism based on game theory [19,20]. Some scholars have considered credit when studying contractor selection. Credit affects the performance of construction enterprises [21,22,23]. The fuzzy evaluation method can be used to establish a standard system that considers credit to evaluate contractors’ capabilities [24,25,26]. The reciprocal preference relation and credit function can also be used to select the best contractor in situations with incomplete information [27]. Furthermore, some researchers have surveyed opinions on prequalification and reported that cost, experience, and reputation are the main selection factors [28,29,30]. Credit is considered in the evaluation system for the owner’s inspection of contractors [31]. Based on the improved D-S evidence theory, a credit evaluation feedback mechanism for owners with regard to contractors was established for contractor selection [32].

2.2. Research on Recommendation Algorithms Related to Trust

Trust and social relationships among social network users are important indicators of user preferences. Several studies on social network recommendation algorithm modeling have considered these two sets of information [33,34,35]. The graph neural network recommendation algorithm, which combines trust and social reputation, provides accurate and interesting services to users based on social relationships [36]. Social reputation refers to the social evaluation based on social relations. The Slope One algorithm is based on the fusion of trusted data and user similarity; it can be deployed in various recommender systems to solve personalized recommendation tasks concerning the relationship among users [37]. Furthermore, the collaborative filtering algorithm can be applied to a social network awareness recommendation system, employing user ratings of items and the social relationships of users. The density and utility of the collaborative filtering field and social network of each user are considered to solve the problem of limited information [38]. Based on the community in the network, the collaborative filtering algorithm selects a part of the user community as a candidate neighboring user set of the target user, to reduce the computational time and improve the speed and accuracy of the recommendation system [39].

2.3. Research Gap

The participants in the construction market are regarded as network nodes, and the relationships between them are indicated as connection lines. Thus, the spread of credit in this social network leads to the formation of a credit network. The trust among owners may vary depending on various factors. Most researchers study contractors based on the trust of former owners in contractors; however, recommendation trust does not consider the trust between the decision-making owner and former owners. Therefore, the credit network constructed in this study considers the trust among various owners and also uses the PageRank algorithm to calculate the credit of owners in the construction market. The decision-making owner can thus select the recommended contractor based on the credit ratings of contractors who previously cooperated with the other owners. This collaborative filtering algorithm considering credit improves the accuracy and recommendation of contractors’ credit scores based on the evaluations of the trust of previous owners.

3. Methods

Theoretical Modeling and Computer Simulations

Owners and contractors are divided into two different layers, O and C, respectively. Here, O₁, O₂, O₃, and O₄ are gathered into a small world owing to the similar nature of enterprises and types of projects undertaken by them. We assume that O₁ is the decision-making owner and has a high level of trust with O₂, O₃, and O₄ and that O₃ cooperates with contractors C₂ and C₄. Because O₁ has an indirect trust with O₃, C₂ and C₄ are likely to become potential partners of O₁, as shown in Figure 3.

The choice of contractors by owners is similar to the manner in which users choose products in e-commerce, that is, a collaborative filtering algorithm is used. Since collaborative filtering technology was proposed in 1992 [40], it has been widely used in recommendation systems. The collaborative filtering algorithm does not consider the content characteristics; it only predicts the behavioral preferences of users based on their historical project score information and identifies individuals similar to a user in the group to form neighbors. The item or information that a neighbor user is interested in is most likely the factor that attracts the attention of the user, leading to recommendation to the user. As shown in Figure 4, user A is interested in items 1, 2, and 3; user B is interested in items 2 and 3; and user C is interested in item 4. Therefore, users A and B have a high similarity, and item 1 is likely to be the object that user B is interested in. Thus, it will be recommended to user B. If two users have similar scores for the same items, then the two users have a high degree of similarity. In this case, it is reasonable to recommend the items preferred by similar users to the target users. This algorithm has been applied in different fields [41,42,43].

In this study, the trust relationship among owners was considered based on trust recommendations; the similarity of owners is an influencing factor for the neighbor set. The formation of the neighboring set for owners is key to the contractor’s credit scores. Based on the idea of the owner set selecting the contractor, the user-based collaborative filtering algorithm is a more suitable method for owners to select contractors based on trust and credit conditions. Accordingly, an owner-based collaborative filtering algorithm is proposed herein.

This owner-based collaborative filtering algorithm was divided into three parts: information collection, formation of the owner neighbor set, and the contractor’s credit score. The first part calculates the composite trust value after the trust and credit spread among the owners and the similarity of the owners. The second part integrates the information collected in the first part to form the neighbor set of the owner. Finally, the credit scores of the contractors who cooperated with owners from the neighbor set of the decision-making owner are obtained, along with the recommendation list. The higher the score, the more likely it is for the contractor to be a part of the recommendation list, as shown in Figure 5.

The composite trust value among owners includes trust and credit values. The degree of cooperation reflects the trust relationship among owners. Owners who trust each other are likely to be long-term partners. Both the number of legally effective contract documents and the degree of familiarity after communication are greater than those in the case of low trust. The amount of cooperation can be used to calculate the trust value between owners.

The credit value refers to the values obtained using the PageRank algorithm [44]. The PageRank algorithm is a webpage ranking algorithm based on link analyses. If a web page is linked by many other web pages, it is highly reliable and ranked, and the links on the web page are reliable. Similarly, if an owner consistently receives positive reviews from owners in the construction market, it shows that the owner has good credit and that their evaluations are authentic.

The similarity function of owners is obtained using the similarity of the trust assessments of the owners for certain contractors and the commonalities across their attributes. The Pearson correlation coefficient is then used to analyze and calculate the similarity of the trust evaluations of contractors by the owners, considering the differences in preferences for factors affecting their trust and evaluation methods. Owners with similar attributes cooperate with similar types of contractors. The similarity in the common attributes of owners is measured according to the ratio of the number of common attributes to the total attributes of owners.

The composite trust and similarity values are fitted to obtain the degree of comprehensive trust. Owners with a high comprehensive trust form a neighbor set. The decision-making owner scores the credit of the contractors with cooperation experience in the neighbor set of the owner. Contractors with high scores are then included in the recommendation list to provide reference information to the decision-making owner.

A few important concepts of the current study, along with brief explanations, are listed in

Table 1. Explanation of important concepts in this study.

Concepts	Explanation
Trust	Subjective judgment of an owner of the expected behavior of a contractor under risk and uncertainty based on past cooperation experience(s) [32].
Credit	Comprehensive scores of construction market participants on the performance, attitude, and behavior of the contractor [45,46,47].
Composite trust	Decision-making owner integrates his or her knowledge based on past cooperation experience and the trust evaluation of former construction market owners; a certain calculation rule is used to obtain a composite evaluation of the trust level of the former owner. The composite trust comprises the trust and credit values.
Similarity	Similarity among owner expectations of the contractor and their attributes. It is formed by fitting similarities in the owner’s trust evaluations of contractors and the similarity across owner attributes.
Comprehensive trust	Comprehensive evaluation of the trust a decision-making owner has in former owners. It is obtained by combining the composite trust of a former owner by the decision-making owner and the similarity with the former owner, using a certain calculation rule.

.

4. Contractor Recommendation Model Based on Credit Network

4.1. Composite Trust Value

4.1.1. Trust Value

The degree of trust can be measured by calculating the trust value. The owner-based collaborative filtering algorithm mainly considers the trust relationship between owners, which can be divided into direct and indirect trust.

Decision-making owners establish direct trust (DT) with owners with whom they have cooperated in the past. DT is measured using the number of business transactions and communications. The number of business transactions refers to the number of formal documents, such as contracts and agreements, whereas the number of communications refers to the time an owner seeks advice from an experienced owner. The formula for DT can be expressed as follows:

$$D{T}_{mn}=\left\{\begin{array}{l}\frac{CN\left(m\right)\bigcap CN\left(n\right)}{CN\left(m\right)\bigcup CN\left(n\right)},I_{mn}=0,I_{nm}=0\\ \frac{I_{mn}+I_{nm}}{I_m+I_n},I_{mn}\ne 0 or I_{nm}\ne 0\end{array}\right.,$$

(1)

where

• CN(m) is the number of owners who had business transactions and communications with owner m;
• CN(n) is the number of owners who had business transactions and communications with owner n;
• $D{T}_{mn}$ is the DT from owner m to owner n;
• $I_m$ is the total number of businesses and communications between owner m and other owners;
• $I_{mn}$ is the business and communication time between owner m and owner n.

Target owners who have never cooperated with the decision-making owner can establish indirect trust (IT) with the decision-making owner, thereby realizing trust transfer through third-party owners. IT mainly solves the problems associated with determining trust delivery and paths, which are divided into serial and parallel trust transfers, as shown in Figure 6 and Figure 7, respectively. The owner chooses a transfer path according to his or her behavior preferences.

Serial trust transfer can be expressed as follows:

$$S{T}_{mn}=D{T}_{m,t1}\times D{T}_{t1,t2}\times \dots \times D{T}_{d-1,n},$$

(2)

where

• $D{T}_{m,t1}$ is the DT from owner m to intermediate owner t₁;
• $S{T}_{mn}$ is the serial trust transfer from owner m to owner n.

Parallel trust transfer is established based on a combination of multiple series of transfer paths. It is divided into three types—conservative, neutral, and aggressive—according to the attitude of the owner toward the trust value; each owner chose a different path. The formulas for these three types are given below.

Conservative: decision-making owners are cautious about the trust of the target owner.

$$P{T}_{mn}=min\left(S{T}_{m{n}_1},S{T}_{m{n}_2},\dots ,S{T}_{m{n}_k}\right),$$

(3)

where $P{T}_{mn}$ is the parallel trust transfer from owner m to owner n.

Neutral: decision-making owners are insensitive to the trust value of the target owner.

$$P{T}_{mn}=\frac{1}{k}{{\displaystyle \sum }}_{i=1}^{k}S{T}_{m{n}_i}.$$

(4)

Aggressive: decision-making owners are optimistic about the trust value of the target owner.

$$P{T}_{mn}=max\left(S{T}_{mn1},S{T}_{mn2},\dots ,S{T}_{mnk}\right).$$

(5)

Finally, the IT value is obtained as follows:

$$I{T}_{mn}=\left\{\begin{array}{c}S{T}_{mn}, Path=1\\ P{T}_{mn}, Path>1\end{array}\right..$$

(6)

4.1.2. Credit Value

The credit value considers both positive and negative evaluations from other owners; thus, it adopts a two-point system: 1 represents a positive evaluation (the trust evaluation factor is not less than 0.6), and −1 represents a negative evaluation. The formula for the trust evaluation factor is

$$TE\left(m,n\right)=\frac{H_{mn}}{I_{mn}},$$

(7)

where

• $H_{mn}$ is the number of times owner m feels happy to cooperate and communicate with owner n;
• $I_{mn}$ is the amount of business and communication from owner m to owner n;
• $TE\left(m,n\right)$ is the trust evaluation factor.

$$C\left(n\right)=\frac{1-\beta }{N}+\beta ·{{\displaystyle \sum }}_{O_{tx}\in n^{+}}\frac{C\left(O_{tx}\right)}{N\left(O_{tx}\right)},$$

(8)

where

• $C\left(n\right)$ is the credit value generated by the evaluation of other owners who communicate with owner n;
• $N$ is the number of owners in the credit network;
• $N\left(O_{tx}\right)$ is the number of evaluations given by owner $O_{tx}$ to other owners;
• $n^{+}$ is the collection of all owners who evaluate owner n;
• $O_{tx}$ are the owners who communicate with owner n;
• $\beta$ is the decay factor.

Generally, β = 0.85 (the number of evaluations between the owners is sparser than the number of owners; calculating the credit ranking of owners must smooth zero-probability and low-probability events, such as the owners who do not evaluate other owners).

To simplify the calculations, the aforementioned formula can be expressed in the following matrix form:

$$\mathit{C}=\left[\frac{\left(1-\beta \right)\times \mathit{E}{\mathit{E}}^T}{N}+\beta {\mathit{P}}^T\right]\mathit{C},$$

(9)

where

• C is the credit vector of the owner;
• E is the N-dimensional full 1 column vector;
• P is the probability transition matrix ($P_{i,j}$ represents the value of the element in row i and column j in the evaluation matrix divided by the sum of row i).

C can be obtained by solving for the eigenvector when the eigenvalue of the matrix $\frac{ \left(1-\beta \right)\times \mathit{E}{\mathit{E}}^T}{N}+\beta {\mathit{P}}^T$ is 1:

$$P_{i,j}=\frac{M_{i,j}}{{{\displaystyle \sum }}_{j=1}^N\left|M_{i,j}\right|},$$

(10)

where

• $M_{i,j}$ is the value of the element in row i and column j of the owner’s matrix, representing the communication and evaluation between the ith and jth owners; it is 1 for positive, −1 for negative, and 0 for owners without communication and evaluation.
• $N$ is the number of owners in the credit network.

4.1.3. Composite Trust Value of Owners

The composite trust value (CTV) is calculated using the trust and credit values, as follows:

$$CTVm,n=\left\{\begin{array}{l}C\left(n\right)\times D{T}_{mn},m and n have cooperation\\ C\left(n\right)\times I{T}_{mn},m and n have no cooperation\end{array}\right..$$

(11)

4.1.4. Time Decay Correction

Trust relationships change over time; recent cooperation and exchanges between owners become more convincing than trust values from the past. The time decay function was thus introduced to correct for the influence of the cooperation time on trust. The weight of the current cooperation was higher when the trust value was calculated, indicating that when the number of businesses and communications between owners was the same, the trust value calculated in near-term cooperation was more accurate, as shown in the following formula:

$$\gamma \left(t\right)={\gamma }_0+a{e}^{\frac{-t}{b}},$$

(12)

where

• $a,b$ are the time decay parameters;
• $t$ is the cooperation time;
• ${\gamma }_0$ is the basic trust value;
• $\gamma \left(t\right)$ is the time decay function.

The time decay parameters can be determined based on simulations using Origin 2019 software. After processing the decimals, ${\gamma }_0$ = 0.17, a = 0.8, and b = 15 were found to be the most appropriate values (red line). The time decay function is depicted in Figure 8. The red line indicates that trust decreases rapidly in the early stage and gently in the late stage. The yellow line decreases proportionally. The blue line is the opposite of the red line.

The CTV between owners changes when the time decay function is modified.

4.2. Similarity

The similarity function between owners is fitted according to the similarity in the owners’ trust assessments for the same contractor and the commonality across their attributes.

4.2.1. Similarity in Owners’ Trust Assessments for Same Contractor

In this study, Pearson’s correlation coefficient was used to analyze and calculate the similarity in the trust evaluations of a contractor by the owners. The correlation coefficient between the owners is denoted as R and calculated as follows:

$$R\left(m_1,m_2\right)=\frac{{{\displaystyle \sum }}_{x\in N\left(m_1,m_2\right)}\left(T{V}_{m_{1}x}-\overline{T{V}_{m_1}}\right)\left(T{V}_{m_{2}x}-\overline{T{V}_{m_2}}\right)}{\sqrt{{{\displaystyle \sum }}_{x\in N\left(m_1\right)}{\left(T{V}_{m_{1}x}-\overline{T{V}_{m_1}}\right)}^2}\sqrt{{{\displaystyle \sum }}_{x\in N\left(m_2\right)}{\left(T{V}_{m_{2}x}-\overline{T{V}_{m_2}}\right)}^2}},$$

(13)

where

• $N\left(m_1\right)$ is the collection of contractors who have worked with owner $m_1$;
• $N\left(m_1,m_2\right)$ is the collection of contractors who have worked with both owners $m_1$ and $m_2$;
• $R\left(m_1,m_2\right)$ is the correlation coefficient between owners $m_1$ and $m_2$;
• $\overline{T{V}_{m_1}}$ is the average trust score of owner $m_1$ for all contractors who have ever cooperated with the owner;
• $T{V}_{m_{1}x}$ is the trust value of owner $m_1$ for contractor x.

The closer the absolute value of R is to 1, the stronger the correlation between two owners and the greater the correlation in the evaluations of owners $m_1$ and $m_2$ for the same contractor.

4.2.2. Similarity in Common Attributes of Owners

The similarity in the common attributes of owners is calculated as follows:

$$F\left(m_1,m_2\right)=\frac{F_{m_1}\bigcap F_{m_2}}{F_{m_{12}}},$$

(14)

where

• $F\left(m_1,m_2\right)$ is the similarity in common attributes of owners $m_1$ and $m_2$;
• $F_{m_1}$ is the number of attributes of owner $m_1$;
• $F_{m_{12}}$ is the number of attributes of owner $m_1$ or $m_2$ (owners $m_1$ and $m_2$ have the same number of attributes for the comparison).

When $F\left(m_1,m_2\right)$ is closer to 1, the number of common attributes between owners $m_1$ and $m_2$ is greater, and $m_1$ and $m_2$ are more similar.

4.2.3. Similarity of Owners

The similarity function of owners is calculated as follows:

$$S\left(m_1,m_2\right)=\alpha R\left(m_1,m_2\right)+\left(1-\alpha \right)F\left(m_1,m_2\right),$$

(15)

where

• $S\left(m_1,m_2\right)$ is the similarity between owners $m_1$ and $m_2$;
• $\alpha$ is the scale factor.

4.3. Recommendation List

The comprehensive trust degree is expressed by T and defined as follows:

$$T\left(m,n\right)=CTV{\left(m,n\right)}^{’}\times S\left(m,n\right),$$

(16)

where

• $CTV{\left(m,n\right)}^{’}$ is the modified CTV;
• $T\left(m,n\right)$ is the degree of comprehensive trust between owners.

The decision-making owner selects other owners with higher degrees of comprehensive trust as the neighbor set and scores the credit of contractors who have had cooperation experience in the neighbor set. The credit formula is as follows:

$$P_c\left(m,a\right)=\overline{T{V}_m}+\frac{{{\displaystyle \sum }}_{n\in N_t}T\left(m,n\right)\times (T{V}_{na}-\overline{T{V}_n})}{{{\displaystyle \sum }}_{n\in N_t}T\left(m,n\right)},$$

(17)

where

• $N_t$ is the neighbor set of the decision-making owner;
• $P_c\left(m,a\right)$ is the credit score of owner m for contractor a;
• $\overline{T{V}_m}$ is the average trust score of owner m for contractors who have previously cooperated with them;
• $T{V}_{na}$ is the trust value of owner n who has cooperated with contractors a to a.

Finally, the first few contractors with high credit scores are used to form the recommendation list. The contractors on this recommendation list are suitable potential partners of the decision-making owner.

5. Simulation Experiments

5.1. Simulation Approach

In this work, the nodes in the simulation system were grouped into two categories, classes O and C, representing the virtual owners and virtual contractors, respectively. Here, the owners included the decision owners and target owners, whereas class O nodes were divided into request and response nodes. After interacting with each other in a class O hierarchy, a neighbor set was formed, which could query related nodes in the class C hierarchy and feed them back to the class O hierarchy. The C level could answer the O level query request.

Table 2. Simulation system nodes and their descriptions.

Simulation System Node	Real Environment Object	Notation
Class O request node	Decision-making owner	O1, O2, O3, …, Om
Class O response node	Target owner	O1, O2, O3, …, Om
Class C node	Contractor	C1, C2, C3, …, Cn

lists the interpretations of all the nodes used in the simulation system. The neighbor set of the class O request nodes depended on the feedback results from the class O response nodes, and the query of the class O request nodes to the class C nodes was related to the class O response nodes. Depending on the scenario, the class O nodes might be of different node types.

For a project to be performed at any given location, owner O₁ intends to choose the most suitable C_x as the object of cooperation from many contractors, that is, C₁, C₂, C₃, C₄, …, C_n. According to the modeling idea proposed herein, first, node O₁ sends a response to the query request of O₂, O₃, O₄, …, O_m, and all the class O nodes that have interacted with O₁ respond; these are denoted as O_t1. The number of third-party owners is less than or equal to three, and the longest path to reach the target owner is four. Here, O_t1 issues a query request to the class O nodes, and the class O nodes that have interacted with O_t1, excluding O₁, generate a response, which is denoted as O_t2, and so on. It is likely that O_t1, O_t2, O_t3, and O_t4 are neighbors of owner O₁. According to the comprehensive trust calculation rule, a trust score for the class O response node can be obtained. Class O response nodes with high comprehensive trust are selected as the neighbor set of the class O request node O₁, which are assumed to be O₂, O₃, and O₄. Here, O₂, O₃, and O₄ send requests to the class C nodes, and all the class C nodes that have interacted with O₂, O₃, and O₄ respond and feed back to the class O requesting node O₁. According to the calculation rules for the credit score, class C nodes with high credit scores, such as C₁ and C₂, are obtained to form the contractor recommendation list. The selection range of contractors is narrowed, and thus owner O₁ can compare C₁ and C₂ to make the final decision. At this point, the credit network recommendation model, constructed using the collaborative filtering algorithm of the owner, completes one iteration. Here, the effectiveness of the built model was proved by simulating the process of the owner choosing the contractor.

5.2. Simulation Hypothesis

We considered a certain city with a moderately difficult and medium-sized project issued by the owner and that the best partner must be chosen from 10 selected contractors. Further, we assumed that the owner had no past cooperation with these 10 contractors and knew nearly nothing about their performance and abilities. Thereafter, the credit evaluation of the contractors by owners who had cooperated with them was used to eliminate contractor candidates with poor credit. The number of other owners who had direct or indirect contact with the owner was 99.

The abilities and behaviors of the contractors are the primary reasons for their inherent attributes that do not change with the trust evaluation. The value range of the inherent attributes of trust of the contractors was set as [0, 100], where 100 represented excellent performance and a very high level. Meanwhile, zero implied that the contractor was extremely poor and had no advantage in almost any aspect. According to the normal distribution with a mean value of 70, the inherent attributes of trust were randomly assigned to class C nodes, representing the capability value of each contractor; these inherent attribute values of trust obeyed X − N (70, 10²).

5.3. Simulation Process

According to the abovementioned simulation conditions, the simulation process was defined using the design links, as illustrated in Figure 9.

5.3.1. Trust Evaluation between Owners

After determining the inherent attribute of the trust evaluation factor of the class O node, the respective credit value could be calculated. The intrinsic attributes of the trust evaluation factor of class O nodes followed X − N (0.7, 0.1²), as shown in Figure 10. The specific steps were as follows. Firstly, a random O class node was simulated, based on the inherent nature of the trust evaluation factor value, which determined the performance of cooperation. If TE ≥ 0.6, then O had a better ability, indicating the trust evaluation assignment s = 1, which suggested that the other O nodes provided positive opinions. If TE < 0.6, then s = −1, which suggested that the other O nodes provided negative opinions. According to the logic of the PageRank algorithm, the PR value of O was calculated and sorted, that is, the value and order of the credit.

5.3.2. Owner’s Assessment of Trust in Contractor

The simulation system randomly selected a class C node and assigned it the trust inherent attribute value, according to the law of normal distribution. Based on the trust inherent attribute value, a normal distribution with a standard deviation of 10 was used to form the trust evaluation distribution of this node; some distributions were selected for the trust evaluation for the class C node from the class O nodes, as shown in Figure 11.

The credit scores obtained using the contractor-type nodes after the simulation were sorted to represent the calculation results of the model. The similarity h between the actual scenario and simulations was compared based on the set measurement. The number of intersection elements in the sets corresponding to the two sequences at different depths may differ. The similarity of the sorted list could then be obtained using the average intersection ratios at different depths. If the similarity was high, then the simulation results were consistent with the results of the actual situation.

5.3.3. Owner’s Neighbor Set

The owner set formed by O_t1, O_t2, O_t3, and O_t4 reduced the number of owners according to the trust value, and as a result, the owners who were less connected with the decision owner were excluded; the number of owners was reduced by a factor of one-third and sorted according to the CTV. By comparing the similarity of the contractor trust assessments between request node O₁ and response nodes O_t1, O_t2, O_t3, and O_t4, the number of owners in the owner set was further reduced by one-half to form the owner neighbor set with one-third of the original O_t1, O_t2, O_t3, and O_t4 owners, according to the ranking of the comprehensive trust degree.

5.3.4. Owner Chooses a Contractor

Here, O_t1, O_t2, O_t3, and O_t4 in the neighbor set provided recommendations to the class C nodes with which requesting node O₁ intended to cooperate, assuming that C₁ was one of them. The selected O-type nodes that had interacted with C₁ in the neighbor set formed set N_C1. Each O-type node in N_C1 had a trust evaluation for C₁. The trust score followed a normal distribution with the trust inherent attribute of C₁, with a mean and standard deviation of 10. Owing to the high reliability of the O-type nodes in N_C1, the random value range of the trust score was (μ − 10, μ + 10). The average value of the trust scores of the class O nodes in N_C1 with regard to the class C nodes that had interacted was calculated according to the number of class C nodes that had interacted with this recommendation. Here, O₁ took the trust inherent attribute as the trust evaluation value for the C-type nodes that had responded. The comprehensive trust degree of O₁ to O-type nodes in N_C1 was combined to form the credit score of O₁ to C₁.

5.4. Simulation Results

We assumed that the decision-making owner was aggressive. In the construction market, there was approximately one direct communication among every five owners, and the probability of direct interactions between the owner-type nodes was 20%. Furthermore, there were up to four iterations when calculating IT. The number of properties of the owner-type node was 10, and the O-type nodes in the neighbor set had a complete evaluation of the 10 C-type nodes. The simulation of the program yielded the following results.

The decision-making owner evaluated the CTV and similarity of other connected owners to form a comprehensive trust degree, and they collected the top 34 owners with high comprehensive trust degrees as members of the neighbor set.

Table 3. CTVs of decision-making owners with respect to other owners.

Owner ID	CTV	Owner ID	CTV
……	……	……	……
25	0.009254	60	0.008537
26	0.007779	61	0.007245
27	0.009282	62	0.009927
28	0.007052	63	0.010271
29	0.014805	64	0.011784
……	……	……	……

lists the CTVs of the decision-making owners with respect to the other owners,

Table 4. Similarity of decision-making owners to some other owners.

Owner ID	Similarity	Owner ID	Similarity
……	……	……	……
7	0.665929	82	0.638158
8	0.572265	83	0.668775
19	0.496514	84	0.685942
10	0.625432	85	0.658776
11	0.551873	86	0.555459
……	……	……	……

presents the evaluation of the similarity of the decision-making owners to some owners, and

Table 5. Comprehensive trust of decision-making owners of neighboring owners.

Number	Owner ID	T	Number	Owner ID	T
1	33	0.011748	18	45	0.007819
2	3	0.010527	19	51	0.007587
3	55	0.009536	20	93	0.007239
4	29	0.009219	21	50	0.007234
5	81	0.009114	22	32	0.007206
6	64	0.008767	23	15	0.007177
7	4	0.008757	24	53	0.007032
8	78	0.008663	25	58	0.006987
9	68	0.008413	26	36	0.006925
10	98	0.008408	27	63	0.006885
11	95	0.008269	28	8	0.006855
12	91	0.008208	29	20	0.006827
13	67	0.008197	30	62	0.006745
14	97	0.008184	31	10	0.006660
15	54	0.007922	32	34	0.006627
16	35	0.007890	33	47	0.006484
17	24	0.007821	34	89	0.006464

shows the comprehensive trust of the decision-making owners in their neighboring owners, in a descending order.

Table 6. Inherent attributes of a trustworthy contractor.

Number	Contractor Cn	Inherent Attributes	Contractor Cn	Inherent Attributes of Trust in Descending Order
1	C1	77.54	C8	86.38
2	C2	84.00	C6	84.90
3	C3	65.50	C2	84.00
4	C4	66.28	C1	77.54
5	C5	73.44	C5	73.44
6	C6	84.90	C7	73.20
7	C7	73.20	C4	66.28
8	C8	86.38	C3	65.50
9	C9	62.81	C10	63.36
10	C10	63.36	C9	62.81

shows the inherent attributes of trust assigned to a contractor by random values, according to the normal distribution curve of X − N (70, 10²). This was processed in descending order according to the inherent property of contractor trust, and two decimal digits were reserved as the evaluation standards for the contractor ability, quality, and morality levels in actual situations. Here, C₈, C₆, and C₂ had high trust inherent property values and were ideal partners for cooperation; by contrast, C₃, C₄, C₉, and C₁₀ had low trust inherent property values, and the decision-making owner did not expect to cooperate with them.

Table 7. Contractor trust evaluation for the owner with ID 33.

Cn	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10
Evaluation	86.48	77.26	58.06	76.28	82.27	92.52	76.96	81.15	57.45	57.77

presents the trust evaluation of an owner with ID 33 for 10 different contractors.

Table 8. Credit ranking comparison.

Number	Contractor Cn	Inherent Properties of Trust	Contractor Cn	Credit Score
1	C8	86.38	C8	13.23
2	C6	84.90	C6	12.41
3	C2	84.00	C2	11.14
4	C1	77.54	C1	4.75
5	C5	73.44	C7	2.51
6	C7	73.20	C5	−1.67
7	C4	66.28	C4	−7.80
8	C3	65.50	C3	−9.16
9	C10	63.36	C9	−9.62
10	C9	62.81	C10	−9.80

compares the rankings between the inherent attributes of trust and the contractor’s credit scores assigned by the decision-making owner.

Table 9. Credit ranking similarity comparison.

Depth	Real Ranking of the Top K Contractors	Simulation Ranking of the Top K Contractors	Intersection Contractor	Proportion
1	C8	C8	{C8}	1/1 = 1
2	C8, C6	C8, C6	{C8, C6}	2/2 = 1
3	C8, C6, C2	C8, C6, C2	{C8, C6, C2}	3/3 = 1
4	C8, C6, C2, C1	C8, C6, C2, C1	{C8, C6, C2, C1}	4/4 = 1
5	C8, C6, C2, C1, C5	C8, C6, C2, C1, C7	{C8, C6, C2, C1}	4/5 = 0.8
6	C8, C6, C2, C1, C5, C7	C8, C6, C2, C1, C7, C5	{C8, C6, C2, C1, C5, C7}	6/6 = 1
7	C8, C6, C2, C1, C5, C7, C4	C8, C6, C2, C1, C7, C5, C4	{C8, C6, C2, C1, C5, C7, C4}	7/7 = 1
8	C8, C6, C2, C1, C5, C7, C4, C3	C8, C6, C2, C1, C7, C5, C4, C3	{C8, C6, C2, C1, C5, C7, C4, C3}	8/8 = 1
9	C8, C6, C2, C1, C5, C7, C4, C3, C10	C8, C6, C2, C1, C7, C5, C4, C3, C9	{C8, C6, C2, C1, C5, C7, C4, C3}	8/9 = 0.89
10	C8, C6, C2, C1, C5, C7, C4, C3, C10, C9	C8, C6, C2, C1, C7, C5, C4, C3, C9, C10	{C8, C6, C2, C1, C5, C7, C4, C3, C10, C9}	10/10 = 1
Similarity h = 0.969

shows the similarity h obtained via the method of set measurements.

From Table 9, it is evident that h = 0.969 > 0.75, which indicates that the similarity between the two sequences is high, and the simulation results reflect the credit level of a contractor.

Figure 12 shows a scatter plot of the similarity h obtained after performing multiple simulations. According to the distribution, the similarity is concentrated around 0.9, which verifies the effectiveness of the model.

According to the credit scores listed, contractors C₈, C₆, and C₂ had better evaluations and were the top three candidates in the recommendation list. Their ranking was the same as that of the intrinsic contractor’s trust properties. The ranking results were similar to those in the actual scenario, indicating that the model and simulation experiments could narrow the scope of contractor selection and reflect the capability and quality of the contractors in terms of serving the decision-making owner. The credit scores for C₃, C₄, C₉, and C₁₀ were lower, and they failed to meet the requirements of the decision-making owner. Hence, they were replaced with better contractors, which was also in agreement with the actual scenario. Based on the simulation results, ranking errors, such as those for C₅ and C₇, were because the inherent trust values of these contractors were relatively similar; in such cases, the sensitivity of the model was weakened. Thus, it was difficult to identify their true ranking. For contractors with a large difference in their inherent trust values, the model could provide ranking results that were consistent with the actual scenario. Thus, the basic ranking of the credit of a contractor could be calculated using this credit network recommendation model.

6. Conclusions

In this study, we established a credit network recommendation model using an owner-based collaborative filtering algorithm. In this approach, contractors’ credit scores were obtained using trust evaluations from owners who were trusted by the decision-making owner, to narrow the scope of the contractor selection.

(1)

We defined the meaning and application scope of trust and credit in the field of construction, analyzed different methods of trust and credit transmission using the principles of trust chain and the PageRank method, and determined the trust values of decision-making owners to other owners and the credit values of the target owners. Considering the effects of cooperation time on the trust relationship between owners, a time decay function was introduced to correct the trust and credit values with respect to time.

(2)

According to the idea of the collaborative filtering algorithm, a contractor recommendation model based on the credit network was constructed. The neighbor set was established using the trust relationship between owners. A comprehensive trust degree between the owners served as the criterion for selecting the neighbor owners, and it was fitted considering trust, credit, and similarity. A recommendation from a neighbor owner was more credible than that of a general owner, which subsequently improved the satisfaction of the decision-making owner when choosing contractors based on the recommendation trust. The decision-making owner scored the credit of contractors who had cooperated with the neighborhood set, and contractors with high ratings were included in the recommendation list.

(3)

Based on a comparison of the simulation cases and model output results, it is concluded that the contractor recommendation model based on the collaborative filtering algorithm can select the contractor with a high credit rating to serve the owner.

In this study, the trust relationship between owners was established; however, less emphasis was placed on the trust between former owners and prospective contractors. It was previously assumed that the inherent trust of a contractor did not change with time. However, we proved that the influence of time on the ability of a contractor is important. In addition, the model is less sensitive to contractors with similar inherent trust. Hence, future work should consider the combined effects of time on both owners and contractors and distinguish between similar contractors carefully.