1. Introduction

2. Related Work

3. The Framework of Blockchain-Assisted Reputation Management Scheme for IoV

4. The MSMWSL Algorithm for Reputation Management

4.1. Direct Opinion Combination

Based on the Subjective Logic (SL) model, by considering the direct opinion weights between shared vehicle nodes such as familiarity, timeliness, and trajectory similarity, a more accurate quantification of the differences in subjective opinions between vehicle nodes can be achieved, resulting in a direct opinion combination.

4.1.1. Direct Opinion Three Weights

1.

Familiarity

Familiarity measures the degree of familiarity between vehicles; a higher familiarity implies a higher interaction frequency and more prior information, resulting in more reliable feedback. In this study, the familiarity between vehicle nodes is the ratio of the total interaction count between vehicle nodes within a certain period to the average interaction count of other vehicle nodes, denoted as $F_{i\to j}$:

(1)

where $i$ and $j$ represent data users and data providers,$N_{i\to j}$denotes the total number of information interactions between vehicle $i$ and $j$ within a specific time window, $\overline{N_j}$represents the average interaction count of vehicle $j$with other vehicle nodes, $N$ denotes the total number of vehicles $j$ interacting with, and $M$ represents the set of vehicles that have interacted with the vehicle node.

2.

Timeliness

Newly uploaded data are emphasized for information sharing. This study defines the timeliness of direct opinions from vehicle nodes to vehicle nodes as an $TI{M}_{i\to j}$:

(2)

where $\eta$ and $\epsilon$ are predefined parameters for adjusting the timeliness, $t_i^{}$ represents the time point when the data user $i$ completes the transaction, and $t_j^{}$ represents the time point when the data provider $j$ uploads shared information.

3.

Trajectory Similarity

Trajectory similarity measures the similarity between the driving states of the data user and the data provider. In this study, similarity is calculated based on the velocity and direction of the trajectory data in the continuous trajectory segments covered by the onboard sensors of both vehicles during sharing, denoted as $SI{M}_{i\to j}$:,

(3)

where $S_{sp\mathrm{d}}$ represents the velocity similarity of the trajectory; $S_{dirc}$ represents the direction similarity of the trajectory; and their weights in the trajectory similarity are ${\tau }_1$ and ${\tau }_2$, respectively, with ${\tau }_1+{\tau }_2=1$.

The similarities of velocity and direction are calculated using the cosine similarity formula:

(4)

where $c_k^i$ represents the velocity or direction in the trajectory of vehicle node $i$; $c_k^j$ represents the velocity or direction in the trajectory of vehicle node $j$; and $k$ represents the number of trajectory points in a similar trajectory segment during the information sharing process between the two vehicles.

4.

Direct Opinion Weights

The final direct weight is obtained by taking the weighted average of the three factors in from equation 1 to Equation (3):

(5)

where the direct opinion weight parameters are ${\rho }_1$, ${\rho }_2$, ${\rho }_3$, with ${\rho }_1+{\rho }_2+{\rho }_3=1$.

4.1.2. Event Validity Based on Growth Curve Function

1.

Growth Curve Function

The growth curve function is a class of mathematical functions used to describe the developmental process of things. Generally, the development process is similar to the biological development process, which includes three stages: initiation, development, and maturity, with different development speeds at each stage. In the initial stage, the change is slow; in the development stage, the change accelerates; and in the maturity stage, the change slows again. The curve of the development process drawn according to the development rules of these three stages is usually called a growth curve or logistic growth curve. This curve has been widely used to describe and predict various fields of technical and economic development. There are many mathematical growth curve models, among which the Gompertz and Pearl models are the most widely used. In reference [33], the Gompertz model was employed to calculate and update the reputation values. In contrast, reference [34] utilized the Piel model, incorporating the difference between positive and negative events for reputation value calculation. Consequently, this study refers to these publications and adopts a weighted average of negative event counts in conjunction with the Piel model for reputation calculation.

2.

Event Effectiveness

Event effectiveness indicates that in the reputation value calculation, the weights of positive and abnormal events are different. The weight of the negative events decreased as the number of negative feedbacks increased, whereas that of the positive events increased as the number of negative feedbacks increased. In this study, the weighted sum of negative event numbers is used, and according to the Piel growth curve function, the effectiveness of negative event $\theta$ is obtained, whereas the effectiveness of positive event $1-\theta$ is:

(6)

where $\mu$ is the adjustment factor of the growth curve, which determines the value range of $\theta$. $Er{r}_{x\to j}$is the weighted average of the abnormal event numbers; $X$ represents the set of vehicle nodes that have interacted with vehicle node; ${\delta }_{x\to j}$ represents the direct opinion weight between two vehicle nodes; and $er{r}_{x\to j}$ represents the number of abnormal events in the interaction between the two vehicle nodes.

3.

Direct Opinions Based on Event Effectiveness

Through the effectiveness of negative and positive events, the weighted vehicle node pairs’ positive event number ${\alpha }_{{}_{i\to j}}^{\theta }$and the weighted vehicle node pairs’ negative event number ${\beta }_{{}_{i\to j}}^{\theta }$ were obtained:

(7)

where represents the number of positive events between vehicle nodes, and represents the number of negative events between vehicle nodes.

Subsequently, according to the evidence-mapping operator of subjective logic, a direct opinion is obtained ${\omega }_{i\to j}=(T_{i\to j},D_{i\to j},I_{i\to j})$:

(8)

4.1.3. Direct Opinion Combination Based on Three Weights and Event Validity

Subsequently, based on the TWSL algorithm [28,29] and considering the direct opinion weight, the direct combined opinion ${\omega }_j^{dir}=(T_j^{dir},D_j^{dir},I_j^{dir})$ is obtained:

(9)

where $X$ represents the set of vehicles that interact with vehicle node $j$.

4.2. Indirect Combined Opinions

The blockchain stores direct interaction information between vehicles in the system. It is necessary to obtain indirect opinion paths using an algorithm and calculate the indirect combined opinions using an indirect weight formula.

4.2.1. Indirect Opinion Path Search Algorithm Based on Depth-First Search

Using an indirect opinion path search algorithm based on Depth-First Search (DFS), we can obtain the required indirect opinions for the discount operator using subjective logic. The algorithm process is as follows:

Algorithm 1: Indirect Opinion Path Search Algorithm

1: Initialization

2: Input: Opinion set G of nodes, Complete set of nodes V, Target node Vt.

3: Output: All indirect opinion paths Ws reaching the target node Vt.

4: for all element Vs //Consider nodes in set V, excluding Vt, as source nodes Vs

5: Ws=[]; //Define the path set Ws for Vs.

6: Opinion_Walk(G,Vs,Vt) //Recursively search for vehicles that have interactions

7:  if Vs≠Vt and G[Vs]!=[]

8:  W←Vs; //Add qualifying nodes to the path W

9: for node in G[Vs]

10: if node not in W and len(W)<3

11:  Opinion_Walk(G,node,Vt);

12:  if len(W)==3 and Vs==Vt //If an indirect path is found, add it to the path set Ws

13:  Ws←W; //Add qualifying nodes to the path W

14:  end if

15: end if

16: end for

17: end if

18: end for

19: END

4.2.2. Indirect Combined Opinions Based on Discount Operator and Indirect Weights

Calculate indirect opinions based on all indirect opinion paths obtained in the previous subsection and the discount operator using subjective logic. We then computed the combined indirect opinions based on indirect weights.

4.2.3. Indirect Opinions Based on Discount Operator

After determining the opinion path using the indirect opinion-path search algorithm, the discounted opinion definition based on the indirect path can be calculated using the discount operator. Let the opinion of node A on node B be ${\omega }_{A\to B}=(T_{A\to B},D_{A\to B},I_{A\to B})$ and the opinion of node B on node C be ${\omega }_{B\to C}=(T_{B\to C},D_{B\to C},I_{B\to C})$. The indirect opinions of both nodes C is defined as ${\omega }_C^{A:B}=(T_C^{A:B},D_C^{A:B},I_C^{A:B})$:

(10)

4.2.4. Indirect Weights

The indirect weights ${\delta }_C^{A:\mathrm{m}}$ are obtained according to the weight transfer formula in reference as

(11)

where m represents the intermediate nodes that meet the serial relationship and $N$ represents the vehicle node set meeting the serial relationship obtained by the indirect opinion path search algorithm.

4.2.5. indirect combined opinions

Based on indirect opinions and indirect weights, the weighted average was used to obtain the indirect combined opinion ${\omega }_C^{ind}=(T_C^{ind},D_C^{ind},I_C^{ind})$:

(12)

where $N$ and $M$ represent the vehicle node set that satisfies the serial relationship obtained by the indirect opinion path search algorithm, and ${\delta }_C^{n:m}$ represents the indirect weight obtained from the serial relationship.

4.3. Fusion of Opinions and System Reputation Value

By using the fusion operator of the subjective logic trust model, direct and indirect opinions are combined to obtain the final system opinion. Suppose that the system’s direct combined opinion on node C is ${\omega }_C^{\mathrm{dir}}=(T_C^{\mathrm{dir}},D_C^{\mathrm{dir}},I_C^{\mathrm{dir}})$, and the indirect combined opinion on node C is ${\omega }_C^{ind}=(T_C^{ind},D_C^{ind},I_C^{ind})$. The fusion opinion on node C is derived from both and is denoted as ${\omega }_C^{\mathrm{dir},\mathrm{ind}}=(T_C^{\mathrm{dir},\mathrm{ind}},D_C^{\mathrm{dir},\mathrm{ind}},I_C^{\mathrm{dir},\mathrm{ind}})$:

(13)

In summary, based on the subjective logic algorithm, the final system reputation value for vehicle $E_c$ is

(14)

5. Simulation and Results

6. Conclusions

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