A complex network-based system simulation system credibility prediction method

Abstract

A method for predicting the credibility of a system simulation based on complex networks, belonging to the field of simulation technology, addresses the technical problems of existing simulation credibility assessment methods, which struggle to effectively describe the complex coupling and interaction relationships between subsystems in a system simulation, rely on system-level reference data, and have poor applicability. The technical approach is as follows: S1, the simulation entities of the system simulation are abstracted as network nodes with initial credibility, and the information interaction relationships between entities are abstracted as directed edges. Node weights and edge weights are defined to construct a weighted directed network; S2, based on this network, a credibility probability propagation algorithm composed of a neighbor node propagation function, a credibility preservation function, and an iterative solution algorithm is used to iteratively calculate and converge to obtain the corrected credibility of each node; S3, based on the corrected credibility of each node and its corresponding node weight, a weighted synthesis is performed to obtain the system-level credibility prediction result of the system simulation. This invention has promising application prospects in the field of simulation credibility assessment technology.

Description

Technical Field

[0001] This invention relates to the field of simulation technology, specifically to a method for predicting the credibility of a system simulation based on complex networks. Background Technology

[0002] With continuous breakthroughs in modern simulation technology, advanced modeling methods, multidisciplinary joint simulation, and multiphysics coupled simulation have been widely applied, leading to a rapid increase in the complexity of simulation systems. Systematic simulation systems possess stronger simulation capabilities for large-scale, complex, correlated, and uncertain physical models, and the systematization of simulation systems has become one of the important directions for the development of simulation technology in the new era. Simulation credibility prediction is a crucial technique for analyzing and evaluating simulation credibility. How to efficiently describe the complex and coupled interactions between subsystems in a systematic simulation system, eliminate dependence on system-level simulation system evaluation data, and simultaneously provide a reasonable explanation for the credibility of the systematic simulation system has become a pressing problem to be solved.

[0003] System simulation systems are characterized by networking, complex subsystem interactions, and nonlinear operational logic. Existing simulation evaluation techniques struggle to fully represent the interactions between these systems, and system-level reference data is often difficult to obtain, thus failing to adequately meet such evaluation needs. Current solutions for simulation credibility prediction employ Bayesian hypothesis testing for credibility assessment. This involves introducing a Structural Equation Model (SEM) to represent the relationships between the system, model, system output, and model output. Bayesian inference is then used to infer the system-level output based on subsystem experimental data. Finally, hypothesis testing verifies the consistency between the simulation system and the actual system parameters. However, most existing methods are designed for complex simulation systems, requiring the construction of Bayesian networks using methods such as Monte Carlo sampling, depending on the specific simulation system structure.

[0004] While Bayesian theory-based simulation credibility prediction methods achieve the process of reasoning from lower-level simulation components to higher-level simulation systems, several problems remain: First, existing credibility extrapolation methods have poor applicability, requiring recalculation of relationship networks for different simulation systems. This process involves complex sampling calculations, consuming significant computational resources, time, and cumbersome steps. Second, in the absence of sufficient data, confidence intervals or confidence regions of model parameter errors are typically used as credibility assessment results, which differ somewhat from the actual connotation of simulation credibility. Finally, obtaining the parameters and posterior distribution of the credibility extrapolation model based on Bayesian networks and Monte Carlo sampling still requires a certain amount of system-level output; therefore, this method essentially only reduces the need for system-level data. Furthermore, for system simulation systems, due to the involvement of numerous simulation subsystems and simulation inputs / outputs, constructing SEM relationships is extremely complex, and system-level systems may be limited by various factors, making it difficult to meet the evaluation data requirements. Therefore, credibility extrapolation cannot be directly applied to system simulation systems. Therefore, it is necessary to study a simulation credibility prediction method based on complex networks for system simulation systems, which can effectively describe the structural composition and interaction relationships of system simulation systems, get rid of the dependence on system-level reference data, and improve the interpretability of the credibility of system simulation systems. Summary of the Invention

[0005] To address the technical problems of existing simulation credibility assessment methods being unable to effectively describe the complex coupling and interaction relationships between subsystems in a system simulation system, relying on system-level reference data, and having poor applicability, this invention provides a system simulation system credibility prediction method based on complex networks, comprising: S1, abstracting each simulation entity in the system simulation system as a network node, wherein the attribute value of the node is the initial credibility of the corresponding simulation entity; abstracting the information interaction relationship between the simulation entities as directed edges, the direction of which follows the actual information transmission direction in the simulation experiment; defining node weights to characterize the contribution of the simulation entity to the credibility of the system simulation system, defining the edge weights of the directed edges to characterize the importance of information transmission between nodes, and finally obtaining a weighted directed network;

[0006] S2. Based on the weighted directed network, the corrected credibility of each node under the influence of interaction is calculated by the credibility probability propagation algorithm; the initial credibility of the nodes in the weighted directed network is combined with the network topology, edge weights and node weights by the neighbor node propagation function, credibility preservation function and iterative solution algorithm, and iterative calculation is performed until convergence to obtain the corrected credibility of each node.

[0007] S3. Based on the corrected credibility of each node and its corresponding node weight, a weighted comprehensive calculation is performed to obtain the system-level credibility prediction result of the system simulation system.

[0008] Furthermore, in S1, the edge weights satisfy the global network normalization constraint, that is:

[0009]

[0010] in, Let N be the edge weight from node i to node j, and N be the total number of nodes.

[0011] Furthermore, in S2, the calculation of the correction credibility of each node under the influence of interaction specifically involves:

[0012]

[0013] in, Let i be the corrected confidence level. A credibility preservation function for node i. Let be the initial confidence level of node i. Propagation function for neighboring nodes, Let i be a vector consisting of the truth values ​​of the neighboring nodes of node i.

[0014] Furthermore, the neighbor node propagation function is defined as follows:

[0015]

[0016] Where N(i) is the set of incoming neighbor nodes of node i. For an effective propagation function, For the influence function, This is a compensation item for failure to spread the message.

[0017] Furthermore, the influence function is defined as follows:

[0018]

[0019] Where x is the corrected confidence value of the neighboring node. To affect the quantization function, To influence the strengthening function, As a credibility-sensitive factor, The credibility impact coefficient. This is the credibility threshold.

[0020] Furthermore, the credibility preservation function is specifically as follows:

[0021]

[0022] in, The maximum retention factor, The minimum retention coefficient has a parameter range of [value missing]. ; The credibility propagation threshold, As a credibility dissemination index, To propagate weight, For input strength, The average credibility of neighboring nodes. To determine the standardized values ​​for the common interval of the intensity input, This represents the standardized value of the common interval of the mean credibility of neighboring nodes.

[0023] The beneficial effects of this invention are:

[0024] This invention abstracts the system simulation system into a weighted directed network and combines it with a confidence probability propagation algorithm to achieve system-level confidence prediction. This effectively characterizes the complex coupling and interaction relationships among the simulated entities within the system simulation, eliminating reliance on system-level reference data. It avoids complex sampling calculations, significantly reducing computational resource requirements and simplifying operation steps. Simultaneously, by constructing neighbor node propagation functions and confidence preservation functions to accurately quantify the confidence influence between nodes, and combining this with Picard iterative solutions, it ensures the accuracy and convergence of the corrected confidence calculation. Finally, the system-level confidence prediction result obtained through weighted synthesis has an acceptable error compared to the actual evaluation result, improving the interpretability, applicability, and accuracy of the system simulation system's confidence prediction. Attached Figure Description

[0025] Figure 1 This is a flowchart of the present invention.

[0026] Figure 2 This is a general framework diagram of the present invention;

[0027] Figure 3 A concept graph of a weighted directed network for simulation credibility prediction;

[0028] Figure 4 A network diagram for predicting the credibility of a simulation system for an intelligent warehousing and logistics system. Detailed Implementation

[0029] The technical solution of the present invention will be further described below with reference to embodiments, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention. In the following embodiments, process equipment or devices not specifically specified are all conventional equipment or devices in the art. Unless specifically specified, the technical means used in the embodiments of the present invention are all conventional means well known to those skilled in the art.

[0030] Example 1, combined with Figure 1This embodiment describes a method for predicting the credibility of a system simulation based on complex networks, comprising: S1, abstracting each simulation entity in the system simulation as a network node, wherein the attribute value of the node is the initial credibility of the corresponding simulation entity; abstracting the information interaction relationship between the simulation entities as directed edges, the direction of which follows the actual information transmission direction in the simulation experiment; defining node weights to characterize the contribution of the simulation entity to the credibility of the system simulation, defining the edge weights of the directed edges to characterize the importance of information transmission between nodes, and finally obtaining a weighted directed network;

[0031] S2. Based on the weighted directed network, the corrected credibility of each node under the influence of interaction is calculated by the credibility probability propagation algorithm; the initial credibility of the nodes in the weighted directed network is combined with the network topology, edge weights and node weights by the neighbor node propagation function, credibility preservation function and iterative solution algorithm, and iterative calculation is performed until convergence to obtain the corrected credibility of each node.

[0032] S3. Based on the corrected credibility of each node and its corresponding node weight, a weighted comprehensive calculation is performed to obtain the system-level credibility prediction result of the system simulation system.

[0033] Specifically, in combination Figure 2 As can be seen, this invention is divided into three core stages: S1 Constructing a complex network, which involves abstracting each simulation entity into a network node based on the entity interaction relationship of the system simulation system, abstracting the information interaction relationship between entities into directed edges, and determining the initial credibility of nodes, edge weights, and node weights, thereby constructing a weighted directed network; S2 Credibility propagation, which involves calculating the credibility retention coefficient, effective propagation function, and influence function, and updating the node credibility round by round in conjunction with synchronous Picard iteration until the iteration termination condition is met, thereby obtaining the corrected credibility of each node; S3 Credibility prediction, which involves weighting and combining the corrected credibility of each node with the corresponding node weight, and finally outputting the system-level credibility prediction result of the system simulation system.

[0034] Furthermore, in S1, the edge weights satisfy the global network normalization constraint, that is:

[0035]

[0036] in, Let N be the edge weight from node i to node j, and N be the total number of nodes.

[0037] Specifically, the edge weights in the network are the weight values ​​of directed edges in the global network, representing the importance of information transmitted between nodes. They need to comprehensively consider factors such as data volume, data transmission frequency, and the impact of the transmitted information content on the simulation system's operating results, and cannot be measured solely by a single network or simulation property. Since determining the edge weights is complex, and this study focuses on the problem of simulation credibility prediction, it is assumed that the edge weights are known (in practice, they can be obtained through expert scoring, etc.), and that the edge weights must meet the global network normalization requirements. Based on the above definitions and constraints, and combined with the specific structure of the system simulation and the simulation experiment process, a preliminary weighted directed network for system simulation credibility prediction can be constructed, as shown in the conceptual diagram below. Figure 3 As shown.

[0038] Furthermore, in S2, the calculation of the correction credibility of each node under the influence of interaction specifically involves:

[0039]

[0040] in, Let i be the corrected confidence level. A credibility preservation function for node i. Let be the initial confidence level of node i. Propagation function for neighboring nodes, Let i be a vector consisting of the truth values ​​of the neighboring nodes of node i.

[0041] Specifically, the credibility prediction method for system simulation mainly consists of a credibility propagation algorithm and a credibility synthesis algorithm. Under the operating conditions of the system simulation system, the simulation credibility of each simulation entity may differ from its simulation credibility under independent operating conditions due to factors such as information interaction. From the perspective of the global network, in a fixed simulation experiment, these information interaction relationships are statistically fixed. Therefore, it can be considered that, under specific interaction relationships, each simulation entity in the system simulation system has a theoretical true value of simulation credibility, which is:

[0042]

[0043] Definition, where For nodes after credibility propagation The credibility of the simulation It is a nonlinear function. For nodes The set of incoming neighbor nodes, For nodes Sum of incoming edge weights, Neighbor node influence relationship function. From the perspective of each individual simulated entity, the truth value can be regarded as the result of the initial credibility under the influence of interaction relationships. Therefore, the truth value of a node can be described by the node's initial credibility, network structure, and the truth values ​​of neighbor nodes.

[0044] Furthermore, the neighbor node propagation function is defined as follows:

[0045]

[0046] Where N(i) is the set of incoming neighbor nodes of node i. For an effective propagation function, For the influence function, This is a compensation item for failure to spread the message.

[0047] Specifically, the effective propagation function represents the fact that not every information transmission during the credibility propagation process will necessarily affect the credibility of the downstream simulation entity. Some insensitive inputs may not affect the simulation entity's output, while more important input information has a higher probability of affecting the credibility of the downstream simulation entity's output. Therefore, the effective propagation probability is defined as:

[0048]

[0049] in, It is an empirical distribution function of locally normalized edge weights, using the standard midrank method. Effective propagation probability. The minimum probability of successful dissemination is defined as 0.5, and the introduction of an empirical distribution function does not change the importance of information transmission.

[0050] Furthermore, the influence function is defined as follows:

[0051]

[0052] Where x is the corrected confidence value of the neighboring node. To affect the quantization function, To influence the strengthening function, As a credibility-sensitive factor, The credibility impact coefficient. This is the credibility threshold.

[0053] Specifically, the influence function quantifies the impact of neighboring node credibility values ​​on the current node. The true credibility value of a node consists of the node's own credibility retention value and the contributions from neighboring nodes. When the credibility of neighboring nodes is high, the negative impact on the node is relatively small. A large value indicates that when the trustworthiness of neighboring nodes is low, it has a significant negative impact on the node. The value is relatively small. The credibility sensitivity factor determines the sensitivity of the influence function to the credibility values ​​of neighboring nodes, reflecting the degree to which the "credibility" of the simulated entity affects the neighboring nodes. The smaller the value, the closer the function is to a linear relationship; the credibility influence coefficient Based on the credibility threshold Adjust the difference in influence between high-confidence and low-confidence neighbor nodes; confidence threshold. ∈(0,1) is the criterion for distinguishing whether a node is trustworthy in the credibility propagation process. The larger the number, the stricter the trust standard, and more nodes will be considered "untrustworthy".

[0054] truth value of neighbor node The range of values ​​for the function is ,when At that time, it represents the neighboring node. Absolutely unbelievable, at this time ;when At that time, it represents the neighboring node. Completely trustworthy, at this point Therefore, it is necessary to... The values ​​are subject to strict restrictions. Satisfies: range constraint, Monotonicity constraint The derivative is non-negative. The following conditions must be met:

[0055]

[0056]

[0057] Furthermore, the credibility preservation function is specifically as follows:

[0058]

[0059] in, The maximum retention factor, The minimum retention coefficient has a parameter range of [value missing]. ; The credibility propagation threshold, As a credibility dissemination index, To propagate weight, For input strength, The average credibility of neighboring nodes. To determine the standardized values ​​for the common interval of the intensity input, This represents the standardized value of the common interval of the mean credibility of neighboring nodes.

[0060] Specifically, the credibility retention function uses a logistic function mapping, dynamically adjusted according to node-level conditions. The input strength is the sum of the global network weights of the input edges. In a weighted directed network, node strength is a standard measure of the total amount of external influence on a node; a higher input strength indicates greater susceptibility to external information shocks, meaning it is more easily influenced by neighboring nodes, resulting in a lower credibility retention value. The average credibility of neighboring nodes is the weighted sum of their initial credibility based on the local weights of their input edges. A higher average initial credibility indicates a more trustworthy neighborhood, less negative impact on the node itself, and a higher credibility retention value. The credibility propagation index, obtained by combining these two factors, effectively measures the degree to which a node should maintain its credibility. Because the physical meanings and interval dimensions of these two factors differ, they need to be weighted and combined under the same dimensions.

[0061] , This is the value obtained after standardizing the common interval of the original results. In the following formula... Among them, it refers to , Any one of them, Let be the truncation function, with upper and lower limits respectively. and , for The 95th percentile, for The 5th percentile.

[0062]

[0063] Regarding the minimum retention factor As defined by the credibility propagation principle, for a fixed interaction network and initial credibility, each network node possesses a unique truth value. The truth function... Writing Mapping Format:

[0064]

[0065] Denoted in vector form:

[0066]

[0067] in A vector consisting of the truth values ​​of the nodes. , This is a vector representing the initial credibility of each node. Analysis of the properties of the influence function shows that there exists... Therefore:

[0068]

[0069] Therefore, for any , All fall within closed, bounded, and in Complete interval The initial confidence level of a node is the simulation confidence level of the corresponding simulated entity running independently. Its input is fully confident by default; therefore, its simulation confidence level is strictly non-increasing within the system simulation environment, thus requiring a minimum retention factor. satisfy:

[0070]

[0071] Among them, safety margin , For function about Global Lipschitz constant:

[0072]

[0073] set up , , The remaining parameters are defined by the following formula:

[0074]

[0075] Regarding the maximum retention factor Define a row random matrix as ,in , If node If there is no border to enter, then let The corresponding node for each row. , No. OK Representative node The edge weight at the node The percentage of all neighboring nodes. The sum of the values ​​in each row of vectors must be 1, therefore eigenvalues ​​always exist. And because For any feature pair have: Therefore, there exists a possibility of All eigenvalues ​​can be sorted by modulus to obtain The second largest eigenvalue modulus (SLEM) is defined as the largest eigenvalue modulus other than 1. (Spectral gap) (Spectral gap) is the difference between SLEM and 1.

[0076]

[0077] Based on the consensus conclusion of the distributed consensus algorithm gossip The larger the value, the faster the non-uniform components decay; The smaller the value, the more likely a bottleneck exists in the transmission process, and the differences are not easily averaged out. In credibility dissemination, The large-scale proof indicates that the interactive network has strong connectivity and should have a greater impact on the neighborhood. Small loops and other local structures may exist in hourly networks, and neighborhood influences may accumulate repeatedly in localized areas. In such cases, the confidence retention value should be increased to prevent the true value from being underestimated. Based on this, the following is given: formula:

[0078]

[0079] pass spectral gap The confidence retention interval was converted, taking into account the network's hybrid characteristics. This is a dimensionless constant, with a default value of 0.7, providing a safety margin. Avoid numerical degradation.

[0080] Regarding iterative solutions, due to the mapping function Since this is a nonlinear coupling problem, it is difficult to solve directly. Therefore, it can be solved using the Picard iteration. The Picard iteration must satisfy the requirements of feasible region, existence, and controllable convergence. The update equation is as follows:

[0081]

[0082] The synchronous iteration method is used, with the default iteration starting from k=0, and the iteration termination condition being the iteration number. Reaching the preset maximum number of iterations k max Or all nodes in the network satisfy:

[0083]

[0084] Regarding the credibility synthesis, based on the total number of nodes N in the network (the total number of simulated entities in the system simulation system), the node weights... (The importance of each simulated entity in the system simulation under a specific application scenario / simulation experiment), the simulation credibility of the node after credibility propagation. (The actual simulation credibility value of each simulated entity under a specific application scenario / simulation experiment), the credibility prediction result of the system simulation is obtained through weighted synthesis:

[0085]

[0086] in, This represents the credibility prediction result.

[0087] The effectiveness of this invention is illustrated by taking an intelligent warehousing and logistics autonomous inbound simulation scenario as an example.

[0088] Example 2 uses a simulation scenario of autonomous receiving of goods in an intelligent warehousing and logistics system as an application example to verify the effectiveness and accuracy of the method of the present invention. Four batches of goods are moved from a designated receiving location towards the intelligent warehousing and logistics system. The intelligent warehousing and logistics system contains four robot workstations, each equipped with two handling robots. The composition of the simulation experiment and the simulation reliability under independent operation conditions of the simulation subsystems are shown in Table 1. The reliability of each simulation subsystem has been obtained through conventional simulation reliability evaluation methods. The evaluation data of the simulation subsystems and the intelligent warehousing and logistics system simulation system are obtained from simulation experiments and actual tests under the same input conditions.

[0089] Table 1. Composition and Reliability of Simulation Subsystems in the Intelligent Warehousing and Logistics System Simulation Experiment

[0090]

[0091] Assume four batches of goods travel along preset inbound paths to an intelligent warehousing and logistics system, which autonomously receives and handles them. Stable simulated entity interaction relationships are obtained through repeated simulations: the wide-area perception system detects goods entering the warehousing receiving range and reports to the central dispatch system; the central dispatch system issues tracking instructions to the target positioning system; the target positioning system detects goods entering the precise positioning range and reports to the central dispatch system; the central dispatch system transmits instructions to the task allocation and job sequencing system to prioritize goods reception; the task allocation and job sequencing system sends activation instructions to the robot workstation and standby instructions to the proximity guidance system according to the sequencing results; the robot workstation releases the handling robot, which executes the receiving and handling tasks according to the target specified by the task allocation and job sequencing system; the proximity guidance system assists the handling robot in achieving precise approach, docking, and handling; the handling robot transfers the goods to the designated location, and the target positioning system sends back information that the goods have left the receiving area.

[0092] To obtain the simulation credibility of the intelligent warehousing and logistics system simulation system, an index system was constructed as shown in Table 2. The weights of the underlying indicators were obtained through direct weighting, and the evaluation data were obtained through repeated simulations. Among them, the evaluation data for the three indicators of cargo discovery time credibility, task preparation time credibility, and reception success probability credibility are static data. The first two indicators used the relative average absolute error method, and the last one used the hypothesis testing method. The cargo-robot relative position credibility index used the TIC method for all indicators. Based on the weights of the underlying indicators and the evaluation results, the credibility evaluation result of the handling robot simulation system was obtained by weighted synthesis, which was 0.778.

[0093] Table 2 Reliability of the Intelligent Warehousing and Logistics System Simulation System

[0094] To apply the method presented in this paper for credibility prediction, a complex network is first constructed based on the composition of the intelligent warehousing and logistics system simulation system, the composition of the simulation subsystems, the interaction relationships, and the credibility of the edge weights (assuming they are known). Figure 4 As shown.

[0095] Applying the credibility prediction method of this invention, based on Figure 2 The process shown is calculated according to the parameters in Table 3, and the algorithm converges in the 9th round. The weights of each node and the credibility propagation results are shown in Table 4. The credibility prediction result obtained by weighted summation is 0.770.

[0096] Table 3 Algorithm Parameter Selection

[0097]

[0098] Table 4. Network Node Weights and Propagation Results of the Intelligent Warehousing and Logistics System Simulation

[0099]

[0100] Comparing the prediction results of this method with the conventional simulation credibility evaluation results based on output consistency, the absolute percentage error of the two methods is 1.03%, which is within an acceptable range, proving the correctness of the algorithm.

Claims

1. A method for predicting credibility of a complex network-based system simulation system, characterized in that, include: S1. Abstract each simulation entity in the system simulation system into a network node, and the attribute value of the node is the initial confidence level of the corresponding simulation entity. The information interaction relationship between the simulated entities is abstracted as a directed edge, the direction of which follows the actual information transmission direction in the simulation experiment; the node weight is defined to characterize the contribution of the simulated entity to the credibility of the system simulation, and the edge weight of the directed edge is defined to characterize the importance of the information transmission between nodes, and finally a weighted directed network is obtained. S2. Based on the weighted directed network, the corrected credibility of each node under the influence of interaction is calculated by the credibility probability propagation algorithm; the initial credibility of the nodes in the weighted directed network is combined with the network topology, edge weights and node weights by the neighbor node propagation function, credibility preservation function and iterative solution algorithm, and iterative calculation is performed until convergence to obtain the corrected credibility of each node. S3. Based on the corrected credibility of each node and its corresponding node weight, a weighted comprehensive calculation is performed to obtain the system-level credibility prediction result of the system simulation system. 2.The method of claim 1, wherein, In S1, the edge weights satisfy the global network normalization constraint, that is: wherein, is the edge weight from node i to node j, and N is the total number of nodes.

3. The method of claim 2, wherein the method further comprises: In S2, the calculation of the correction credibility of each node under the influence of interaction is specifically as follows: wherein, is the modified trustworthiness of node i, is the trustworthiness reservation function of node i, is the initial trustworthiness of node i, is the neighbor node propagation function, is the vector of true values of the neighbor nodes of node i.

4. The reliability prediction method for a system simulation based on complex networks according to claim 3, characterized in that, The neighbor node propagation function is defined as follows: Where N(i) is the set of incoming neighbor nodes of node i. For an effective propagation function, For the influence function, This is a compensation item for failure to spread the message.

5. The reliability prediction method for a system simulation based on complex networks according to claim 4, characterized in that, The influence function is defined as follows: Where x is the corrected confidence value of the neighboring node. To affect the quantization function, To influence the strengthening function, As a credibility-sensitive factor, The credibility impact coefficient. This is the credibility threshold.

6. The credibility prediction method for a system simulation based on complex networks according to claim 3, characterized in that, The credibility preservation function is specifically: in, The maximum retention factor, The minimum retention coefficient has a parameter range of [value missing]. ; The credibility propagation threshold, As a credibility dissemination index, To propagate weight, For input strength, The average credibility of neighboring nodes. To determine the standardized values ​​for the common interval of the intensity input, This represents the standardized value of the common interval of the mean credibility of neighboring nodes.

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