Game confrontation situation assessment method and system based on probabilistic consensus

Abstract

The present application relates to the technical field of intelligent confrontation command and control, aiming at the problems of multiple expert conflict fusion and nonlinear evaluation of confrontation unit capability, a game confrontation situation evaluation method and system based on probability consensus are proposed, including: constructing a joint probability density function of multiple confrontation expert consensus, defining a probability target set with confidence levels based on the joint probability density function, obtaining battlefield capability data of the confrontation unit to be evaluated under the current situation and judging the data type, obtaining the corresponding effectiveness evaluation value according to the data type, the data type includes random distribution data and deterministic point data, sorting multiple confrontation units according to the effectiveness evaluation value, and outputting the confrontation capability evaluation result. The present application can significantly reduce the sensitivity of the evaluation result to the subjective weight setting and improve the robustness of nonlinear evaluation in dealing with uncertainty.

Description

Technical Field

[0001] This invention relates to the field of intelligent combat command and control technology, and in particular to a game-theoretic combat situation assessment method and system based on probabilistic consensus. Background Technology

[0002] In modern strategic confrontation (multi-domain coordination across sea, land, air, space, and cyberspace), commanders need to conduct real-time or near-real-time assessments of the comprehensive combat capabilities of both friendly and enemy units to support critical decisions such as force deployment, target allocation, and threat prioritization. However, in actual battlefield environments, the following three major challenges remain:

[0003] (1) Knowledge conflict among multi-source intelligence experts. Staff officers or experts from different fields such as reconnaissance, intelligence, firepower, and electronic warfare often have disagreements or even contradictions regarding the pass / threat thresholds for the same adversarial unit (such as a certain type of enemy fighter jet) in terms of indicators such as "detection range", "maneuver overload", and "electronic warfare capability". Traditional methods (such as weighted average and Delphi method) are difficult to dynamically quantify this consensus and conflict, resulting in highly subjective and unreliable capability assessment results.

[0004] (2) Nonlinear coupling of countermeasure capability indicators. There are complex synergistic or antagonistic effects among the various capability indicators of the countermeasure unit. For example, there is a nonlinear trade-off between the "radar detection range" and "stealth performance" of a fighter jet; the "air defense and anti-missile capability" and "anti-submarine capability" of a ship are mutually constrained by platform resources. Simple linear weighted summation cannot accurately characterize this coupling relationship, which can easily lead to evaluation distortion and thus mislead command decisions.

[0005] (3) The hybrid nature of situational input data types. The sources of adversarial unit capability data obtained on the modern battlefield are diverse: there are probability distributions based on Monte Carlo simulation (such as the hit probability distribution of a certain type of missile against a moving target), and there are also fixed points based on reconnaissance intelligence (such as the precise start-up time of enemy radar, the current speed of a certain ship). Existing methods can usually only handle one type, and there is a lack of a unified evaluation framework.

[0006] Given the conflicting opinions of multi-source intelligence experts, the nonlinear coupling of adversarial capability indicators, and the presence of mixed-type situational input data, a key challenge is how to dynamically, robustly, and interpretably assess and rank the comprehensive adversarial capabilities of each adversarial unit on both sides, providing a quantitative basis for command and control in game-theoretic confrontation. To address this, a systematic fusion and adaptive decision-making mechanism is constructed based on joint probabilistic objectives, exploring feasible paths for optimizing decisions involving the coupling of multiple objective parameters. Summary of the Invention

[0007] To address the issues of multiple expert conflict fusion and nonlinear assessment of adversarial unit capabilities in the existing technologies, this invention proposes a game adversarial situation assessment method and system based on probabilistic consensus.

[0008] The present invention achieves the above objectives through the following technical solutions:

[0009] The first aspect of the technical solution disclosed in this invention is: a game adversarial situation assessment method based on probabilistic consensus, comprising the following steps:

[0010] Construct a joint probability density function for multiple adversarial expert consensuses;

[0011] Based on the joint probability density function, a probabilistic target set with confidence levels is defined;

[0012] Acquire battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Obtain the corresponding effectiveness evaluation value based on the data type. The data types include randomly distributed data and fixed point data.

[0013] The multiple adversarial units are sorted according to their effectiveness evaluation values, and the adversarial capability evaluation results are output.

[0014] As a further preferred option, a joint probability density function for multiple adversarial expert consensuses is constructed, including:

[0015] Receive range assessments from multiple adversarial experts on various adversarial capability indicators of the adversarial unit;

[0016] Each interval assessment is transformed into an individual probability density function on a parameter space, which is composed of multiple adversarial capability indicators;

[0017] A joint probability density function is generated by fusing multiple individual probability density functions.

[0018] A further preferred approach is to define the probabilistic target set with confidence levels, including the following steps:

[0019] Given a confidence level parameter λ∈[0,1], construct the λ-level probability target set, which is expressed as:

[0020] ;

[0021] In the formula: R(λ) represents the λ-level probability target set, p is the adversarial capability index, P is the parameter space, and f joint (p) is the joint probability density function;

[0022] Based on the differences in the generation logic of adversarial expert consensus, the λ-level probability target set is divided into a high-confidence region and an extended-confidence region, and their expressions are as follows:

[0023] ;

[0024] ;

[0025] In the formula: R (λ) represents the high-confidence region. To expand the confidence region, let j be the j-th expert, and j = 1, 2, ..., m, f j (p) is the probability density function.

[0026] As a further preferred option, the corresponding performance evaluation value is obtained based on the data type, including:

[0027] If the data type is randomly distributed data, the probability overlap of the randomly distributed data falling into the probability target set is calculated by the effectiveness measurement model based on overlap, and the first effectiveness evaluation value is obtained.

[0028] If the data type is definite point data, the normalized distance between the definite point data and the boundary of the probabilistic target set is calculated using a distance-based effectiveness measurement model to obtain the second effectiveness evaluation value.

[0029] Based on the above scheme, the performance measurement model based on overlap further integrates the high-confidence region and the extended-confidence region, and its expression is as follows:

[0030] ;

[0031] In the formula: E R is the first performance evaluation value, fsim(p) is the probability distribution function of the simulation adversarial capability index, k∈[0,1] is the balance coefficient, and II(.) is the indicator function.

[0032] As a further preferred option, the probability overlap of randomly distributed data falling into the probability target set is calculated using an overlap-based performance measurement model to obtain a first performance evaluation value, including:

[0033] By introducing the Monte Carlo integral approximation to calculate the probability overlap, the expression for the effectiveness measurement model based on overlap is:

[0034] ;

[0035] In the formula: p i Let i be the i-th adversarial capability index, and i = 1, 2, ..., N;

[0036] Based on the binary search algorithm, the efficiency equilibrium point is iteratively solved within the confidence level interval;

[0037] The performance equilibrium point is used as the output of the first performance evaluation value.

[0038] A further preferred approach is to express the distance-based performance measurement model as follows:

[0039] ;

[0040] In the formula: D R (P) represents the second performance evaluation value, and dis(P, λ) represents the weighted distance under the confidence level parameter λ. For the confidence level range that policymakers are concerned with, , For adjustment coefficients, For intermediate confidence level The corresponding high confidence boundary, Indicates the middle confidence level Corresponding high confidence boundary All points With evaluation points The maximum relative Euclidean distance between them. The relative Euclidean distance. As evaluation points To the high confidence boundary The closest relative distance, For intermediate confidence level The corresponding high confidence boundary.

[0041] A further preferred approach is to calculate the normalized distance between the determined point data and the boundary of the probabilistic target set using a distance-based performance measurement model, thereby obtaining a second performance evaluation value, including:

[0042] Mahalanobis distance is used to determine the proximity of a point to the boundary of the probabilistic target set;

[0043] The emphasis on high-confidence regions and extended-confidence regions is adjusted by the balance coefficient;

[0044] A second performance evaluation value is output using a distance-based performance measurement model. The smaller the second performance evaluation value, the higher the threat level of the adversary unit.

[0045] The second aspect of the technical solution disclosed in this invention is: a game-theoretic adversarial situation assessment system based on probabilistic consensus, the system being used to implement the steps of the above-described method, the system comprising:

[0046] The knowledge fusion module is used to receive interval assessments of various adversarial capability indicators of adversarial units from multiple adversarial experts, and to transform each interval assessment into an individual probability density function on the parameter space. The individual probability density functions are then fused to construct a joint probability density function of consensus among multiple adversarial experts.

[0047] The probability target set construction module is used to define a probability target set with confidence levels based on the joint probability density function;

[0048] The classification module is used to acquire battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Based on the data type, it evaluates the relationship between the data type and the probabilistic target set and calculates the corresponding effectiveness evaluation value. The data types include random distribution data and fixed point data.

[0049] The evaluation module obtains the corresponding performance evaluation value based on the data type. If the data type is randomly distributed data, the probability overlap of the randomly distributed data falling into the probability target set is calculated through the performance measurement model based on overlap, and the first performance evaluation value is obtained. If the data type is fixed point data, the normalized distance between the fixed point data and the boundary of the probability target set is calculated through the performance measurement model based on distance, and the second performance evaluation value is obtained.

[0050] The output module is used to sort multiple adversarial units according to their effectiveness evaluation values ​​and output the adversarial capability evaluation results.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] This invention systematically constructs a closed-loop system of probabilistic fusion, nonlinear evaluation, and adaptive decision-making. First, based on a dynamic confidence fusion mechanism using the overlap of probability distributions, the interval evaluations of multiple experts are transformed into probability distributions in the parameter space. By calculating the overlapping areas between probability distributions, the consensus and conflict areas among experts are quantified. The weight of each expert's opinion in the fusion is dynamically adjusted according to the overlap, realizing the fusion of expert knowledge from qualitative and discrete judgments to quantitative and continuous probability confidence. Second, by constructing a dual-coupled nonlinear integration framework with the SM model, a performance measurement model based on overlap (VM ​​model) and a performance measurement model based on distance (SM model) are designed for different types of data to replace the traditional linear weighting method. This jointly solves the problem of nonlinear interaction relationships in complex systems and achieves a performance evaluation that is more in line with the overall system. Finally, by introducing a balance coefficient to adjust the decision-maker's preference for "relaxed consensus" and "strict consensus," and using the confidence level parameter λ to dynamically adjust the confidence level of the probability target set boundary, the two work together to enable the model to respond to different risk tolerances and changes in task objectives without relying on external data, significantly enhancing the flexibility and robustness of the decision-making process. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0054] Figure 1This is a flowchart of a game adversarial situation assessment method based on probabilistic consensus according to the present invention;

[0055] Figure 2 This is the overall framework structure of a game adversarial situation assessment method based on probabilistic consensus according to the present invention;

[0056] Figure 3 This is a schematic diagram illustrating how five individual experts determine a probabilistic target set in a three-dimensional parameter space according to the present invention.

[0057] Figure 4 This is an intuitive geometric interpretation diagram of the VM model of the present invention;

[0058] Figure 5 This is an intuitive geometric interpretation diagram of the SM model of the present invention;

[0059] Figure 6 This is a schematic diagram illustrating the algorithmic solution process of the VM model of the present invention;

[0060] Figure 7 This is the comprehensive evaluation value of the N1-N6 network scheme in Case 1 of the simulation examples of this invention;

[0061] Figure 8 The results are Monte Carlo simulations of the N1-N6 network scheme in Case 1 of this invention.

[0062] Figure 9 This is the target set and evaluation measure values ​​for each scheme in Case 2 of the simulation examples of this invention when λ=0.7;

[0063] Figure 10 This refers to the target set and evaluation measures for each scheme in Case 2 of the simulation examples of this invention when λ=0.8;

[0064] Figure 11 This is the target set and evaluation measure values ​​for each scheme in Case 2 of the simulation examples of this invention when λ=0.6;

[0065] Figure 12 This shows the changes and ranking of the three indicators Cost, Disqualification, and Delivery reliability in Case 2 of the simulation case of this invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0067] In modern game-based confrontation (multi-domain collaboration across sea, land, air, space, and cyberspace), commanders need to conduct real-time or near-real-time assessments of the comprehensive combat capabilities of various combat units (such as fighter jets, ships, radar stations, electronic jammers, and ground armored forces) on both sides (red) and the enemy (blue) to support key decisions such as troop deployment, target allocation, and threat prioritization. However, in actual battlefield environments, there are conflicting opinions from multiple intelligence experts, nonlinear coupling of combat capability indicators, and mixed types of situational input data, posing greater challenges to game-based confrontation command. Therefore, this invention studies and proposes a game-based confrontation situational assessment method and system based on probabilistic consensus.

[0068] Example 1:

[0069] Reference Figures 1-6 This invention provides a method for assessing the adversarial situation in a game based on probabilistic consensus, comprising the following steps:

[0070] S1: Construct a joint probability density function for multiple adversarial expert consensuses;

[0071] S2: Based on the joint probability density function, define a probabilistic target set with confidence levels;

[0072] S3: Obtain battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Evaluate its relationship with the probabilistic target set based on the data type and calculate the corresponding effectiveness evaluation value. The data type includes randomly distributed data and fixed point data.

[0073] S4: Sort multiple adversarial units according to their effectiveness evaluation values ​​and output the adversarial capability evaluation results.

[0074] Specifically, in adversarial scenarios, such as the destructive effectiveness of an anti-ship missile, the destructive power is determined by multiple parameters including velocity, accuracy, and explosive yield. The reasonable range of these parameters constitutes a high-dimensional feasible region. Different experts may have differing or even conflicting definitions of this feasible region. Therefore, traditional static weighting methods are insufficient to quantify the strength of expert consensus or characterize the nonlinear coupling relationships between parameters. To address this, this embodiment addresses the consensus of multiple adversarial experts by providing a "1"-dimensional system parameter space p. It invites m experts to evaluate the reasonable range of parameters, with each expert providing a multi-dimensional hyper-rectangle. By fusing these conflicting expert opinions, a joint probability density function f is constructed. joint (p) represents the set of probabilistic targets in the following text.

[0075] In step S1, the specific steps for constructing the joint probability density function of multiple adversarial expert consensuses are as follows:

[0076] 1) Receive interval assessments of various adversarial capability indicators of the adversarial unit from multiple adversarial experts; assuming the adversarial system has n parameters, invite m domain experts to independently evaluate the parameter space P, and the j-th expert evaluates parameter p. i The given reasonable range of values ​​is denoted as:

[0077] (1)

[0078] The integrated interval evaluations of all n parameters by the j-th expert are represented as a multidimensional hyperrectangle in the parameter space P:

[0079] (2)

[0080] This multidimensional hyperrectangle represents the "qualified" parameter region recognized by the j-th expert.

[0081] 2) To perform quantitative fusion, each interval evaluation is transformed into an individual probability density function in the parameter space. Suppose the adversarial system contains multiple control parameters, and the i-th control parameter p i The range of values ​​is The parameter space P of the resulting adversarial system is expressed as:

[0082] (3)

[0083] The performance of an adversarial system is characterized by an effective performance metric function f: P → R, which maps any combination of parameters to a real-valued performance index.

[0084] The parameter space P consists of multiple adversarial capability indices p i In this embodiment, there are a total of 5 adversarial capability indicators, including: =Detection capability (radar / infrared detection range) =Maneuverability (maximum overload or turning angular velocity) =Firepower capability (damage probability or range). =Protection capability (armor thickness or stealth RCS) =Information processing capability (data link bandwidth or decision latency);

[0085] Meanwhile, given the minimum acceptable performance threshold of the adversarial system Establish a classical target set D, i.e., D = {p ∈ P | f(p) ≥ 1} The target set D is the set of all parameter points in the parameter space P that enable the performance of the adversarial system to meet the target.

[0086] Based on the multidimensional hyperrectangle H of the j-th expert j The corresponding individual probability density function is f j(p) satisfies the following expression:

[0087] (4)

[0088] To construct a probability density function more accurately from expert interval evaluation Here, kernel density estimation (KDE) is introduced to evaluate the hyperrectangle H of the j-th expert. j N is obtained through uniform sampling j sample points Then its probability density function for:

[0089] (5)

[0090] In the formula: K (.) is the kernel function (such as Gaussian kernel), and h is the bandwidth parameter.

[0091] 3) Combine multiple individual probability density functions to generate a joint probability density function.

[0092] By fusing the individual probability distributions of all experts using a linear fusion method, a joint probability density function representing the group consensus is obtained, the expression of which is as follows:

[0093] (6)

[0094] The value of the joint probability density function at any point p in the parameter space P reflects the overall probability density level at which the adversarial expert group reaches a consensus. Thus, the discretized interval evaluations of multiple adversarial experts are integrated into a continuous and differentiable probability distribution model.

[0095] In step S2, the joint probability density f is obtained through the above process. joint (p) After that, it needs to be further transformed into a "target set" that can support dynamic decision-making. To this end, this embodiment introduces probability confidence theory to represent the target set as a soft boundary with confidence levels, as follows:

[0096] 1) Given the confidence level parameter λ∈[0,1], construct the λ-level probability target set, whose expression is:

[0097] (7)

[0098] In the formula: R(λ) represents the λ-level probability target set, p is the adversarial capability index, P is the parameter space, and f joint (p) is the joint probability density function;

[0099] The λ-level probability target set here includes all parameter points whose expert consensus probability density is not lower than λ, and λ acts as the threshold of "consensus strength": the larger its value, the stricter the target set and the higher the required degree of consensus; conversely, the looser the target set and the stronger its inclusiveness.

[0100] 2) To further describe the internal structure of expert consensus, the λ-level probability target set is divided into a high-confidence region and an extended confidence region according to the difference in generation logic of adversarial expert consensus:

[0101] High-confidence region (strict consensus): Defined in the form of probability product, it requires that a parameter point is recognized by all experts with a relatively high probability at the same time, representing the decision-making core with high group consistency, and its expression is as follows:

[0102] (8)

[0103] In the formula: R (λ) is the high-confidence region, f j (p) is the probability density function, j is the j-th expert, and j=1,2,…m, the boundary of the high-confidence region is recorded as .

[0104] Extended confidence region (loose consensus): Defined in the form of probability mean, it allows a parameter point to be recognized by only some experts, representing the decision-making extension that takes into account both diversity and explorability, and its expression is as follows:

[0105] (9)

[0106] In the formula: is the extended confidence region; the boundary of the extended confidence region is recorded as .

[0107] As shown in Figure 3 , the individual opinions of five experts, the joint probability density and the corresponding contour lines of confidence levels are intuitively displayed. For example, Figure 3 the blue point cloud region in (a) represents the parameter space recognized by expert 1, and its probability density function satisfies , Figure 3 (k) in the figure represents the contour lines of the joint probability density generated by integrating the distributions of the five experts correspond to the target set boundaries of different confidence levels, Figure 3 the high-confidence region in the figure (red core) has a small range, representing a strict consensus region; while the low-confidence region (cyan periphery) has a larger range, covering looser consensus. By continuously adjusting the value of λ, decision-makers can dynamically weigh between "conservativeness" and "exploration", so as to flexibly adapt to different risk preferences and task requirements.

[0108] After establishing the probability target set with confidence levels as described above, the evaluation strategy varies depending on the data type. In this embodiment, in step S3, if the data type is a random distribution number in the parameter space, the evaluation focuses on measuring the probability that the distribution as a whole falls into the target region. Therefore, a performance measurement model based on overlap, also known as the VM model, is proposed for randomly distributed data. This model is used to calculate the probability overlap of the randomly distributed data falling into the probability target set, obtaining the first performance evaluation value. Figure 4 For an intuitive geometric interpretation of the VM model, Figure 4 The blue grid area represents the target set D, and the space S represents the parameter space region covered by the simulation results. The intersection of the two is Ec. Figure 4 The volume (or probability measure) of the cyan portion yields the first performance evaluation value.

[0109] When the data type consists of a set of fixed points, an overlap-based effectiveness measurement model cannot be used for adversarial effectiveness evaluation. In this case, the evaluation focus should shift to the relative positional relationship between these fixed points and the boundary of the probabilistic target set. A distance-based effectiveness measurement model, also known as the SM model, is proposed for these fixed points. This model is used to calculate the normalized distance between the fixed point data and the boundary of the probabilistic target set to obtain a second effectiveness evaluation value. Figure 5 This is an intuitive geometric diagram of the SM model. Figure 5 The midpoint p represents a defined point in a simulation result, and the hypersurface M represents the boundary of the target set at a certain confidence level λ. (Right now (The contour surface). By calculating the directed distance from point p to this boundary, the second performance evaluation value can be obtained.

[0110] Therefore, the SM model provides an intuitive, sensitive, and statistically significant metric for evaluating the performance of deterministic simulation data. Together with the VM model, it forms a complete evaluation system covering both random and deterministic simulation output types.

[0111] Specifically, the VM model incorporates high-confidence regions in the process of calculating the weighted first performance evaluation value. R (λ) and extended confidence region Its expression is:

[0112] (10)

[0113] In the formula: E Ris the first performance evaluation value; fsim(p) is the probability distribution function of the simulation adversarial capability index; k∈[0,1] is the balance coefficient, used to adjust decision preference. When k → 1, it focuses on expanding the consensus region and reflects optimistic decision-making. When k → 0, it focuses on the high-confidence consensus region and reflects conservative decision-making; II(.) is the indicator function, which takes the value of 1 when the condition is met, and 0 otherwise.

[0114] High confidence area R (λ) and extended confidence region The specific range depends on the preset confidence level parameter. and (usually set to default) = 0.5 and = 0.95), and their expressions are as follows:

[0115] (11)

[0116] (12)

[0117] Monte Carlo integrals are used to approximate the probability overlap if N independent samples are drawn from the probability distribution function fsim(p) of the simulation adversarial capability index. Then the first performance evaluation value E R The formula can be approximated as:

[0118] (13)

[0119] In the formula: p i Let i be an independent sample, where i is the i-th independent sample, and i = 1, 2, ..., N.

[0120] The following is the implementation process of the VM model for randomly distributed data:

[0121] a1. Input m experts' interval evaluation of n-dimensional parameters {H j Simulation data for each alternative scheme were collected, and all indicators were normalized to eliminate the influence of dimensions.

[0122] a2. Assess each expert's interval rating H j Transform into a smooth probability density function f j (p), for all f j (p) Perform an arithmetic average to generate the joint probability density function f, which represents the group consensus. joint (p);

[0123] a3. Set the balance coefficient k and the baseline confidence level based on risk preference. , Based on the simulation sample {p} of the current schemei} and joint probability density function f joint (p) is the input. The "Efficiency Equilibrium Point Solving Algorithm" is run. Through iterative search, it outputs the unique optimal cutoff threshold λ* and its corresponding first efficiency evaluation value E. R ;

[0124] a4. Regarding the first performance evaluation value E R The results are sorted in descending order, and the highest-ranked result represents the optimal alignment of multiple expert consensus objectives.

[0125] In a3 above, due to the first performance evaluation value E R It is a function of the confidence level parameter λ, so the key is to find an optimal cutoff threshold λ* such that the system performance value evaluated under this optimal cutoff threshold λ* is in equilibrium with itself, that is, satisfying E R (λ*) = λ*, this point is called the efficiency equilibrium point (λ*, E R This represents the optimal match between system performance and decision stringency requirements. Given E R It is a monotonically non-increasing continuous function of λ. A binary search algorithm is used to iterate within the confidence level interval, efficiently and stably solving for the performance equilibrium point; combined with... Figure 6 The solution process for the efficiency equilibrium point is shown below. The horizontal axis represents the cutoff threshold λ, which ranges from [0,1], and the vertical axis represents the index effectiveness value E under the corresponding threshold λ. λ The goal is to find curve E. R The intersection of (λ) and the line Y = λ, point A represents the indicator validity in the high confidence region taken within the confidence level interval (0.4, 0.6], and point B represents the indicator validity in the extended confidence region taken within the same interval.

[0126] The algorithm for finding the efficiency equilibrium point is as follows:

[0127]

[0128] The above algorithm is based on the intermediate value theorem for monotonic functions, ensuring the existence and uniqueness of solutions within the interval [0, 1]. It has a convergence speed of O(log (1 / E)) and high computational efficiency, typically reaching 10^10 after about 10-15 iterations. -3 To meet the accuracy requirements, the core operation of this algorithm is to compare E. R The relationship between (λ) and λ is independent of the specific form or derivative information of the function, and it exhibits good stability against random fluctuations in the simulated samples. By inputting the balance coefficient k, the algorithm incorporates the decision-maker's risk preference into the search process; adjusting the value of k will change E. R (λ) curve, thus affecting the final equilibrium point (λ*, E RThe position of the options allows the ranking of the options to reflect different decision-making tendencies.

[0129] Specifically, for simulation results with data types of deterministic points, the evaluation goal of the SM model is to quantify the proximity of each deterministic point to the boundary of the probabilistic target set formed by multi-expert consensus, and to integrate the decision-makers' risk preferences to ultimately output a ranking of the schemes.

[0130] The boundary of the target set is defined by the contour surface S at a given confidence level λ. λ Defined, and further distinguished into high confidence boundaries. R (λ) and extended confidence boundary First, Mahalanobis distance is used to determine the proximity of a point to the boundary of the probability target set.

[0131] 1) Evaluation point P to extended confidence boundary The normalized Mahalanobis distance is:

[0132] (14)

[0133] In the formula: and Extended confidence boundaries The mean vector and covariance matrix can be obtained from the joint probability density function f. joint (p) Estimated from the sample in this region, denominator This ensures the relative stability of the distance metric, which measures both the distance between a point and the statistical "center" of the boundary, and also eliminates the influence of dimensions through normalization.

[0134] 2) Evaluation point P to high confidence boundary R The normalized Mahalanobis distance of (λ) is:

[0135] (15)

[0136] In the formula: and Let R(λ) be the mean vector and covariance matrix of the high confidence boundary, respectively.

[0137] To integrate the attention given by decision-makers to different consensus levels, a balance coefficient k∈[0,1] is introduced, and the weighted distance under the confidence level parameter λ is constructed as follows:

[0138] (16)

[0139] Policymakers adjust k to weigh the importance of the boundaries between "relaxed consensus" and "strict consensus" in the evaluation. When k→1, the evaluation relies more on the extended boundary and tends to make optimistic decisions; when k→0, it relies more on the high confidence boundary and tends to make conservative decisions.

[0140] A single confidence level parameter λ is insufficient to fully reflect the overall shape of the target set boundary. Therefore, an interval integral of the confidence level parameter λ is introduced to comprehensively evaluate the overall proximity of point P across multiple confidence levels, and to add consideration for specific key boundaries (such as intermediate confidence levels). The special attention items (corresponding to the high confidence boundary) ultimately form the distance measure of the SM model as follows:

[0141] (17)

[0142] In the formula: D R (P) represents the second performance evaluation value, and dis(P, λ) represents the weighted distance under the confidence level parameter λ. For intermediate confidence level The corresponding high-confidence boundary, [λ1, λ2], represents the confidence level interval of interest to the decision-maker. ; The adjustment coefficient is used to control the weight of the second term (the relative distance to the critical boundary) in the overall measurement. When α → 1, the model focuses more on the approximation of the observation point P to the strictest consensus boundary, which is suitable for high-risk avoidance scenarios. When α → 0, the model focuses more on the average distance between the observation point P and the overall boundary band, which is suitable for general robust assessment. Indicates the middle confidence level Corresponding high confidence boundary All points With evaluation points The maximum relative Euclidean distance between them. This refers to the relative Euclidean distance, which is defined by element-wise division. , , The relative Euclidean distance is dimensionless, reflecting the point. With boundary points Relative deviations in various dimensions, outer layer Taking the larger value between 1 and the maximum relative distance is a lower bound protection operation. As evaluation points To the high confidence boundary The closest relative distance, For intermediate confidence level The corresponding high confidence boundary (i.e. the boundary of the expert strict consensus region). : indicates taking any point on the boundary. D R The smaller the (P) value, the closer the evaluation point P is to the multi-expert consensus target set, and the better the corresponding solution performance.

[0143] The following is the implementation process of the SM model for a specific point:

[0144] b1. Based on the interval assessments of all experts, a joint probability density function f is generated using a kernel density estimation and averaging fusion method. joint (p);

[0145] b2. Within the defined confidence level interval [λ1, λ2], N+1 levels are discretely selected. For each level λ, its high confidence boundary is estimated. R (λ) and extended confidence boundary The mean vector μ and covariance matrix Σ of the corresponding regions are obtained and stored for subsequent queries;

[0146] b3. For a specific point P to be evaluated, iterate through all discrete confidence levels. At each level, calculate the normalized weighted distance using pre-calculated statistics. By numerically integrating these discrete values, we obtain ;

[0147] b4. Regarding the intermediate confidence level Corresponding high confidence boundary Calculate the relative Euclidean distances from point P to all sampling points on the boundary, and determine the minimum value among them. With the maximum value , used to construct the relative distance term;

[0148] b5. Integral term With relative distance term Add them together to obtain the final comprehensive distance measure. .

[0149] The algorithm execution process of the SM model for a given point is as follows:

[0150]

[0151] This algorithm follows a "one-time preprocessing, multiple queries" approach, which can significantly improve the online response efficiency of decision support systems. The preprocessing stage (step b2) dominates the overall computational complexity, accounting for approximately [missing information]. Where N is the number of discrete confidence levels, M is the number of sampling points required to estimate the statistic, and n is the parameter dimension. This stage only needs to be executed once. The evaluation stage (steps b3-b5) is efficient in calculating the new point P: the integration loop (step b3), with the covariance matrix inverse pre-calculated, has a time complexity of O(n). The relative distance calculation (step b4) requires... Time, and K is the number of boundary sampling points. Therefore, once the expert consensus model is established, the evaluation complexity of the new scheme is linearly related to the discretization resolution N and quadratically related to the parameter dimension n, making it feasible for medium-sized problems.

[0152] The final result It has the following good characteristics: (1) Scale invariance, which ensures fair comparison between parameters of different dimensions through Mahalanobis distance and normalized denominator; (2) Risk perception, which enables the model to capture the overall fit with the "boundary zone" of the target set (integral term) and to impose a sensitivity penalty on the case of approaching the strictest consensus boundary (relative distance term); (3) Decision flexibility, which can be achieved by adjusting parameters. and Decision-makers can flexibly balance overall adaptability with boundary risks to adapt to different application scenarios.

[0153] Example 2:

[0154] This invention provides a game-theoretic adversarial situation assessment system based on probabilistic consensus. The system is used to implement the steps of the method described in Embodiment 1, and includes:

[0155] The knowledge fusion module is used to receive interval assessments of various adversarial capability indicators of adversarial units from multiple adversarial experts, and to transform each interval assessment into an individual probability density function on the parameter space. The individual probability density functions are then fused to construct a joint probability density function of consensus among multiple adversarial experts.

[0156] The probability target set construction module is used to define a probability target set with confidence levels based on the joint probability density function;

[0157] The classification module is used to acquire battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Based on the data type, it evaluates the relationship between the data type and the probabilistic target set and calculates the corresponding effectiveness evaluation value. The data types include random distribution data and fixed point data.

[0158] The evaluation module obtains the corresponding performance evaluation value based on the data type. If the data type is randomly distributed data, the probability overlap of the randomly distributed data falling into the probability target set is calculated through the performance measurement model based on overlap, and the first performance evaluation value is obtained. If the data type is fixed point data, the normalized distance between the fixed point data and the boundary of the probability target set is calculated through the performance measurement model based on distance, and the second performance evaluation value is obtained.

[0159] The output module is used to sort multiple adversarial units according to their effectiveness evaluation values ​​and output the adversarial capability evaluation results.

[0160] In addition, the present invention also provides an electronic device, the electronic device including at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the method described in the above embodiments.

[0161] The memory and processor are connected via a bus, which can include any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further. The bus interface provides an interface between the bus and the transceiver, which can be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over a wireless medium via an antenna, which further receives data and transmits it to the processor.

[0162] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management and other control functions, while the memory can be used to store the data used by the processor when performing operations.

[0163] Simulation Case:

[0164] The effectiveness of the method proposed in Embodiment 1 of this invention is verified through two typical decision-making scenarios. Case 1 corresponds to a scenario where the simulation results are randomly distributed data, and a VM model is used; Case 2 corresponds to a scenario where the simulation results are fixed-point data, and an SM model is used.

[0165] Case 1: Application of the VM Model

[0166] Reference Figures 7-8This study focuses on DDoS defense capability assessment in existing technologies (reference: Almotiri, SH, Improving network resilience against DDoS attacks: A fuzzy TOPSIS-based quantitative assessment approach. Heliyon, 2024. Vol.10(No.22): p. e40413). Using the Fuzzy TOPSIS method, based on five core security attributes (intrusion detection, prevention, response, tolerance, and mitigation capabilities), the study compares and analyzes the methods and their effects using the raw data (corresponding to attributes F1-F5), and conducts a comprehensive performance evaluation of six network schemes (N1-N6).

[0167] Interval assessments from 10 cybersecurity experts (m=10) were collected as expert knowledge input (Table 2), and the normalized performance intervals of six schemes in the literature on each attribute were used as simulation data input (Table 1). Regarding parameter settings, to reflect different risk attitudes, the preference coefficient k was set to 0.2, 0.5, and 0.8 for testing; the confidence level was fixed at λ. low =0.5 and λ high =0.95, convergence accuracy set to E=10 -3 During implementation, N=10000 points are uniformly sampled from the performance range of each network scheme as input samples for the VM model.

[0168] Table 1. Normalized performance ranges of the six schemes on various attributes.

[0169]

[0170] Ten cybersecurity industry experts were selected to submit their requirements for DDoS attack defense capabilities, which were compiled into a requirements table, as shown in Table 2.

[0171] Table 2. Interval Assessments by 10 Cybersecurity Industry Experts

[0172]

[0173] Taking k = 0.5, we obtain the equilibrium points for schemes N1-N6. ,like Figure 7 As shown, the various schemes The values ​​and order are shown in the second row of Table 3; similarly, when k = 0.8, the values ​​of each scheme are... The values ​​and sorting are shown in the third row of Table 3; when k=0.2, the values ​​of each scheme are... The values ​​and rankings are shown in the fourth row of Table 3. Despite the balance coefficient k varying between 0.2 and 0.8, the ranking results for the six network configurations remained completely consistent. This indicates that the evaluation results of the VM model are highly robust to the decision-maker's risk preference (optimistic / pessimistic), and the ranking of the schemes is primarily determined by the intrinsic fit between their simulation distribution and the multi-expert consensus objective set, rather than by specific weight choices.

[0174] Table 3 Evaluation values ​​and ranking of N1-N6 network schemes (k=0.2, 0.5, 0.8)

[0175]

[0176] As shown in Table 4, the ranking of the Fuzzy Topsis method in the literature is roughly the same as that of the method proposed in this invention. The evaluation results of N6 are significantly better than other schemes. This is because its simulation parameters (Table 1) tend to be in the higher performance range across all attributes, making its parameter distribution more consistent with the high confidence region of the expert consensus target set (refer to the evaluation results corresponding to Figure 8), demonstrating a comprehensive performance advantage. Among the two methods, the evaluation results of schemes N1 and N5 are very close. Combining the data in Table 1 with expert opinions (Table 2), it can be seen that these two schemes have different adaptation modes in satisfying the multi-faceted expert consensus target, resulting in a high degree of conflict in expert opinions. It can be seen that the two methods have different strategies in handling expert opinion conflicts. The VW model performs overall fusion through probability overlap, while Fuzzy TOPSIS relies on static weights and distance calculations, which leads to differences in the subtle rankings of N1 and N5. In N2, N3, and N4, the expert opinions are more unified, and the rankings obtained by the two methods are consistent.

[0177] Table 4. Comparison of VWOM and Fuzzy Topsis rankings

[0178]

[0179] Furthermore, the total complexity of Fuzzy TOPSIS is polynomial (approximately). As the number of attributes (n) increases exponentially, the method in this paper achieves rapid convergence through Monte Carlo integration and bisection, reducing the total complexity to linear order (approximately). This new method achieves more efficient multidimensional optimization on the same dataset. For example, to obtain the result of N6, FuzzyTOPSIS requires multiple matrix normalizations (5×6 matrix), calculations of positive and negative ideal solutions (5 times of extreme value screening), and distance calculations (6 times of multidimensional vector operations). The new method only requires 10 iterations to achieve the required accuracy, reducing the time by less than one-sixth of that of FuzzyTOPSIS.

[0180] Case 2: Application of the SM Model

[0181] Reference Figures 9-12 To verify the effectiveness of the SM model, this case study takes the selection of suppliers and the allocation of orders among suppliers in the existing technology (reference: Karpak, B., E. Kumcu and RR Kasuganti, Purchasing materials in the supply chain: managing a multi-objective task. European Journal of Purchasing and Supply Management, 2001. Vol.7(NO.3): p.209-216.) as an example, and only extracts the supply information of gray cast iron for exemplary analysis, as shown in Table 5.

[0182] Table 5 Information on gray cast iron provided by suppliers

[0183]

[0184] The gray cast iron provided by the four suppliers differs in price, quality, and delivery reliability, but these values ​​are certain. This is equivalent to the suppliers providing customers with four supply solutions with certain outcomes. Similar to Case 1, several typical customer representatives were selected (Table 6), and a set of capability indicator targets was constructed by reaching a consensus on expert knowledge.

[0185] Table 6 Customer Representative Requirements

[0186]

[0187] Of the three indicators in Table 6, Cost is a cost-related indicator, while Quality and Delivery Reliability are benefit-related indicators. For ease of analysis, the latter two indicators are transposed to evaluate Disqualification and Delivery Reliability. Customer representatives reached a consensus that the cost of gray cast iron is $6 per unit, with a maximum price of $40 per unit, and that Quality and Delivery Reliability must be greater than 60%. After normalizing and dimensionless processing of Tables 2 and 3, Tables 7 and 8 are obtained.

[0188] Table 7 Information provided by the supplier regarding gray cast iron after processing

[0189]

[0190] Table 8 Customer Representative Requirements After Transposition Processing

[0191]

[0192] When λ=0.7, the target set of customer representatives can be obtained as the blue point cloud portion in Figure 9. The comprehensive evaluation measure of the four supplier supply schemes can then be calculated, as shown in the first row of Table 9. Clearly, Supplier 2 is the optimal solution. The literature, through VIG optimization results and case application verification, concludes that "Supplier 2 is clearly considered the most cost-effective option due to its low cost, high quality, and flexible capacity." The analysis results of this case are consistent with the conclusions obtained in the literature.

[0193] Next, the λ value was adjusted for sensitivity analysis. When Δλ = +0.1, the combined measure values ​​for the customer representative's target set and the supplier were obtained as follows: Figure 10 As shown in the second row of Table 9, Supplier 2 is the optimal solution. When Δλ = -0.1, the combined measure values ​​of the customer representative's target set and the supplier are shown in Figure 11 and the third row of Table 9, and Supplier 2 is still the optimal solution.

[0194] Table 9 Evaluation Measure Values ​​for Different Values ​​of λ

[0195]

[0196] Based on the above analysis, we used Δλ=±0.1 to increase or decrease the values. The comprehensive metric values ​​of all four suppliers changed, but the ranking remained relatively stable, and the optimal recommendation method remained unchanged, demonstrating the good stability of this method. The results shown in Figure 12 are obtained by varying the Cost, Disqualification, and Delivery unreliability metrics by Δ=±0.1.

[0197] Figure 12In the model, as the values ​​of various indicators increase or decrease, the distance measure changes accordingly, but the ranking remains 2→4→1→3. Supplier 2 consistently remains the optimal solution across all scenarios, exhibiting minimal E(λ) fluctuation (range only 0.022), highlighting the unity of its supply chain resilience and model robustness. This empirically demonstrates that the SM model effectively solves the ranking reversal problem of traditional methods by replacing linear weighting with Mahalanobis distance. Supplier 3's high sensitivity to delivery unreliability (a +10% disturbance causes E(λ) to increase by 9.0%) is directly related to its low initial delivery reliability (70%). This indicator falls into the low confidence interval of the expert joint probability density, confirming the dynamic confidence fusion mechanism's ability to identify conflict areas. In summary, Supplier 2 maintains optimal performance with minimal efficiency fluctuations under various disturbances, revealing its inherent robustness advantage in multi-indicator synergy. Meanwhile, Supplier 3's high sensitivity to disturbances in specific indicators highlights the SM model's accurate identification of key bottleneck indicators in supply chain decision-making, providing a quantitative basis for supplier risk management. Therefore, supply chain decisions should prioritize suppliers with high robustness across multiple metrics (such as Supplier 2) and avoid over-reliance on a single advantageous metric (such as Supplier 3's low cost but high delivery risk).

[0198] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A game-theoretic adversarial situation assessment method based on probabilistic consensus, characterized in that, Includes the following steps: Construct a joint probability density function for multiple adversarial expert consensuses; Based on the joint probability density function, a probabilistic target set with confidence levels is defined; Acquire battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Evaluate its relationship with the probabilistic target set based on the data type and calculate the corresponding effectiveness evaluation value. The data types include random distribution data and fixed point data. The multiple adversarial units are sorted according to their effectiveness evaluation values, and the adversarial capability evaluation results are output.

2. The game-theoretic adversarial situation assessment method based on probabilistic consensus as described in claim 1, characterized in that, Construct a joint probability density function for multiple adversarial expert consensuses, including: Receive range assessments from multiple adversarial experts on various adversarial capability indicators of the adversarial unit; Each interval assessment is transformed into an individual probability density function on a parameter space, which is composed of multiple adversarial capability indicators; A joint probability density function is generated by fusing multiple individual probability density functions.

3. The game-theoretic adversarial situation assessment method based on probabilistic consensus as described in claim 1, characterized in that, The steps to define a probabilistic target set with confidence levels include: Given a confidence level parameter λ∈[0,1], construct the λ-level probability target set, which is expressed as: ； In the formula: R(λ) represents the λ-level probability target set, p is the adversarial capability index, P is the parameter space, and f joint (p) is the joint probability density function; Based on the differences in the generation logic of adversarial expert consensus, the λ-level probability target set is divided into a high-confidence region and an extended-confidence region, and their expressions are as follows: ； ； In the formula: R (λ) represents the high-confidence region. To expand the confidence region, let j be the j-th expert, and j = 1, 2, ..., m, f j (p) is the probability density function.

4. The game-theoretic adversarial situation assessment method based on probabilistic consensus according to claim 3, characterized in that, Based on the data type, the corresponding performance evaluation value is obtained, including: If the data type is randomly distributed data, the probability overlap of the randomly distributed data falling into the probability target set is calculated by the effectiveness measurement model based on overlap, and the first effectiveness evaluation value is obtained. If the data type is definite point data, the normalized distance between the definite point data and the boundary of the probabilistic target set is calculated using a distance-based effectiveness measurement model to obtain the second effectiveness evaluation value.

5. The game-theoretic adversarial situation assessment method based on probabilistic consensus according to claim 4, characterized in that, The performance measurement model based on overlap integrates the high-confidence region and the extended-confidence region, and its expression is as follows: ； In the formula: E R is the first performance evaluation value, fsim(p) is the probability distribution function of the simulation adversarial capability index, k∈ [0,1] is the balance coefficient, and II(.) is the indicator function.

6. The game adversarial situation assessment method based on probabilistic consensus according to claim 5, characterized in that, The first performance evaluation value is obtained by calculating the probability overlap of randomly distributed data falling into the probabilistic target set using an overlap-based performance measurement model, including: By introducing the Monte Carlo integral approximation to calculate the probability overlap, the expression for the effectiveness measurement model based on overlap is: ； In the formula: p i Let i be the i-th adversarial capability index, and i = 1, 2, ..., N; Based on the binary search algorithm, the efficiency equilibrium point is iteratively solved within the confidence level interval; The performance equilibrium point is used as the output of the first performance evaluation value.

7. The game adversarial situation assessment method based on probabilistic consensus according to claim 4, characterized in that, The expression for the distance-based performance measurement model is: ； In the formula: D R (P) represents the second performance evaluation value, and dis(P, λ) represents the weighted distance under the confidence level parameter λ. For the confidence level range that policymakers are concerned with, , For adjustment coefficients, For intermediate confidence level The corresponding high confidence boundary, Indicates the middle confidence level Corresponding high confidence boundary All points With evaluation points The maximum relative Euclidean distance between them. The relative Euclidean distance. As evaluation points To the high confidence boundary The closest relative distance, For intermediate confidence level The corresponding high confidence boundary.

8. The game adversarial situation assessment method based on probabilistic consensus according to claim 7, characterized in that, The second performance evaluation value is obtained by calculating the normalized distance between the determined point data and the boundary of the probabilistic target set using a distance-based performance measurement model, including: Mahalanobis distance is used to determine the proximity of a point to the boundary of the probabilistic target set; The emphasis on high-confidence regions and extended-confidence regions is adjusted by the balance coefficient; A second performance evaluation value is output using a distance-based performance measurement model. The smaller the second performance evaluation value, the higher the threat level of the adversary unit.

9. A game-theoretic adversarial situation assessment system based on probabilistic consensus, characterized in that, The system is used to implement the steps of the method according to any one of claims 1-8, the system comprising: The knowledge fusion module is used to receive interval assessments of various adversarial capability indicators of adversarial units from multiple adversarial experts, and to transform each interval assessment into an individual probability density function on the parameter space. The individual probability density functions are then fused to construct a joint probability density function of consensus among multiple adversarial experts. The probability target set construction module is used to define a probability target set with confidence levels based on the joint probability density function; The classification module is used to acquire battlefield capability data of the adversary unit to be evaluated in the current situation and determine the data type. Based on the data type, it evaluates the relationship between the data type and the probabilistic target set and calculates the corresponding effectiveness evaluation value. The data types include random distribution data and fixed point data. The evaluation module obtains the corresponding performance evaluation value based on the data type. If the data type is randomly distributed data, the probability overlap of the randomly distributed data falling into the probability target set is calculated through the performance measurement model based on overlap, and the first performance evaluation value is obtained. If the data type is fixed point data, the normalized distance between the fixed point data and the boundary of the probability target set is calculated through the performance measurement model based on distance, and the second performance evaluation value is obtained. The output module is used to sort multiple adversarial units according to their effectiveness evaluation values ​​and output the adversarial capability evaluation results.

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