Cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision

Abstract

This invention relates to the field of integrated defense and early warning technology for clustered targets, and discloses a clustered target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making. This method collects raw data from multiple sensors and quantifies it into an intuitionistic fuzzy set to generate a clustered integrated decision matrix; calculates the degree of consensus and hesitation potential energy; when consensus is insufficient, it generates resource focusing instructions to drive sensors to adjust physical parameters and perform feedback correction to form a consensus closed loop; it constructs a strategic conflict model to perform game-theoretic linkage analysis to solve for optimal attribute weights and calculates a dynamic early warning threshold; finally, it calculates the final early warning score based on the MABAC algorithm, compares it with the dynamic threshold to trigger an alarm, and outputs a dynamic interpretation vector. This invention solves the problems of decision oscillation and poor adaptability to fixed thresholds in complex electromagnetic environments by using physical information synergy enhancement and strategic game threshold drift mechanisms, thereby improving the accuracy and interpretability of early warnings.

Description

Technical Field

[0001] This invention relates to the field of integrated defense and early warning technology for cluster targets, specifically a cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making. Background Technology

[0002] With the rapid development of swarm warfare tactics such as drone swarms, ground-based air defense and early warning systems face increasingly complex challenges. Swarm targets are characterized by their large numbers, wide distribution, high mobility, and strong cooperative jamming capabilities, making accurate threat assessment and early warning difficult with a single sensor. Therefore, information fusion using multiple sensors has become a mainstream technical means to improve early warning capabilities for swarm targets. Existing multi-source information fusion technologies typically employ algorithms such as DS evidence theory, fuzzy integrals, or Bayesian networks to correlate and synthesize data collected from different sensors, obtaining a more accurate situational awareness than a single source.

[0003] However, in real-world complex electromagnetic environments and highly dynamic combat scenarios, existing early warning methods still have several technical limitations.

[0004] First, in the processing and correction of multi-source information, existing technologies mainly focus on numerical calculations at the data level. When sensor networks are interfered with or observation conditions deteriorate, leading to a decrease in data consistency, traditional consensus algorithms typically use mathematical methods such as weighted averaging, outlier removal, or iterative approximation to force data consensus. This approach only performs numerical-level repairs based on existing data, neglecting the interaction between the information processing layer and the physical sensing layer. The system lacks a mechanism to reverse-engineer the physical resources of the underlying sensors based on the uncertainty of the information. For example, it cannot automatically instruct the radar to extend its dwell time or adjust the integral parameters of photoelectric detection when data is ambiguous. This prevents the quality of the data source itself from being improved at the physical level, thus limiting the reliability of the final fusion result.

[0005] Secondly, in the threshold setting stage of threat assessment, existing technologies mostly employ fixed thresholds or statistically adaptive thresholds based on a constant false alarm rate. These threshold setting methods often assume a relatively stable background environment or adjust only based on the signal-to-noise ratio. However, when facing deceptive interference from clustered targets or highly uncertain situations, the consensus among sensors decreases. In such cases, maintaining a conventional threshold easily leads to missed alarms; simply lowering the threshold causes a surge in the probability of false alarms. Existing technologies lack a mechanism that can link the quality of information within the system (such as consensus) to the decision threshold, making it impossible to dynamically adjust the sensitivity of warnings according to the ambiguity of the situation, and thus difficult to achieve agile and accurate warnings in chaotic battlefield environments.

[0006] Furthermore, in the output of early warning results and the human-machine interaction process, existing technologies typically only output a quantitative threat score or a simple alarm signal. For commanders, this output method is a black box, failing to intuitively demonstrate the deeper logic behind the alarm triggering. Commanders struggle to determine whether the current alarm is driven by the target's physical motion characteristics (such as speed and distance) or by the system's strategic preferences (such as focusing on a particular attack intent). This lack of interpretive information based on the coupling of weights and features reduces decision-making efficiency and mutual trust in human-machine collaborative operations. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making. This method solves the problems of existing cluster target early warning methods, which rely solely on data numerical correction without physical layer feedback to improve source quality, have difficulty dynamically adapting early warning thresholds to highly uncertain situations based on consensus, and lack interpretive logic based on the coupling of strategic weights and physical characteristics in early warning output.

[0008] The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making provided by this invention mainly includes the following steps: First, perform time-series weighting and primary aggregation of dynamic information. Collect raw evaluation data of multi-source sensor nodes for the cluster target in continuous time series, and quantize the raw evaluation data into an intuitionistic fuzzy set.

[0009] The time series weights at each time point are calculated based on the dynamic characteristics of the cluster target. The time series weights are then used to dynamically weight and fuse the evaluation information of each multi-source sensor node in the form of intuitionistic fuzzy sets at different times to obtain the multi-time aggregation matrix of a single sensor node. Finally, the multi-time aggregation matrices of all single sensor nodes are aggregated to generate the group comprehensive decision matrix.

[0010] Secondly, a resource-focused and consensus-closed-loop mechanism based on hesitation potential energy is implemented. The deviation distance between the multi-time aggregation matrix of a single sensor node and the group integrated decision matrix is ​​calculated, and the degree of consensus is calculated based on the deviation distance. At the same time, the hesitation potential energy of the system is calculated based on the hesitation degree of time series weights and intuitionistic fuzzy set.

[0011] If the consensus level is lower than the preset consensus threshold, the hesitant potential energy is used to generate resource focusing instructions to adjust the physical parameters of the underlying multi-source sensor nodes. The resource focusing instructions are then used to perform feedback correction on the evaluation information in the form of intuitionistic fuzzy sets that have not reached consensus, generating the corrected evaluation information. The multi-time aggregation matrix of a single sensor node is then updated to regenerate the group integrated decision matrix until the consensus level meets the requirements.

[0012] Secondly, strategic game theory linkage and dynamic threshold drift are implemented. A strategic conflict model between sensitive agents and stable agents is established. The optimal attribute weights are solved through game theory linkage analysis. The coupling relationship between the threshold sensitivity factor derived from the optimal attribute weights and the degree of consensus is used to calculate the dynamic early warning threshold that adaptively drifts with information quality.

[0013] Finally, MABAC threat scoring and intelligent interpretation are performed. Based on the optimal attribute weights and the swarm integrated decision matrix, the MABAC algorithm is used to calculate the final warning score for the cluster target, and the final warning score is compared with the dynamic warning threshold. When the final warning score is greater than the dynamic warning threshold, an alarm is triggered, and a dynamic alarm interpretation vector is generated based on the optimal attribute weights.

[0014] Furthermore, in the time-weighted and initial assembly steps of dynamic information, the evaluation attributes of cluster targets are defined, including operational intent, survivability, support capability, and command and control capability.

[0015] The original evaluation data is mapped to an intuitionistic fuzzy set containing membership, non-membership, and hesitation degrees using a membership function. Based on the time series weight calculation formula, and using an inverse Poisson distribution model, the time series weights are calculated according to the time point index, inverse Poisson distribution parameters, and the total number of time points, so that data closer to the current time is assigned a higher weight value.

[0016] Based on the HM operator aggregation formula, the multi-time aggregation matrix of all individual sensor nodes is subjected to horizontal aggregation operation using the HM operator and adjustment parameters to obtain a group comprehensive decision matrix containing the group judgment results.

[0017] Furthermore, in the resource focusing and consensus closed-loop steps based on hesitation potential energy, the deviation distance is obtained by calculating the root mean square error of the membership degree, non-membership degree, and hesitation degree of the intuitionistic fuzzy set according to the intuitionistic fuzzy deviation distance formula and the normalized intuitionistic fuzzy distance model based on three-dimensional features.

[0018] Based on the consensus degree formula, the degree of consensus is obtained by establishing an inverse relationship with the deviation distance. Based on the hesitation potential energy calculation formula, the hesitation potential energy, which represents the total accumulated uncertainty within the current time window, is obtained by accumulating the products of the hesitation degree of all cluster targets and all evaluation attributes within the detection range with the time series weights at the corresponding times.

[0019] Furthermore, during the generation of resource-focusing instructions and the execution of feedback corrections, conflicting attributes that lead to a decrease in consensus are identified. Hesitation potential energy and the degree of hesitation of these conflicting attributes are used to generate resource-focusing instructions, which are control parameter gain vectors for the underlying multi-source sensor nodes. Based on the feedback correction and resource allocation formulas, the corrected evaluation information is calculated using elements in the group integrated decision matrix, the evaluation information before correction, and the numerical mapping value of the resource-focusing instructions.

[0020] The preset consensus threshold is a lower limit of consensus set in advance based on the statistical distribution of historical consistency data of the sensor network under standard operating conditions or expert experience.

[0021] Furthermore, in the strategic game linkage and dynamic threshold drift steps, a strategic conflict model including sensitive agents and stable agents is constructed.

[0022] Among them, the sensitivity proxy is constructed based on the weighting method that reflects the conflict of indicators, while the stability proxy is constructed based on the weighting method that reflects the dispersion of data.

[0023] Based on the formula for solving the optimal weight in game linkage and the minimization of deviation model, the basic weight vectors corresponding to sensitive agents and stable agents are regarded as game participants. By solving the linkage coefficient in the linear combination, the total deviation between the combined weight vector and each basic weight vector is minimized, thus obtaining the optimal attribute weight.

[0024] Furthermore, in the process of calculating the dynamic early warning threshold, the dynamic early warning threshold is calculated based on the dynamic early warning threshold calculation formula, using the basic threshold, the threshold sensitivity factor derived from the optimal attribute weight, and the degree of consensus.

[0025] This calculation makes the dynamic early warning threshold positively correlated with the degree of consensus, realizing the drift characteristic that the early warning threshold automatically drops as the degree of consensus decreases.

[0026] Among them, the basic threshold is an alarm threshold value that is preset based on the false alarm rate requirements of the early warning system in peacetime or standard electromagnetic environment.

[0027] Furthermore, in the MABAC threat scoring and intelligent interpretation steps, the group integrated decision matrix is ​​first numericalized and standardized using an intuitionistic fuzzy scoring function.

[0028] Subsequently, based on the formula for calculating the weighted decision matrix, the standardized matrix is ​​weighted using the optimal attribute weights to obtain the weighted decision matrix. Then, based on the formula for calculating the boundary approximation region, the geometric mean of each evaluation attribute in the weighted decision matrix is ​​calculated to form the boundary approximation region matrix.

[0029] Based on the distance matrix calculation formula, the difference between the weighted decision matrix and the boundary approximation region matrix is ​​calculated to obtain the distance matrix. Based on the final early warning score formula, the differences of the same cluster targets in the distance matrix across all evaluation attributes are summed to calculate the final early warning score.

[0030] Furthermore, in the alarm triggering determination, the final warning score is compared with the dynamic warning threshold; if the final warning score is greater than the dynamic warning threshold, the target threat level is determined to be high and an alarm is triggered; if the final warning score is not greater than the dynamic warning threshold, the target is determined to be in a safe or low-threat state and no alarm is triggered.

[0031] Furthermore, in the process of generating the dynamic alarm interpretation vector, based on the dynamic alarm interpretation vector formula, the dynamic alarm interpretation vector is obtained by performing a Hadamard product operation on the optimal attribute weight vector and the standardized value vector of the evaluation attribute, which is used to characterize the dominant factor that triggers the alarm.

[0032] This invention provides a cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making. It has the following beneficial effects: 1. This invention establishes a feedback loop between the information layer and the physical layer by introducing hesitation potential energy and resource focusing instructions. When the consensus level is low, the hesitation potential energy is used to generate a control parameter gain vector, which directly drives the underlying sensor nodes to adjust physical parameters. The physical gain is then combined to correct the evaluation data. This mechanism differs from traditional methods that only perform numerical correction at the data level. It can reduce data uncertainty by improving physical observation conditions, thereby improving the quality and reliability of multi-source information fusion.

[0033] 2. This invention utilizes strategic game theory and linkage analysis to solve for optimal attribute weights and constructs a dynamic drift mechanism for the early warning threshold, which varies with the degree of consensus. By deriving a threshold sensitivity factor, the dynamic early warning threshold is positively correlated with the degree of consensus. In scenarios where there are significant disagreements among sensor nodes or the situation is ambiguous, the early warning threshold automatically decreases. This expands the alarm triggering range under the positive scoring logic of the MABAC algorithm, achieving adaptive adjustment of the early warning threshold and effectively reducing the risk of missed alarms in high-uncertainty environments.

[0034] 3. This invention generates a dynamic alarm interpretation vector simultaneously with the alarm triggering. This vector is obtained by performing a Hadamard product operation on the optimal attribute weight vector and the standardized value vector of the evaluation attribute, which can quantitatively represent the dominant factor triggering the alarm. This mechanism provides commanders with a decision-making basis based on the coupling of strategic game weights and physical threat characteristics, solving the problem that traditional early warning systems only output alarm signals without supporting judgment logic. Attached Figure Description

[0035] Figure 1 The flowchart shows the cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making of the present invention. Figure 2 This is a flowchart of the resource focusing and feedback closed-loop process based on hesitation potential energy of the present invention. Figure 3 This is a flowchart of the strategic game linkage and dynamic threshold drift of the present invention. Detailed Implementation

[0036] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Please see the appendix Figure 1 This invention provides a cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making, comprising the following steps: S100, Time-series weighted and primary aggregation of dynamic information: Raw evaluation data of a cluster target from multiple sensors over continuous time series are collected and quantized into an intuitionistic fuzzy set. Considering the dynamic characteristics of the cluster target, the inverse Poisson distribution method is used to calculate the time series weights at each time point. These time series weights are then used to dynamically weight and fuse the evaluation information from each sensor at different times, resulting in a multi-time-step aggregation matrix for a single sensor. The formula for calculating the time series weights is as follows: ; In the formula: For time series weights; Indexed by time point; These are parameters of the inverse Poisson distribution; The total number of points in time; This represents the factorial operation.

[0038] Subsequently, the multi-time aggregation matrices of each sensor are aggregated using the HM operator to generate the group integrated decision matrix; the HM operator aggregation formula is as follows: ; In the formula: The value after the HM operator is aggregated; In this context, it specifically refers to the total number of sensors participating in the assembly; and The input is an intuitive fuzzy number; and To adjust the parameters.

[0039] S200, based on the resource focus and consensus loop of hesitation potential energy: The deviation distance between the multi-time aggregation matrix of a single sensor and the group integrated decision matrix is ​​calculated, and the degree of consensus is calculated based on the deviation distance. Simultaneously, the hesitation potential energy of the system is calculated based on the current time series weights and hesitation degree. The formula for the intuitionistic fuzzy deviation distance is as follows: ; In the formula: This is the deviation distance; The number of cluster targets; For target index; For attribute indexing; Membership degree; Non-membership degree; Hesitation level; For the first A multi-moment aggregation matrix of multiple sensors; For group-based comprehensive decision matrix.

[0040] The formula for calculating hesitant potential energy is as follows: ; In the formula: For hesitation potential energy; This corresponds to the degree of hesitation. These are the weights for the time series.

[0041] The formula for consensus is as follows: ; In the formula: The degree of consensus.

[0042] If the consensus level is lower than a preset threshold, a resource focusing instruction is generated based on the hesitation potential energy. The resource focusing instruction is used to adjust the physical parameters of the underlying sensors. Feedback correction is performed on the evaluation values ​​that have not reached a consensus, and the resource focusing instruction is added. The feedback correction and resource allocation formulas are as follows: ; In the formula: This is the revised evaluation value; For elements in the group integrated decision matrix; The original assessment value; The mapping value of the resource focus instruction in the numerical field.

[0043] S300, Strategic Game Interaction and Dynamic Threshold Drift: A strategic conflict model between sensitive agents and stable agents is constructed. A game-theoretic linkage analysis is conducted using a minimum deviation model to solve for the optimal linkage coefficient and then determine the optimal attribute weights. The formula for finding the optimal weights in a game-theoretic interaction is as follows: ; In the formula: Represents the objective function of the minimization operation; The Euclidean norm (L2 norm) of a vector is used to measure spatial distance. For traversal indexes in linear combinations; This is the linkage coefficient; and This is the attribute weight vector; This represents the total number of attribute weight vectors.

[0044] The dynamic early warning threshold is calculated using the degree of consensus and the threshold sensitivity factor derived from the game outcome. The formula for calculating the dynamic early warning threshold is as follows: ; In the formula: The threshold is a dynamic early warning threshold; Basic threshold; Threshold sensitivity factor; The degree of consensus.

[0045] S400, MABAC Threat Scoring and Intelligent Interpretation: Based on the optimal attribute weights obtained in step S300, the MABAC (Multi-Attributive Border Approximation area Comparison) algorithm is used to rank and decide the threat of cluster targets. This process first calculates the weighted decision matrix of cluster targets, then determines the boundary approximation area, obtains the final warning score by calculating the distance matrix between the target to be evaluated and the boundary approximation area, and then executes the alarm trigger determination.

[0046] Calculation of the weighted decision matrix. The intuitionistic fuzzy elements in the group comprehensive decision matrix generated in step S100 are converted into numerical values ​​using the intuitionistic fuzzy scoring function, and then standardized to obtain a standardized matrix. Subsequently, combined with the optimal attribute weights obtained in step S300, the weighted values ​​of each objective are calculated according to the weighted decision matrix calculation formula. The weighted decision matrix calculation formula is as follows: ; In the formula: The first in the weighted decision matrix The first goal in Weighted values ​​on each attribute; The optimal attribute weight; These are the standardized attribute values.

[0047] Weighted decision matrix Expanded as follows: ; Calculation of the boundary approximation region matrix. Based on the weighted decision matrix, determine the baseline boundary value for each evaluation attribute. According to the boundary approximation region calculation formula, calculate the boundary approximation region value for each attribute, thus constructing the boundary approximation region matrix. The formula for calculating the boundary approximation region is as follows: ; ; In the formula: It is the first The boundary approximation region value of each attribute indicator represents the geometric average level of that attribute dimension; The total number of targets in the cluster; To evaluate the total number of attributes; It is the boundary approximation region vector composed of the boundary values ​​of each attribute.

[0048] Distance matrix calculation. The offset between the target to be evaluated and the boundary approximation region is calculated. Based on the distance matrix calculation formula, the weighted decision matrix and the boundary approximation region matrix are subtracted to obtain the distance matrix. The formula for calculating the distance matrix is ​​as follows: ; Distance matrix elements It represents the offset; like This indicates that the attribute belongs to the upper approximation region, i.e., it is in the high threat zone; like This indicates that the attribute belongs to the lower approximation region, i.e., it is in the low threat zone.

[0049] Final warning score calculation and alert determination. The attribute distance values ​​of each target in the distance matrix are summed, and the overall threat level is calculated according to the final warning score formula. The final warning score formula is as follows: ; In the formula: For the first The final early warning score for each target to be evaluated.

[0050] according to The values ​​are used to rank the targets to be evaluated, where... The larger the value, the greater the degree to which the target deviates from the safety boundary, and the higher the threat level.

[0051] After obtaining the final warning score, it is compared with the dynamic warning threshold output in step S300. Comparison. Due to the dynamic early warning threshold in this invention... It possesses the characteristic of automatically decreasing (drifting downwards) as information quality declines; therefore, the judgment logic for alarm triggering is as follows: When the final warning score is greater than the dynamic warning threshold ( If the target is determined to be a high-threat target, an alarm will be triggered immediately; When the final warning score is not greater than the dynamic warning threshold, the target is determined to be in a safe or low-threat state, and no alarm is triggered.

[0052] Generation of Dynamic Alarm Interpretation Vectors. Upon triggering an alarm, to reveal the strategic and physical causes behind it, interpretive information is generated based on the dynamic alarm interpretation vector formula. The dynamic alarm interpretation vector formula is as follows: ; In the formula: This is the dynamic alarm interpretation vector; This is the optimal attribute weight vector; To evaluate the standardized value vector of the attribute (corresponding to the standardized value vector mentioned above) (The vector formed) This is the Hadamard product operator.

[0053] This dynamic alarm interpretation vector illustrates the dominant factors coupled with weighted features that lead to alarm triggering, aiding in decision-making.

[0054] The temporal weighting and initial aggregation of dynamic information in step S100 involves converting sensor observation data from the physical world into intuitionistic fuzzy numbers suitable for computation, and then fusing them through both temporal and spatial dimensions. This process can be further broken down into the following sub-steps for detailed explanation: S101, Intuitive Fuzzy Quantization and Matrix Construction of Raw Data. Addressing the multi-source heterogeneous data characteristics present in cluster target threat assessment, the system first defines the target set. and evaluation attribute set The specific content of the assessment attributes includes, but is not limited to, operational intent, survivability, support capabilities, and command and control capabilities. For each assessment attribute, units deployed in different locations... Each sensor node serves as an information source, in continuous... The target was observed at several points in time.

[0055] For any point in time , No. The sensor is for the first The first goal The raw observation data obtained from each attribute is typically a physical quantity with dimensions (such as distance, velocity, radar cross section change rate, etc.). To eliminate the influence of dimensions and handle measurement uncertainties, this embodiment uses a fuzzy membership function to map the raw observation data into an intuitionistic fuzzy set (IFS). Specifically, for each observation value, its membership degree is calculated using a preset membership function (such as a trapezoidal distribution or a sigmoid distribution function). Non-membership degree The specific construction methods for membership functions and non-membership functions can be set by those skilled in the art based on the accuracy characteristics of the detection equipment and the prior knowledge of the target. These are well-known techniques in the field and will not be elaborated here.

[0056] After quantification, each evaluation element is represented as an intuitionistic fuzzy number. Calculate the degree of hesitation of the observation based on intuitionistic fuzzy set theory. Therefore, at every point in time... For each sensor Construct the initial decision matrix .

[0057] S102, Time series weight calculation based on inverse Poisson distribution. Considering the high dynamism of cluster targets in the battlefield environment, the contribution of data collected at different times to the threat assessment at the current time varies. Data closer to the current time contains more recent situational information and has higher reference value; conversely, data farther away from the current time has lower timeliness. To scientifically quantify this timeliness difference, this embodiment uses the inverse Poisson distribution method to calculate the time series weights.

[0058] The time series weights at each time point are calculated according to the following time series weight calculation formula: ; In the formula: For the first The time series weights at each time point, after normalization, satisfy the following conditions: ; This is a time point index, with values ​​ranging from 1 to... ,in This indicates the total length of the selected time series, i.e., the size of the time window; This is the inverse Poisson distribution parameter, which is used to adjust the rate at which the weights decay over time. The smaller the value, the greater the weight of recent data. This represents the factorial operation.

[0059] Through this step, the system obtains a set of weight vectors reflecting the timeliness of the data. .

[0060] S103, dynamic weighted fusion of multi-time information from a single sensor. After obtaining the time series weights, the system performs weighted fusion of information from a single sensor. exist The initial decision matrices at consecutive time points are vertically fused. This process utilizes the Intuitive Fuzzy Weighted Arithmetic Mean (IFWAA) operator or other equivalent Intuitive Fuzzy Integration operators to... matrices This is aggregated into a multi-moment aggregation matrix that reflects the comprehensive observation results of the sensor over a period of time. .

[0061] Merged matrix elements It retains the properties of intuitive fuzzy numbers, namely, including the fused membership degree, non-membership degree, and hesitation degree. This step effectively smooths out the instantaneous noise present in single-frame observations and enhances the robustness of the data by utilizing historical information.

[0062] S104, Multi-source group decision aggregation based on the HM operator. After completing the temporal fusion of a single sensor, the system needs to process the information fusion between multiple sensors in the spatial dimension. Since there is often an inherent correlation between the observation data of different sensors (e.g., radar and electronic reconnaissance equipment) on the same target, a simple weighted average may ignore the coupling relationship between these attributes. Therefore, this embodiment uses the Hamy Mean (HM) operator to perform multi-source group decision aggregation on all sensors. Multi-moment aggregation matrix of multiple sensors Perform horizontal aggregation to generate a group comprehensive decision matrix. .

[0063] The specific calculation basis for HM operator aggregation is as follows: HM operator aggregation formula execution: ; In the formula: The value after the aggregation of HM operators, i.e., the group integrated decision matrix. elements in ; In this context, it specifically refers to the total number of sensors participating in the assembly; and The input is an intuitive fuzzy number; and The non-negative parameter is used to adjust the sensitivity of the operator, controlling the sensitivity of the aggregation process to outliers and the degree of emphasis on the relationship between variables.

[0064] Through the above HM operator operations, the system will The observation data from individual heterogeneous sensors are fused into a unified swarm integrated decision matrix. ,in This comprehensively reflects the response of all sensors to the first [unclear] within the time window. Target No. The group judgment results for each attribute. This matrix. This will serve as the benchmark data for subsequent consensus assessment and threat ranking.

[0065] Please see the appendix Figure 2 Regarding step S200, the core logic of resource focusing and consensus closure based on hesitation potential energy lies in evaluating the quality of the fused information in two dimensions: first, the evaluation of consistency, i.e., determining whether the observation results of a single sensor deviate from the group consensus; second, the evaluation of determinism, i.e., quantifying the degree of ambiguity in the current situational awareness through hesitation potential energy. This step quantifies the above indicators through a mathematical model, providing a basis for subsequent physical resource scheduling. The specific implementation process is further broken down into the following sub-steps: S201, Calculation of intuitionistic fuzzy bias distance. To identify potentially faulty or interfered nodes in the network, the system needs to measure the difference between the judgments of individual sensors and the overall collective judgment. The system calls the multi-time aggregation matrix of the individual sensor nodes generated in step S100. Group Integrated Decision Matrix Since the elements of both matrices are intuitionistic fuzzy numbers, the traditional Euclidean distance cannot accurately reflect the differences in hesitation they contain. Therefore, this embodiment adopts a normalized intuitionistic fuzzy distance model that includes three-dimensional features of membership, non-membership, and hesitation.

[0066] The deviation distance between the individual sensor node matrix and the group integrated decision matrix is ​​calculated using the following intuitive fuzzy deviation distance formula: ; In the formula: For the first The deviation distance between individual sensors and the collective consensus; The total number of cluster targets within the detection range; For target index ( ); For attribute index ( ); , and The first The sensor for the first The first goal The membership degree, non-membership degree, and hesitation degree of each attribute evaluation value; , and Group integrated decision matrix The membership degree, non-membership degree, and hesitation degree of the corresponding elements.

[0067] This formula calculates the root mean square error in three-dimensional space by traversing all targets and all attributes, thereby achieving global quantification of the degree of sensor deviation.

[0068] S202, Determination of Consensus Level. Based on the deviation distance calculated above, the system further transforms it into an intuitive consensus level indicator. This indicator is used to measure the reliability of a single sensor node within the current observation period.

[0069] The degree of consensus is calculated according to the following formula: ; In the formula: For the first The degree of consensus among the individual sensors.

[0070] As can be seen from the formula, when the deviation distance When it approaches 0, the degree of consensus A value approaching 1 indicates that the sensor is highly consistent with the group's viewpoint; conversely, when... When it increases, Reduce. The system presets a consensus threshold. (For example This is used to determine whether a feedback correction mechanism needs to be activated.

[0071] S203, Quantitative calculation of hesitation potential energy. Besides assessing consistency, another core feature of this embodiment lies in assessing certainty. In cluster target threat early warning, sensors often produce ambiguous observation results due to long distances, significant interference, or target stealth characteristics; that is, the degree of hesitation within an intuitionistic fuzzy set. The potential energy is relatively large. In order to transform this microscopic hesitation into a macroscopic system state indicator, this embodiment introduces the physical concept of hesitation potential energy.

[0072] The hesitation potential depends not only on the current observational ambiguity but also on the temporal validity of the data. The system combines the time series weights calculated in step S100. Calculate the total hesitation potential energy of the system at the current moment. Specifically, follow the hesitation potential energy calculation formula: ; In the formula: Hesitation potential energy is a physical quantity that characterizes the total accumulated uncertainty after time weighting within the current time window. This corresponds to the degree of hesitation. The time series weights are the corresponding times when the observation data was generated.

[0073] This hesitation potential energy This is a key input variable for generating resource focusing instructions in subsequent steps. A high entropy value indicates that while the system may have reached a consensus (i.e., everyone agrees that it's unclear), the entropy of the information is too high to support accurate decision-making. In this case, the system needs to allocate physical resources based on this hesitation potential value to reduce the entropy, rather than simply making mathematical numerical corrections. This step represents a leap from data-layer evaluation to physical-layer perception.

[0074] Regarding the handling mechanism in step S200 when the consensus level does not meet the preset requirements, the system will initiate the generation and execution process of resource focusing instructions, and combine physical feedback to correct the evaluation value. This process realizes the leap from simple information layer data processing to physical layer sensor resource scheduling. The specific implementation process is further broken down into the following sub-steps: S204, Resource Focusing Instruction Generation Based on Hesitation Potential. When the calculated consensus level is lower than a preset consensus threshold, it indicates that there is a significant disagreement in the sensor network's observation of the cluster target at the current moment, and this disagreement is often accompanied by high uncertainty (i.e., high hesitation potential). The system first identifies the set of key attributes that lead to a decrease in consensus. Specifically, the system iterates through various evaluation attributes and selects the attributes that contribute the most to the deviation distance calculation (such as target speed or maneuver trajectory), which are denoted as conflict attributes.

[0075] Subsequently, the system uses the hesitation potential energy calculated in the aforementioned steps. And the degree of hesitation of conflict attributes, to generate resource focusing instructions. This resource focus instruction It is a gain vector of control parameters for the underlying physical sensor. For different types of sensors, Implementation corresponding to different hypothetical features: For radar detection equipment Specifically, this is manifested as an increase in the dwell time extension factor or the increase in the pulse repetition frequency (PRF), which aims to improve the signal-to-noise ratio by increasing the echo accumulation time, thereby reducing the uncertainty of the observation; For photoelectric / infrared detection equipment Specifically, this is reflected in the increase in the adjustment step size of the focal length or the amount of increase in the integration time, with the aim of obtaining higher resolution target image features. For electronic reconnaissance equipment Specifically, this is manifested in narrowing the scanning bandwidth or increasing the sampling rate of a specific frequency band, with the aim of enhancing the probability of intercepting signals from a specific radiation source.

[0076] In order to convert the above physical parameter adjustments into scalars suitable for mathematical formulas This embodiment uses a normalized mapping function. For example, let the increase in radar dwell time be... ,but ,in To adjust the coefficient, ensure The range of values ​​is within the range allowed by intuitionistic fuzzy number operations.

[0077] The specific adjustment control protocol and interface communication method for the aforementioned sensor parameters can be configured by those skilled in the art according to the specific hardware device manual. The underlying communication implementation is well-known in the field and will not be elaborated upon here. Resource focusing instructions are generated. The system transforms abstract mathematical uncertainties into specific physical resource requirements, ensuring that subsequent corrections are not merely numerical convergences, but are based on higher-quality physical observation data.

[0078] S205, Feedback Correction and Closed-Loop Control of Coupled Physical Gain. Simultaneously with issuing resource focusing commands, the system performs feedback correction operations on sensor node evaluation values ​​for which consensus has not been reached. Traditional feedback mechanisms rely solely on the group average to mathematically guide outliers, while the feedback correction mechanism proposed in this embodiment introduces resource focusing commands. As a correction, a modified model of physical-information coupling was constructed.

[0079] The feedback correction will be executed based on the following feedback correction and resource allocation formulas: ; In the formula: For the revised version The sensor for the first The first goal The evaluation value of each attribute; Group Integrated Decision Matrix Elements in; The original assessment value; This is the mapping value of the resource focusing instruction in the numerical domain. In the operation of intuitionistic fuzzy sets, this value is expressed as a positive gain on the membership degree or a negative suppression on the hesitation degree (the specific operation follows the rules of intuitionistic fuzzy algebra).

[0080] The physical meaning of this formula is that the corrected evaluation value retains the sensor's own observation characteristics (e.g., a weight of 0.5), absorbs the consensus information of the group (e.g., a weight of 0.5), and also adds the expected information gain brought about by the focusing of physical resources (e.g., enhanced radar power). ).

[0081] S206, Iterative determination of consensus state. After completing the correction of the evaluation value and the adjustment of physical resources, the system will submit the corrected evaluation matrix. The data is re-entered into the assembly process in step S100 to generate a new group comprehensive decision matrix, and the consensus determination in step S200 is executed again. The system detects the new deviation distance and consensus level. If the updated consensus level is still lower than the preset threshold, steps S204 to S205 are repeated, and the system is dynamically adjusted based on the new hesitation potential. The intensity of the iteration continues until the level of consensus reaches a preset requirement or a preset maximum number of iterations. Through this iterative closed loop, the system can force multi-source sensors to achieve a consistent understanding of the threat posed by the target by continuously optimizing physical observation conditions when facing complex cluster targets.

[0082] Please see the appendix Figure 3 Regarding the strategic game linkage and dynamic threshold drift in step S300, this process aims to resolve the decision-making conflict between high sensitivity and high stability in early warning systems under complex battlefield environments. Traditional early warning systems typically employ fixed thresholds or simple statistical adaptive thresholds, which are ill-equipped to handle deceptive interference from clustered targets. This embodiment introduces non-cooperative game theory, models different decision preferences as game participants, determines the optimal attribute weights by finding the Nash equilibrium point, and transforms the result of this strategic trade-off into the dynamic drift of the early warning threshold. The specific implementation of this process can be further broken down into the following sub-steps for detailed explanation: S301, Game Theory Linkage Analysis and Optimal Weight Solution Based on Minimizing Deviation. In cluster target threat assessment, the contribution of different assessment attributes (such as target speed, distance, maneuvering amplitude, electromagnetic radiation intensity, etc.) to threat determination dynamically fluctuates with changes in the situation. To obtain objective attribute weights that conform to the current situation, the system first constructs an attribute weight vector set. This set contains basic weight vectors calculated by various weighting methods (such as intuitionistic fuzzy entropy weighting, coefficient of variation method, or CRITIC method (Criteria Importance Through Intercriteria Correlation)).

[0083] Among them, the Intuitive Fuzzy Entropy Weight Method focuses on the degree of data dispersion and is defined as a stability proxy; while the CRITIC method focuses on the conflict between indicators and is defined as a sensitivity proxy.

[0084] For the specific calculation method of the above basic weight vector, those skilled in the art can use existing multi-attribute decision weight algorithms, and the calculation process is a well-known technology in this field, so it will not be described in detail here.

[0085] Suppose the system has obtained Basic weight vectors , ,……, To find an optimal compromise among these potentially conflicting weight allocation schemes, this embodiment constructs a game theory-based linkage analysis model. This model treats each weight allocation scheme as a game participant (e.g., the intuitionistic fuzzy entropy weighting method represents a participant concerned with data volatility). The goal of the game is to find an optimal linear combination coefficient that minimizes the total deviation between the combined weight vector and the individual basic weight vectors, thereby achieving an equilibrium state acceptable to all parties.

[0086] The optimal linkage coefficient and attribute weights are determined by following the formula for finding the optimal linkage weights in game theory: ; In the formula: Represents the objective function of the minimization operation; The Euclidean norm (L2 norm) of a vector is used to measure spatial distance. For traversal indexes in linear combinations; This is the linkage coefficient; and This is the attribute weight vector; This represents the total number of attribute weight vectors.

[0087] The system obtains the normalized optimal linkage coefficient by solving the above system of linear equations. And based on this, the final optimal attribute weight vector is calculated. .Should This reflects the objective laws inherent in the data itself, providing a robust parameter basis for subsequent threat scoring.

[0088] S302, Derivation of threshold sensitivity factor and calculation of dynamic early warning threshold. Obtaining optimal attribute weights. Subsequently, the system does not stop at static evaluation, but further utilizes the results of game theory analysis to adjust the system's alarm threshold. This embodiment defines a threshold sensitivity factor. This factor is composed of The weighting of key high-risk attributes (such as attack intent or distance within weapon range) determines the risk level. The physical meaning of this term lies in characterizing the system's tolerance for the risk of underreporting under the current strategic situation: The larger the value, the more likely the system is to issue alerts quickly.

[0089] Subsequently, the system combines the consensus level calculated in step S200. The system calculates dynamic early warning thresholds in real time. The core logic of this calculation mechanism is as follows: when the consensus of the sensor network is high, the information is highly reliable, and the system maintains a normal threshold to avoid false alarms; when the consensus is low (i.e., the situation is ambiguous and chaotic), the system automatically lowers the alarm threshold and implements a drift strategy to improve the ability to detect potential hidden threats.

[0090] The dynamic early warning threshold is calculated according to the following formula: ; In the formula: This value serves as the dynamic early warning threshold and is the direct benchmark for determining whether an alarm should be triggered. This is a preset baseline threshold, which is typically set based on the false alarm rate requirements in peacetime or standard environments, for example... ; This is the threshold sensitivity factor, and its value range is typically [value range missing]. Its value is determined by the distribution characteristics of the game weights; To determine the degree of consensus, the range of values ​​is: .

[0091] From this formula, we can see that the dynamic early warning threshold is... Degree of consensus They show a positive correlation. When As the value approaches 1, the correction term approaches 0. ;when When the signal is significantly reduced (e.g., due to strong interference causing disagreement among sensors), The item increased rapidly, leading to Significantly lower This downward drift characteristic of the threshold enables the system to automatically enter a high-alert state when facing cluster targets with high uncertainty (high hesitation potential energy). This allows for early warning to be triggered before the threat signal reaches an absolute high level but the situation is extremely chaotic, effectively solving the technical problem of slow response of traditional fixed thresholds in complex electromagnetic environments.

[0092] Based on the dynamic warning threshold and optimal attribute weight output in step S300, step S400 further performs specific threat level quantification and decision response.

[0093] This step utilizes the MABAC (Multi-Attributive Border Approximation area Comparison) algorithm in the Multi-Criterion Decision Method (MCDM) to measure the degree of deviation of targets by constructing a border approximation area, thereby ranking the comprehensive threat level of cluster targets, and implementing alarm determination in combination with the dynamic threshold calculated in the previous steps.

[0094] Furthermore, to enhance the interpretability of the early warning system, this step also generates explanation vectors for human-computer interaction. The specific implementation process is further broken down into the following sub-steps: S401, Construction of the weighted decision matrix and boundary approximation region. The system first processes the group comprehensive decision matrix generated in step S100. Preprocessing is performed. Because... The elements in the matrix are intuitionistic fuzzy numbers. The system uses an intuitionistic fuzzy scoring function to convert them into real values ​​and then performs standardization to obtain a standardized matrix. This process eliminates the influence of different dimensions and provides a unified data foundation for subsequent calculations.

[0095] Subsequently, the system combines the optimal attribute weights obtained from the game theory solution in step S300. A weighted decision matrix is ​​constructed. This matrix not only reflects the physical characteristics of the target, but also incorporates strategic preferences under the current tactical situation (e.g., sensitivity to speed is higher than that to distance).

[0096] The weighted decision matrix is ​​calculated according to the following formula: ; In the formula: The first in the weighted decision matrix The first goal in Weighted values ​​on each attribute; The optimal attribute weight; These are the standardized attribute values.

[0097] Based on this, a weighted decision matrix is ​​constructed. .

[0098] Based on this, the system calculates the Border Approximation Area (BAA) for each evaluation attribute. The BAA represents the average or baseline state of the current cluster target across each attribute dimension.

[0099] The boundary approximation region is calculated according to the following formula: ; ; In the formula: It is the first The boundary approximation region value of each attribute indicator represents the geometric average level of that attribute dimension; The total number of targets in the cluster; To evaluate the total number of attributes; It is the boundary approximation region vector composed of the boundary values ​​of each attribute.

[0100] S402, Distance matrix calculation and final early warning score generation. After determining the baseline boundary... Then, the system calculates the distance matrix between the target to be evaluated and the boundary approximation region. .

[0101] This matrix quantifies the degree of deviation of each target from the baseline state for each attribute. A positive deviation value indicates that the attribute is in the upper approximation region, meaning it exhibits a threat characteristic above average for that attribute; a negative deviation value indicates that the attribute is in the lower approximation region, meaning it has a lower threat level.

[0102] The distance matrix is ​​calculated according to the following formula: ; Elements in the distance matrix .

[0103] Subsequently, the attribute distance values ​​of each target in the distance matrix are summed to obtain the final warning score. This score reflects the overall degree of deviation of the target from the safety boundary.

[0104] The final warning score is calculated according to the following formula: ; In the formula: For the first The final early warning score for each target to be evaluated.

[0105] according to The values ​​are used to rank the targets to be evaluated, where... The larger the value, the greater the degree to which the target deviates positively from the security boundary, that is, the higher the overall threat level of the target to be assessed.

[0106] S403, alarm triggering determination based on drift threshold. After obtaining the final warning score... Then, the system compares it with the dynamic early warning threshold calculated in real time in step S300. The comparison is performed. The judgment logic is as follows: like If the target is identified as a high-threat target, the system will immediately trigger an alarm.

[0107] This embodies the core innovative mechanism of the present invention: due to the dynamic early warning threshold. Degree of consensus Positive correlation (i.e.) Follow (decreases due to a drop in data), when inconsistent sensor data or chaotic situation leads to... When it decreases, It will execute a downward drift strategy (e.g., drifting from a positive value to a negative value). Under the MABAC logic that a higher value represents a higher threat, the threshold... The reduction means a lower threshold for triggering alarms.

[0108] Therefore, in a chaotic situation, even the target's threat score It has not yet reached an absolute high level, making it easier to satisfy [the needs of those in need]. This enables agile early warning (high-sensitivity response) of covert threats or deceptive interference.

[0109] S404, Generation and Output of Dynamic Alarm Explanation Vector. To address the problem that traditional early warning systems only output alarm signals without providing decision-making support, the system generates a dynamic alarm explanation vector simultaneously with the triggering of an alarm. This vector combines the underlying attribute evaluation values ​​with the top-level strategic game weights, intuitively revealing the root cause of the alarm triggering.

[0110] Generate dynamic alarm interpretation vectors, specifically based on the following dynamic alarm interpretation vector formula: ; In the formula: This is the dynamic alarm interpretation vector, and its dimension is consistent with the number of evaluation attributes; The optimal attribute weight vector reflects the system's current strategic focus (e.g., whether it is currently more concerned with speed or distance). To evaluate the standardized value vector of the attribute (corresponding to the standardized value vector mentioned above) (The vector formed) This is the Hadamard product operator.

[0111] The vector The larger the value in the vector, the higher the physical threat level of the corresponding attribute, and the higher the weight it is assigned by the current strategic game model. Therefore, it is the dominant factor leading to alarm triggering. The system outputs this vector to the display and control terminal to help commanders quickly understand the tactical meaning of the alarm in a visual form (such as a radar chart or heat map).

[0112] In summary, the cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making provided in this embodiment first establishes an intuitionistic fuzzy information processing mechanism targeting the dynamic characteristics of cluster targets. By introducing an inverse Poisson distribution model to construct time series weights, the importance of data in the evaluation can be automatically adjusted according to the time label of the data, ensuring that the early warning results can keenly capture the latest maneuver characteristics of the target while retaining the reference value of historical trajectories. Combined with the spatial aggregation capability of the HM operator, this method effectively solves the data fragmentation problem of multi-source heterogeneous sensors when facing distributed cluster targets, fusing scattered observation data into group comprehensive decision-making information with spatiotemporal consistency.

[0113] Building upon this foundation, this embodiment constructs a feedback closed-loop mechanism for deep coupling of physical information. Unlike traditional methods that merely remove outliers at the data level, this method introduces the physical quantity of hesitation potential energy to characterize the macroscopic uncertainties encountered. When a decrease in the consensus level of the sensor network is detected, it is not simply judged as a sensor failure, but rather as a signal of increased environmental complexity. Based on the hesitation potential energy, specific resource focusing instructions are generated, directly driving the underlying physical sensors to adjust their operating parameters, including extending radar dwell time or increasing the integration time of photoelectric detection. This mechanism enables proactive adjustment of the sensing mode, reducing observational ambiguity at the source through dynamic tilting of physical resources, achieving a physical-level improvement in data quality.

[0114] At the decision-making logic level, this embodiment uses game-theoretic linkage analysis instead of traditional fixed weight allocation. By constructing a strategic conflict model between sensitive and stable agents, the optimal attribute weight configuration can be dynamically sought based on the principle of minimizing deviation in each evaluation cycle. More importantly, this method establishes a consensus-based threshold drift mechanism.

[0115] By coupling a sensitivity factor derived from game theory analysis with the real-time level of consensus, an adaptive floating of the early warning threshold is achieved. When the situation is clear, a conventional threshold is maintained to suppress false alarms; however, when the situation is chaotic or there are significant disagreements among sensors, the early warning threshold is automatically lowered, implementing agile early warning. This design improves responsiveness in scenarios with strong interference or covert attacks by establishing an inverse correlation control logic between the threshold and information quality.

[0116] Finally, this method achieves interpretable output of early warning results through the MABAC algorithm and interpretation vector generation mechanism. It not only outputs quantified threat scores and alarm signals but also simultaneously generates dynamic alarm interpretation vectors. These vectors map the underlying physical threat characteristics to the top-level strategic game weights, intuitively showing commanders whether the dominant factor triggering the alarm is the physical approach of the target or strategic attention. This establishes a quantified decision interpretation channel, providing strategically in-depth decision support for cluster target defense.

Claims

1. A cluster target threat early warning method based on intuitionistic fuzzy game theory and consensus decision-making, characterized in that, Includes the following steps: S1. Collect the raw evaluation data of multi-source sensor nodes for the cluster target, and quantize the raw evaluation data into an intuitionistic fuzzy set. Based on time series weights and HM operator aggregation, output the multi-time aggregation matrix and group comprehensive decision matrix of a single sensor node. S2. Calculate the deviation distance and consensus degree between the multi-time aggregation matrix of the single sensor node and the group comprehensive decision matrix, and compare it with the hesitation potential energy and the preset consensus threshold. When the consensus degree is lower than the preset consensus threshold, trigger the resource focusing and feedback correction process, generate the corrected evaluation information, update the multi-time aggregation matrix of the single sensor node to regenerate the group comprehensive decision matrix. S3. Based on a strategic conflict model, the optimal attribute weights are solved through game theory analysis, and a dynamic early warning threshold is output in combination with the consensus level. S4. Based on the optimal attribute weights and the group comprehensive decision matrix, the MABAC algorithm is used to generate the final warning score of the cluster target. The final warning score is compared with the dynamic warning threshold. When the final warning score is greater than the dynamic warning threshold, an alarm is triggered, and a dynamic alarm interpretation vector is generated according to the optimal attribute weights.

2. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, The S1 step specifically includes: Define the evaluation attributes of cluster targets, including combat intent, survivability, support capability and command and control capability, and use the membership function to map the original evaluation data into the intuitionistic fuzzy set containing membership degree, non-membership degree and hesitation degree. Based on the time series weight calculation formula, the time series weight of each time point is calculated, and the time series weight is used to dynamically weight and fuse the intuitionistic fuzzy set of each multi-source sensor node at different times to obtain the multi-time aggregation matrix of the single sensor node. Based on the HM operator aggregation formula, a horizontal aggregation operation is performed on the multi-time aggregation matrices of all the individual sensor nodes to generate the group integrated decision matrix.

3. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S2, the calculation of the deviation distance and the degree of consensus specifically includes: Based on the intuitionistic fuzzy deviation distance formula, the root mean square error of the corresponding elements in the multi-time aggregation matrix of the single sensor node and the group comprehensive decision matrix in terms of membership degree, non-membership degree and hesitation degree is calculated to obtain the deviation distance; Based on the consensus degree formula, the consensus degree is obtained by establishing an inverse relationship with the deviation distance.

4. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 2, characterized in that, In step S2, the calculation of the hesitation potential energy specifically includes: Based on the formula for calculating hesitation potential energy, the hesitation potential energy, which represents the total amount of uncertainty, is obtained by accumulating the product of the hesitation degree of all cluster targets and all the evaluation attributes in the intuitive fuzzy set within the detection range with the time series weight at the corresponding time.

5. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S2, the resource focusing and feedback correction process specifically includes: When the consensus level is lower than the preset consensus threshold, the conflict attribute that causes the consensus level to decrease is identified, and the resource focusing instruction is generated using the hesitation potential energy and the hesitation degree of the conflict attribute. The resource focusing instruction is the control parameter gain vector for the underlying multi-source sensor node. Based on the feedback correction and resource allocation formula, the corrected evaluation information is calculated using the group comprehensive decision matrix, the resource focusing instruction, and the evaluation information that has not reached consensus in the multi-time aggregation matrix of the individual sensor node. The preset consensus threshold is a lower limit of consensus pre-set based on the statistical distribution of historical consistency data of the sensor network under standard operating conditions or expert experience.

6. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S3, the game-theoretic linkage analysis specifically includes: Construct the strategic conflict model that includes sensitive agents and stability agents, wherein the sensitive agents are constructed based on a weighting method that reflects the conflict of indicators, and the stability agents are constructed based on a weighting method that reflects the degree of data dispersion; Based on the optimal weight solution formula of game linkage, the linkage coefficient of the sensitive agent and the stable agent in the combination is solved so that the total deviation between the combined weight vector and the basic weight vectors corresponding to the sensitive agent and the stable agent is minimized, thereby obtaining the optimal attribute weight.

7. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S3, the output of the dynamic early warning threshold specifically includes: The dynamic early warning threshold is calculated based on the dynamic early warning threshold calculation formula, using the basic threshold, the threshold sensitivity factor derived from the optimal attribute weight, and the degree of consensus. The basic threshold is an alarm threshold that is preset based on the false alarm rate requirements of the early warning system in non-wartime or standard electromagnetic environments.

8. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S4, the generation of the final warning score specifically includes: The group integrated decision matrix is ​​numericalized and standardized using an intuitionistic fuzzy scoring function. Based on the formula for calculating the weighted decision matrix, the standardized matrix is ​​weighted using the optimal attribute weights to obtain the weighted decision matrix. Based on the formula for calculating the boundary approximation region, the geometric mean of each evaluation attribute in the weighted decision matrix is ​​calculated to form the boundary approximation region matrix; Based on the distance matrix calculation formula, the difference between the weighted decision matrix and the boundary approximation region matrix is ​​calculated to obtain the distance matrix; Based on the final warning score formula, the differences of the same cluster targets in the distance matrix across all evaluation attributes are summed to calculate the final warning score.

9. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S4, the logic for comparing the final warning score with the dynamic warning threshold specifically includes: The final early warning score is compared with the dynamic early warning threshold; If the final warning score is greater than the dynamic warning threshold, the target threat level is determined to be high, and the alarm is triggered. If the final warning score is not greater than the dynamic warning threshold, the target is determined to be in a safe or low-threat state, and the alarm is not triggered.

10. The cluster target threat early warning method based on intuitionistic fuzzy game and consensus decision-making according to claim 1, characterized in that, In step S4, the generation of the dynamic alarm interpretation vector specifically includes: Based on the dynamic alarm interpretation vector formula, the dynamic alarm interpretation vector is obtained by performing a Hadamard product operation on the vector of the optimal attribute weights and the standardized value vector of the evaluation attribute, which is used to characterize the dominant factor that triggers the alarm.

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