The cloud model is a mathematical tool for addressing uncertainty problems, initially proposed by Chinese Scholar Li Deyi in 1995. It organically integrates fuzziness and randomness through bidirectional transformations between quantitative numerical values and qualitative concepts, enabling the representation, reasoning, and decision-making of uncertain knowledge ([19]).

Definition 1 ([19]; [17]): SupposeU is a given universe of discourse representing the quantitative value range corresponding to qualitative concept C in the cloud model. For any element x in U, the membership degree μ(x) ∈ [0, 1] reflects its belonging intensity to C, constituting a random number with stable tendency. A cloud drop represents a concrete numerical instantiation of the qualitative concept within the universe, where each drop’s positional value x reflects quantitative characteristics while μ(x) indicates qualitative membership strength. The distribution of μ(x) over universe U is termed a cloud, with each constituent cloud drop denoted as (x, μ(x)).

Definition 2 ([18]): The cloud model characterizes the uncertainty of qualitative concepts through three fundamental numerical parameters: expectation E_x, entropy E_n, and hyper-entropy H_e. The expectation E_x represents the central value of the qualitative concept within the universe of discourse, corresponding to the most representative numerical instantiation of the concept, analogous to the peak position in traditional fuzzy sets. The entropy E_n quantifies both the fuzziness and randomness of the qualitative concept, indicating the magnitude of conceptual uncertainty. Greater entropy values correspond to increased conceptual ambiguity and stronger randomness, whereas smaller values indicate clearer concepts approaching traditional precise numerical representations.

Definition 3 ([18]): The most prevalent variant of the cloud model, referred to as the normal cloud model, is mathematically defined as Equation (1):

where E ′ n presents a normally distributed random variable that captures the randomness of entropy, thereby ensuring uncertainty in the determination degree of each cloud droplet. The morphology of the normal cloud model is jointly determined by these three parameters, as shown in Figure 1.

Figure 1. Normal cloud model digital characteristic diagram.

Dempster-Shafer (D-S) theory, initially proposed by Dempster in 1967 ([4]) and later expanded by Shafer in 1978 ([27]), is a mathematical framework for processing imprecise, uncertain, and partial information. Its fundamental principle involves quantifying propositional support through Basic Probability Assignment, enabling the combination of multi-source evidence with particular efficacy for conflict evidence synthesis. Distinct from conventional probability theory, evidence theory permits more flexible representation of uncertainty by avoiding precise probability assignments when evidence remains insufficient. Instead, it characterizes event confidence through interval-valued belief measures.

Definition 4 ([6]): Basic Probability Assignment (BPA) Function. Suppose Θ be the frame of discernment, constituting a complete set of mutually exclusive and exhaustive elementary events. The basic probability assignment function m : 2 Θ → [ 0 , 1 ] satisfies:

m ( A ) represents the precise degree of belief in proposition A, quantifying the evidence’s support for A.

Dempster’s Combination Rule: Suppose m 1 ( B ) and m 1 ( C ) be basic probability assignment functions derived from distinct evidence sources within the same frame of discernment Θ . The combined basic probability assignment function is given by:

where K denotes the conflict coefficient, quantifying the degree of conflict between m 1 and m 2 , with 0 ≤ K ≤ 1 .

3.1.1. Calculation of Cloud Model Parameters

Assume there are m indicators in the evaluation index system, each with a valid universe of discourse [ x min , x max ] . For quantitative indicators, the grade intervals are determined via equidistant partitioning, where the scoring interval for grade k-th is [ a k , b k ] . The theoretical cloud parameters can then be calculated using the following formulas:

where λ denotes the hyper-entropy coefficient, which is typically assigned a value within the range [0.1, 0.3].

3.1.2. Membership Matrix Construction

The membership matrix for each indicator is typically calculated based on the cloud model’s certainty function. Consider a system with m indicators and n evaluation grades. For the i-th indicator, the cloud parameters corresponding to the k-th grade are defined as: expectation value E x i , k , entropy E n i , k , and hyper-entropy H e i , k . The membership degree of the i-th indicator with respect to grade k is computed via the normal cloud generator, expressed by the following formula:

E ′ n i , k is a normally distributed random variable following N ( E n i , k , H e i , k 2 ) , representing the uncertainty of entropy. For practical computation of the membership matrix, a simplified approach typically assumes E n i , k = E ′ n i , k (disregarding the randomness of hyper-entropy by using the expectation value of entropy). Under this simplification, the formula reduces to:

The membership degree vector for the i indicator across all n grades is constructed as: μ i = [ μ i , 1 , μ i , 2 , ⋯ , μ i , n ] , where each element is computed via the Equation (9).

3.2.1. Evidence-Based Processing of Evaluation Trustworthiness

The transformation of cloud model membership degrees into Basic Probability Assignment functions integrates evidence theory with cloud modeling uncertainty characteristics through the introduction of an uncertainty grade θ as a focal element, constructing an extended frame of discernment: Θ = { C 1 , C 2 , ⋯ , C n , θ } , where C k represents definite assessment grades, θ corresponds to unassignable cases. The resulting mass function is defined as:

3.2.2. Correction of Basic Probability Assignment Functions with Tensor Networks

In evidence theory, mass functions are employed to represent the allocation of uncertainty to propositions. However, traditional approaches face the following challenges when processing high-dimensional data or complex evidential relationships: 1) Dimensional explosion: As the dimensionality of evidence increases, the storage and computational complexity of mass functions grow exponentially; 2) Inadequate modeling of complex dependencies: Conventional methods struggle to capture nonlinear and higher-order dependencies among evidence; 3) Incomplete representation: In high-dimensional scenarios, traditional mass functions may fail to accurately characterize evidential conflicts, redundancies, or hierarchical structures. Tensor networks constitute a mathematical tool for efficiently representing and manipulating high-dimensional tensors. By decomposing high-dimensional tensors into structured products of lower-dimensional tensors, they significantly reduce computational complexity while preserving the tensors’ essential geometric and algebraic properties ([30]; [26]). The integration of TN into evidence theory for mass function correction systematically addresses the aforementioned challenges.

Suppose there are m pieces of evidence E 1 , E 2 , ⋯ , E m , where each evidence is associated with a mass function m i : 2 Θ → [ 0 , 1 ] . To embed these mass functions into tensor space, three key operations are performed:

1) Construction of high-dimensional evidence tensors

Each focal element B ∈ Θ is mapped to an n-dimensional binary vector b = ( b 1 , b 2 , ⋯ , b n , θ ) , when b k = 1 if and only if C k ∈ B .

Construction of Evidence Tensor M ∈ ℝ m × ( 2 n − 1 ) : Each evidence E i constitutes the i-th slice of the tensor, containing mass values for its focal elements. The element at row i and column j corresponds to m i ( B j ) , where B j denotes thej-th non-empty focal element. For large n, direct storage of the 2 n -dimensional tensor becomes computationally infeasible. Sparse tensor representation and Tensor Decomposition are employed.

2) Tensor decomposition and high-dimensional correlation modeling

The evidence tensor ℳ is decomposed into a sum of R rank-1 tensors via CP decomposition to capture higher-order correlations among evidence sources:

where u r ( E ) ∈ ℝ m represents the evidence weight vector in the r-th latent dimension, characterizing inter-evidence correlations in the semantic space, while u r ( Θ ) ∈ ℝ 2 n − 1 denotes the focal element semantic vector in the r-th dimension, capturing high-dimensional semantic features of focal elements. The symbol ∘ indicates the tensor outer product operation.

3) Tensor Network-Based Evidence Similarity Computation

The similarity between evidence E i and E j is defined as the cosine similarity of their corresponding tensor slices:

where m i denotes the mass vector of evidence E i .

The collaborative similarity among k pieces of evidence E i 1 , E i 2 , ⋯ , E i k is defined as the higher-order inner product of their corresponding tensor slices:

where the operator “⋅” denotes tensor contraction along the focal element dimension, with the resulting value quantifying the consistency of support patterns across the k pieces of evidence.

4) Tensor network-corrected mass function update

The modified mass function is obtained by using high-dimensional similarity tensor to adjust the credibility of evidence.

Evidence support degree calculation: An hyperparameter λ ≥ 0 is introduced to fuse the k-th order support degrees into an aggregated support measure:

In Equation (14), the hyperparameter λ = 0.5 serves as the neutral value for balancing the second-order similarity (direct evidence correlation) and the higher-order similarity (indirect evidence synergy). Considering that the conflict risk indicators in this study cover multiple dimensions such as politics, military, and economy, direct correlation (such as military expenditure and military force size) and indirect synergy (such as the combined effect of political stability and economic mutual trust) are equally important for risk assessment. With λ = 0.5, it can avoid model deviation caused by single-dimensional dependence and is suitable for the assessment scenarios of multi-factor coupling.

Mass function correction: Weight the original mass function according to the support degree S i .

The corrected mass function must satisfy the normalization condition ∑ B ⊆ Θ m ′ i ( B ) = 1 .

3.3.1. Evidence-Based Processing of Evaluation Trustworthiness

Evidence theory is highly sensitive to the rationality of evidence weights, and unreasonable weights may lead to failure in conflict resolution. To address this issue, this paper comprehensively considers subjective and objective weights, and improves evidence theory based on game-theoretic combination weighting. By using combined weights, the influence of highly conflicting evidence is reduced, thereby minimizing its interference in the fusion process.

1) Subjective weights

The G1 method is used to calculate subjective weights. Its core logic involves ranking the indicators by importance and setting the importance ratio coefficients between adjacent indicators, thereby recursively calculating the weights of each indicator. The ordinal relationships and ratio coefficients directly reflect the relative importance among the indicators. Experts compare the importance of adjacent indicators x k − 1 and x k , providing the ratio coefficient r k , which represents the multiple of importance of x k − 1 relative to x k .

where w k − 1 is the weight relationship between adjacent indicators, w n is the weight of the last indicator and w k is the weight of other indicators.

Calculate the maximum eigenvalue λ max and the eigenvector w s of the judgment matrix. After normalization, the subjective weight vector is obtained:

2) Objective weights

The similarity coefficient between pieces of evidence is employed to measure their degree of similarity. A higher similarity indicates greater support between indicators. The objective weights w 2 are determined based on the degree to which evidence is supported by other evidence. Cosine similarity is adopted to quantify the evidential similarity between indicators:

where e i and e j represent the evidence vectors of indicators i and j, respectively. A higher S i m ( i , j ) indicates stronger evidential consistency between indicators i and j.

The support degree of indicator i is the sum of similarity coefficients from all other indicators:

The support degree reflects the extent to which indicator i is supported by other evidence and the higher the support degree, the greater the objective credibility.

Normalize the support degrees and derive the objective weights.

3) Game-theoretic combined weights

The Lagrangian function is constructed.

where μ is the Lagrange multiplier for the normalization constraint, g k ( w ) is the constraint function for support degree and expert priority, ν k is the multiplier for the constraint condition.

Solve for the optimal weights and take the partial derivative of w i and set it to 0.

Combined with the normalization condition, the solution is obtained as:

The parameter μ is iteratively adjusted to satisfy the condition ∑ w i = 1 .

Evidence support degree calibration. If the support degree of a given indicator i is negatively correlated with the combined weight, its weight is forcibly increased:

δ is the calibration coefficient.

3.3.2. Evidence Fusion Based on Quantum-Entanglement-Weighted Averaging

It should be emphasized that the quantum entanglement utilized in this study refers to a mathematical formalism borrowed from quantum mechanics, rather than physical quantum mechanical phenomena. We employ the mathematical concepts of probability amplitude and interference effect to model the nonlinear correlations and synergistic effects among inter-state conflict risk indicators. The core purpose is to transform the complex interdependencies among multi-dimensional indicators into computable mathematical relationships (i.e., the entanglement coefficient in Equation (25)), rather than implying that the risk assessment process involves physical quantum mechanical mechanisms. This mathematical formalism provides a flexible tool for characterizing the non-independent interactions between indicators, which is consistent with the practical characteristics of inter-state conflict risk factors that are mutually influential and synergistic.

One of the core characteristics of inter-state conflict risk is the interconnectedness of risks across multiple domains, such as the synergistic effects of military deterrence and economic sanctions, or the transmission relationship between political confrontation and social unrest. In traditional evidence theory, the mass functions of indicators are often assumed to be independent events, synthesized merely through simple linear superposition or Dempster’s rule, neglecting the strategic interdependencies among indicators. Quantum-entanglement-weighted evidence fusion introduces the concept of “quantum entanglement” to transform the nonlinear correlations among indicators into “entanglement weights,” enabling the evidence fusion process to dynamically reflect such strategic interaction effects.

Quantum-entanglement-weighted evidence fusion is grounded in the superposition principle of quantum mechanics, representing experts’ perceptions of “uncertain events” as “probability amplitudes” (rather than classical probabilities). Through “entangled superposition,” it more accurately conveys risk information that is “possible yet uncertain.”

Suppose the modified evidence set be { E 1 , E 2 , ⋯ , E m } , which is output through the high-order similarity of the tensor network.

1) Construct the entanglement coefficient matrix Γ ∈ ℝ m × m , where r i j represents the entanglement strength between evidence E i and E j .

Pairwise similarity: s i j = m ′ i ⋅ m ′ j ‖ m ′ i ‖ ⋅ ‖ m ′ j ‖ , normalization of focal element vector dot products.

Third-order similarity: s i j k = ∑ B ⊆ Θ m ′ i ( B ) ⋅ m ′ j ( B ) ⋅ m ′ k ( B ) , Joint support degree of three pieces of evidence for the same focal element

Hyperparameters: λ adopts the setting of λ = 0.5, maintaining consistency with the method in Equation (14). The core logic of this value is the direct and indirect correlations among multiple indicators of the neutral balance, which conforms to the multi-dimensional characteristics of conflict risks between China and ASEAN countries. It ensures that key correlation information is not omitted during the integration process, while avoiding the interference of redundant information.

Symmetry: λ i j = λ j i , Non-directionality of inter-evidence correlations.

2) Calculate the evidence relevance degree to measure the importance of evidence E i in the correlation network.

The larger C i , the stronger the synergistic effect between evidence E i and other evidence.

3) Derive the entanglement weighting factor by integrating game-theoretic weights and relevance degrees to generate dynamic weighting factors.

4) Quantum-entanglement-weighted averaging: Perform weighted fusion on the modified mass functions.

Based on the content of the previous two sections, this section will construct a risk assessment and decision-making method using the improved evidence theory as the decision framework. The game-theoretic combined weighting method is employed to determine the weights of indicators during the decision-making process. Meanwhile, the cloud model is utilized to convert continuous data into discrete data. Additionally, the improved evidence theory is applied to address the high uncertainty in multi-source information fusion during decision-making. In summary, this section will develop a novel risk assessment and decision-making method to tackle real-world problems characterized by numerous risk factors and high uncertainty in multi-source information.

In risk assessment and decision-making problems, identifying the research object and subsequently conducting risk assessment are undoubtedly prerequisites and guarantees for making correct decisions. Therefore, risk factor analysis and the construction of a risk criterion system must be performed before decision-making to establish a scientific and comprehensive risk assessment and decision-making process. This section adopts a method integrating the cloud model and improved evidence theory as the decision framework for multi-criteria decision-making (MCDM). The game-theoretic combined weighting method is incorporated into the MCDM process as a tool for determining indicator weights, thereby forming a novel risk assessment and decision-making approach, as illustrated in Figure 2.

Figure 2. Risk assessment and Decision-Making method based on cloud model and improved evidence theory.

1) Measurement method based on cloud model

The forward cloud generator is employed to determine the numerical characteristics of the cloud model, generating a large number of cloud droplets that conform to the distribution features. By establishing a set of evaluation ratings, the benchmark cloud transformation models for each rating level are obtained. Before the evidence theory yields a comprehensive evaluation result, it is necessary to determine the basic probability assignment (BPA) functions of each evaluation indicator in the scheme, which can be derived from the belief degree functions calculated by the cloud model. After obtaining the numerical characteristics of the cloud model corresponding to each evaluation indicator, the X-conditional forward cloud generator is used to compute the belief degree of each evaluation indicator under the standard cloud. The belief degrees are then normalized to derive the belief degree function of each evaluation indicator across the evaluation ratings.

2) Tensor network correction for high-dimensional evidence

To address the issues of dimensionality explosion and inadequate dependency modeling in traditional evidence theory under high-dimensional scenarios, this study introduces tensor networks for the structured representation and optimization of evidence. The risk belief assignments of each indicator are mapped to multi-dimensional tensors, with structures such as Matrix Product States (MPS) and Tree Tensor Networks (TTN) employed to characterize chain-like, hierarchical, or complex interactive dependencies among indicators. High-dimensional tensors are compressed using canonical multilinear decompositions (CP decomposition), preserving core evidence correlation information while reducing computational complexity. By designing a loss function incorporating regularization terms, the parameters of the tensor network are optimized to correct abnormal belief assignments in conflicting evidence, thereby enhancing the accuracy and completeness of high-dimensional evidence representation. This provides more reliable input for subsequent evidence fusion.

3) Quantum-entanglement-weighted evidence fusion combined with game-theoretic integrated weighting method

This study proposes an integrated fusion framework that combines subjective and objective information while enhancing evidence correlations. First, the G1 method is employed to derive subjective weights reflecting expert knowledge, while objective weights capturing intrinsic data relationships are computed based on inter-evidence similarity. A game-theoretic approach constructs an objective function to balance these weight differences, generating combined weights that integrate both domain expertise and data-driven rationality. Subsequently, the concept of “quantum entanglement” is introduced by constructing an entanglement weighting matrix to simulate nonlinear synergistic effects among evidence. This strengthens the joint support degree of substantively correlated evidence while suppressing interference from independent conflicting evidence. Finally, based on an improved evidence theory fusion method, the weighted evidence undergoes conflict resolution and belief fusion to produce comprehensive assessment results of inter-state conflict risks. This forms a complete closed-loop process from indicator measurement to risk inference, enhancing the scientific rigor and robustness of uncertainty reasoning in complex scenarios.

This section integrates the aforementioned content to propose a risk assessment method based on cloud model and improved evidence theory, with the following steps:

Step 1: Conduct indicator screening and justification to identify key factors influencing inter-state conflict risks. Classify indicator levels to establish a foundation for subsequent cloud model analysis.

Step 2: Based on the cloud model method, use Equations (5)-(7) to calculate the cloud numerical characteristics (expectation Ex, entropy En, hyper-entropy He). Apply Equations (8)-(9) to transform qualitative levels into a quantitative membership degree matrix. Through evidential conversion, employ Equation (10) to convert membership degrees into basic belief assignments (BBAs), achieving the transition from cloud model to evidence theory.

Step 3: Utilize tensor networks for high-dimensional modeling and correction of mass functions in evidence theory, enhancing the accuracy and completeness of evidence representation. Apply Equation (4) to correct the evidence.

Step 4: Adopt the G1 method and Equation (5) to compute subjective weights. Based on evidence similarity, use Equation (6) to derive objective weights. The game-theoretic combined weights integrate subjective and objective weights through game theory principles, with Equation (7) calculating the combined weights to ensure scientific rigor and rationality.

Step 5: Employ the quantum-entanglement-weighted averaging method to weight the evidence, strengthening inter-evidence correlations and holistic consistency. Use Equations (8)-(10) to compute the weighted evidence. Based on improved evidence theory, apply Equation (11) to synthesize and identify conflicting evidence, yielding the final risk assessment results.

China and ASEAN share geographical proximity, forming a geopolitical and geoeconomic complex in the South China Sea. In 2023, bilateral trade between China and ASEAN reached 6.52 trillion RMB, making them each other’s largest trading partners. However, the region faces potential risks such as sovereignty disputes in the South China Sea, military security dilemmas, and economic development disparities. Examples include Vietnam’s oil and gas exploration activities and the Philippines’ joint patrol operations, which may escalate tensions. The ten ASEAN member states are Singapore, Malaysia, Indonesia, Thailand, Vietnam, the Philippines, Myanmar, Cambodia, Laos, and Brunei. Therefore, this study selects China and the ten ASEAN countries as research subjects, utilizing 2023 raw data on geopolitical conflict risk evaluation indicators.

This research systematically constructs a risk assessment indicator system across five dimensions: politics, military, economy, society, and technology. Through bibliometric analysis, core risk factors in the field are identified, supplemented by multiple rounds of expert consultations (involving practitioners and theorists in international relations, security strategy, and regional economics) to form a preliminary indicator pool. Empirical validation and indicator screening are further conducted based on typical geopolitical conflict cases from the past decade (the Russia-Ukraine crisis, U.S.-China technology competition, and South China Sea disputes). Finally, cross-verification from multi-source data and redundancy analysis refine 18 core factors comprehensively reflecting geopolitical conflict risks. This establishes a risk evaluation system (as shown in Figure 3) covering dimensions such as political mutual trust, military deterrence, economic interdependence, social stability, and technological gaps, providing a multidimensional and quantifiable analytical tool for systematic inter-state conflict risk assessment.

Figure 3. Interstate conflict risk assessment indicator system.

To ensure the reliability and traceability of the research data, the specific sources of the 18 observable indicators under the five latent nodes are clearly specified as follows:

For the social conditions dimension, the World Happiness Index relative value is derived from the World Happiness Report (2023), while the Poverty Headcount Ratio relative value, Unemployment Rate relative value, and Public Education Expenditure relative value are all retrieved from the World Bank Database (2023).

Regarding the economic conditions dimension, the Foreign Exchange Reserves relative value, Foreign Direct Investment relative value, Inflation Rate relative value, and GDP Per Capita relative value are uniformly sourced from the World Bank Database (2023).

For the military conditions dimension, the Armed Forces Personnel relative value and Military Expenditure relative value are obtained from the World Bank Database (2023).

In the technological conditions dimension, the Scientific Journal Articles relative value, Patent Applications relative value, R&D Expenditure relative value, and High-technology Exports relative value are all from the World Bank Database (2023).

For the political conditions dimension, the Global Peace Index relative value is from the Center for Systemic Peace (CSP) Global Peace Index Database (2023), and the Government Effectiveness relative value, Government Stability relative value, and Government Corruption relative value are sourced from the World Bank Worldwide Governance Indicators (WGI) Database (2023).

Step 1: Determine evaluation criteria and benchmark clouds.

To facilitate the description of evaluation grade results after the quantitative assessment of geopolitical conflict risks, evaluation benchmarks are constructed as shown in Table 1.

Table 1. Risk evaluation benchmark.

The relative values of indicators in Table 1 are obtained through Min-Max normalization, which maps indicators with different units to the [0, 1] interval while retaining the relative order of raw data. For positive indicators (higher values indicate higher conflict risk), the normalization formula is:

For negative indicators (higher values indicate lower conflict risk), the normalization formula is:

where x ′ i denotes the normalized relative value, x i is the raw data of the i-th indicator, and x m a x / x m i n are the maximum/minimum values of the i-th indicator among the 10 research objects (China and 10 ASEAN countries) in 2023, respectively.

Step 2:Based on the indicator evaluation criteria in Table 1, we calculated the cloud numerical characteristics using Equations (5)-(7), and generated the standard cloud diagram (Figure 4) for the unemployment rate (X3) corresponding to the five evaluation grades via the cloud generator.

Figure 4. Benchmark cloud model.

Step 3:Transform qualitative grades into quantitative membership degree matrices using Equations (8)-(9), with the results presented in Table 2.

Step 4: Convert membership degrees into basic belief assignments (BBAs) through evidential transformation using Equation (10), with the results presented in Table 3.

Step 5: Based on tensor networks, correct the mass functions in evidence theory using Equations (11)-(16), with the results presented in Table 4.

Step 6: Calculate subjective weights using the G1 method through Equations (16)-(17), with the results presented in Table 5.

Table 2. Quantitative membership degree matrix.

Table 3. Basic belief assignment.

Table 4. Tensor network-corrected basic probability assignment.

Table 5. Subjective weights.

Step 7:Compute objective weights based on evidence similarity using Equations (18)-(20), with the results presented in Table 6.

Table 6. Objective weights.

Step 8: Calculate the game-theoretic combined weights using Equations (21)-(24), with the results presented in Table 7.

Step 9:Weight the evidence using the quantum-entanglement-weighted averaging method based on the calculated combined weights to enhance inter-evidence correlations and holistic consistency. Compute Singapore’s final risk assessment results through Equations (25)-(28), with the results presented in Table 8. Repeat the aforementioned steps to obtain basic probability assignments for other countries, as shown in Table 10. The interstate conflict risk zonation map between China and the ten ASEAN nations is presented in Figure 5.

To validate the accuracy and feasibility of the proposed cloud model-improved evidence theory weighted fusion evaluation method, this study compares the results with those obtained from the cloud model-fuzzy comprehensive evaluation method developed by [20] and the traditional cloud model-evidence theory approach proposed by [38]. The comparative results are presented in Table 9.

Table 7. Game-theoretic combined weights.

Table 8. Evidence combination results.

Figure 5. Conflict risk zonation map between China and the ten ASEAN countries.

Table 9. Algorithmic results comparison.

The evaluation results reveal significant differences between the two methods for Indonesia and Singapore. For Indonesia, the traditional cloud model-evidence theory method exhibits abnormal belief concentration in Grade V (High Risk), with a negative θ value. This indicates logical inconsistency, caused by forced normalization of highly conflicting evidence that leads to misjudgment. In contrast, the proposed method demonstrates belief concentration in Grade I (Low Risk) with θ = 0.0003, strongly supporting low risk assessment that aligns with the stable China-Indonesia relations in reality. This discrepancy occurs because traditional evidence theory fails in high-conflict scenarios, while the improved method corrects errors through correlation modeling. For Singapore, the traditional method produces contradictory belief distributions with θ = 0, failing to reflect uncertainty, whereas the proposed method achieves more reasonable Grade I results with θ = 0.115 by incorporating economic interdependence and capturing synergistic effects through tensor networks, overcoming traditional theory’s limitation in handling weakly correlated multi-evidence scenarios.

The two methods yield markedly different results for Myanmar. The fuzzy comprehensive evaluation method shows maximum membership in Grade V (High Risk), while the proposed method concentrates belief in Grade I with θ = 0.103, indicating low risk by effectively suppressing interference from single conflict indicators. This difference arises because fuzzy evaluation is overly sensitive to extreme values, whereas the improved evidence theory mitigates outlier impacts through evidence weighting.

A comprehensive comparison is conducted across five dimensions: evidence fusion mechanisms, weight determination approaches, conflict evidence handling, non-classical uncertainty adaptation, and high-dimensional/correlation processing capabilities, with detailed results presented in Table 10.

Table 10. Comparative analysis of algorithmic principles.

The algorithmic and theoretical comparisons reveal that traditional evidence theory has significant limitations in high-conflict or high-dimensional scenarios, as evidenced by abnormal θ values, making it reliable only for simple cases with highly consistent evidence. While fuzzy evaluation works for independent indicators with complete data, it lacks robust uncertainty characterization, resulting in unstable outcomes. The proposed method systematically addresses these shortcomings through tensor networks and quantum-entanglement weighting, demonstrating superior performance particularly in complex international relations assessments where it effectively resolves conflict handling failures and high-dimensional modeling deficiencies inherent in traditional approaches.