A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention
Abstract
:1. Introduction
- In the selection of threat assessment attributes, most research primarily emphasizes the direct threat posed by the target to our units during threat assessment and seldom considers the influence of external environmental factors [2,5,11,12,14,15,16,17,18,19,20]. Direct threat attributes typically include the target’s static combat capabilities and dynamic situational information [12]. The threat from UAVs is first determined by their inherent capabilities and then manifested through specific events driven by intention. The target operational intention indicator focuses on possible actions the target may take, which evolve based on battlefield command decisions, affecting the threat level. Evaluating these intentions helps anticipate the opponent’s combat strategies, allowing for proactive preparation. Although significant research progress has been made in UAV intention recognition, current target threat assessment methods still lack effective integration of combat intentions.
- Many existing methods for describing and quantifying threat assessment attributes simplify the process by relying on precise real-number data inputs [5,11,12,14,15,16,17,18,19,20]. However, in real combat, information from various sources is often heterogeneous, with varying accuracy levels across sensors. Some methods [19,20] fail to account for the inherent uncertainty in this information, undermining the scientific validity of the results. Given the complexity of the combat environment, both sensor-derived data and human-based judgments exhibit degrees of fuzziness and uncertainty. When employing fuzzy multi-attribute decision making for threat assessment, effectively quantifying, transforming, and standardizing the raw data of threat assessment attributes becomes critical for subsequent threat prioritization.
- In the determination of attribute weights, traditional multi-attribute decision making threat assessment methods are static, treating each time point as an independent event and failing to account for the timing of the target or dynamic changes on the battlefield [2,11,12,14,19,20]. However, target threat assessment is inherently dynamic and requires integrating information from multiple time points for a comprehensive evaluation. Therefore, it is crucial to aggregate multi-time attribute data into a unified matrix across the assessment period, enabling reliable threat assessment in dynamic environments. Additionally, some studies [6] rely on linear weighted combinations for fixed composite weights, leading to a lack of differentiation when addressing multiple targets, which necessitates improvement.
- In multi-attribute decision making, selecting the target threat ranking method constitutes the final step. Nevertheless, the traditional TOPSIS method, which depends on Euclidean distance, struggles to effectively process non-membership and hesitation degree information inherent in the intuitionistic fuzzy environment. Therefore, it is necessary to enhance the TOPSIS method to improve its applicability in fuzzy decision-making contexts.
- This article constructs a UAV threat assessment index system by considering three critical aspects: target capability, target intention, and target opportunity, integrating both the intention and environmental condition attributes into the framework. Furthermore, threat membership functions for each attribute are systematically designed based on the practical requirements of UAV combat scenarios.
- By integrating fuzzy theory with multi-attribute decision making theory, the fuzziness inherent in sensor data errors or subjective judgments is preserved. Specifically, this integration manifests in two key aspects. First, specific threat attributes are fuzzified to address the challenge of “quantifying individual attributes using fuzzy mathematics.” This involves mapping raw data into representation forms within the fuzzy mathematics framework, such as fuzzy linguistic terms, interval numbers, or triangular fuzzy numbers. Second, data formats are standardized to resolve the issue of “enabling all attributes to be collaboratively analyzed under a unified mathematical framework.” All intermediate fuzzy mathematical representations of heterogeneous evaluation attributes are systematically converted into intuitionistic fuzzy numbers, ensuring consistent input for subsequent threat assessment ranking.
- The inverse Poisson distribution is utilized to calculate the time-sequence weights based on real-time situational awareness, enabling effective integration of evaluation information across multiple time points. Objective weights are formulated using cosine intuitionistic fuzzy entropy to capture the dynamic nature of threat assessment. Additionally, a subjective weight determination method incorporating the intention probability matrix is developed to effectively consolidate target combat intention information. Simultaneously, a comprehensive variable weight fusion approach considering IFS scores is proposed to differentiate the integrated weights among multiple targets.
- The TOPSIS method based on the hesitation-degree-weighted similarity measure, which is particularly suited for intuitionistic fuzzy environments, is employed for threat ranking. This method comprehensively accounts for the interactions among membership degree, non-membership degree, and hesitation degree, thereby enhancing the robustness of decision making through a weighted scoring mechanism.
2. Related Works
2.1. Intuitionistic Fuzzy Sets
2.2. Intuitionistic Fuzzy Multi-Attribute Decision Making
3. The Proposed Dynamic Threat Assessment Model
Algorithm 1: The dynamic threat assessment algorithm |
3.1. UAV Threat Assessment Index System
3.1.1. Selection of UAV Threat Assessment Indexes
3.1.2. Quantification of UAV Threat Assessment Indexes
Target Capability
- Step 1: Define an appropriate language assessment scale. If the linguistic scale for target capability is divided into L levels, then the fuzzy evaluation linguistic scale set can be expressed as . In this paper, the value of L is determined as 11, corresponding to the following levels: maximal, very large, large, relatively large, slightly large, moderate, slightly small, relatively small, small, very small, and minimal.
- Step 2: Based on the degree of certainty in the decision-makers’ judgment of the results, a result certainty degree vector is constructed. In this study, C is categorized into 5 levels, specifically absolutely certain, fairly certain, moderately certain, slightly certain, and uncertain.
- Step 3: Based on the decision-maker’s judgment, the fuzzy evaluation language reflecting the degree of certainty in the decision-maker’s own judgment is obtained.
Target Opportunity
- 1.
- Angle threat attribute
- 2.
- Speed threat attribute
- 3.
- Height threat attribute
- 4.
- Arrival Time threat attribute
- 5.
- Environment index
Target Intention
3.1.3. Transforming Heterogeneous Indexes into a Unified IFS
- 1.
- Transformation of Fuzzy Evaluation Language into IFS
- Step 1: Based on the information provided in Table 3 and Table 4, the i-th fuzzy evaluation language can be represented as follows:
- Step 2: Based on Equation (18), the fuzzy evaluation language can be transformed into an intuitionistic fuzzy number .
- 2.
- Transformation of interval numbers into IFS
- 3.
- Transformation of real numbers into IFS
- 4.
- Transformation of triangular fuzzy numbers into IFS
3.2. Weight Determination Method of Indexes
3.2.1. Determination of Time Series Weight
3.2.2. Determination of Objective Weight Based on IFE
- Step 1: Calculating the cosine intuitionistic fuzzy entropy of each attribute based on Equation (26).
- Step 2: Constructing a quadratic nonlinear programming model, with the minimization of IFE serving as the objective function, as presented in Equation (27).
- Step 3: Establishing the Lagrange equation to solve Equation (27).
- Step 4: By taking the derivatives of and in Equation (28), the objective weight of the j-th attribute is obtained by Equation (30).
3.2.3. Determination of Subjective Weight Based on AHP and Target Intention
- Step 1: Constructing the model of the AHP based on the index system for UAV threat assessment, as illustrated in Figure 8.
- Step 2: Constructing the judgment matrix. The 9-level ratio scale method is employed to perform pairwise comparisons of the attributes and construct the judgment matrix . The evaluation criteria consist of equally important (1), slightly important (3), noticeably important (5), strongly important (7), and extremely important (9) in the 9-level scale. Intermediate values between adjacent scales are represented by 2, 4, 6, and 8.
- Step 3: Calculating the weight vector. The eigenvector method is employed to determine the weight of each judgment matrix.
- (1)
- Solving Equation (31) to compute the maximum eigenvalue .
- (2)
- Solving Equation (32) yields the non-zero eigenvector w.
- (3)
- Normalizing the eigenvector into a weight vector using Equation (33).
- Step 4: Performing a consistency check.
- (1)
- Calculating the consistency index (CI) using Equation (34):
- (2)
- Querying the random consistency index (RI), RI = [0, 0, 0.52, 0.89, 1.12, 1.26, 1.36, 1.41, 1.46, 0.49, 0.52, 1.54, 1.56, 1.58, 1.59].
- (3)
- Calculating the consistency ratio (CR), . If CR < 0.1, the test is passed; otherwise, the judgment matrix needs to be adjusted.
- Step 5: Repeating Steps 2~4 to calculate the weights of each attribute for the six combat intention types and constructing the combat intention attribute weight matrix (35).
- Step 6: Calculating the subjective weights of each attribute. By using matrix (35) and the intention probability matrix (16), the subjective weight matrix can be obtained, and the calculation is as follows:
3.2.4. Determination of Comprehensive Variable Weight Based on the Least Squares Method
- Step 1: Calculating the IFS scores for each attribute. The calculation equation for the score of the j-th attribute under the i-th target is presented in (37).
- Step 2: Repeating Step 1 to construct the score matrix for the weighted intuitionistic fuzzy evaluation matrix , as presented in (38).
- Step 3: Defining the weighted decision-making bias by using Equation (39).
- Step 4: Developing a least squares weight fusion model based on minimizing the total decision deviation, as presented in (40).
- Step 5: Solving (40), the comprehensive variable weight for the i-th target is obtained.
- Step 6: By repeating Steps 3~5, the comprehensive variable weight matrix for multiple objectives is obtained, as shown in (41).
3.3. Threat Degree Ranking Based on the Improved TOPSIS Method
- Step 1: Obtaining the relative positive ideal solution and the relative negative ideal solution of the threat assessment attributes. The process for calculating and of each attribute is presented below.
- Step 2: Calculating the hesitation degrees and relative to the positive ideal solution and the negative ideal solution of each evaluation attribute , where ,, and , .
- Step 3: Calculating the degree of similarity and between the corresponding to each attribute of each target and the relative positive ideal solution and the relative negative ideal solution , respectively, thereby constructing the positive similarity degree matrix and the negative similarity degree matrix . The calculation process for the positive similarity degree is presented in Equation (44), while the process for the negative similarity degree is shown in Equation (45).
- Step 4: Based on the comprehensive variable weight matrix W, the weighted positive scores and weighted negative scores for each target are calculated, respectively, using Equations (46) and (47).
- Step 5: Calculating the relative degree of closeness for each target .
4. Simulation and Analysis
4.1. Simulation Example
- Step 2: According to Section 3.1.3, heterogeneous information was transformed into the same IFS form to form the intuitionistic fuzzy decision matrix , at each moment:
- Step 3: According to Equation (23), the time series weight at each moment K was calculated. Subsequently, by integrating the evaluation matrix at each moment with Equation (10), the time series-weighted matrix was obtained.
- Step 4: The objective weight vector was calculated according to Equations (26)–(30).
- Step 5: By utilizing the data in Table 8, the intention probability matrix was constructed. Subsequently, based on Equations (31)–(36), the weight matrix of combat intention indicators and the subjective weight matrix were calculated.
- Step 6: By integrating the objective weight vector and the subjective weight matrix , the comprehensive variable weight matrix for multi-targets was calculated based on Equations (37)–(40).
- Step 7: By integrating the time series-weighted matrix with the comprehensive variable weight matrix W and applying the improved TOPSIS method for ranking, the relative closeness degrees of the targets and their corresponding threat rankings were derived, as presented in Table 14.
4.2. Comparison Analysis
- 1.
- Model 1 [18]: intuitionistic fuzzy TOPSIS method without fuse intention
- Step 1~Step 4: In line with the proposed model, the resulting objective weights are presented as follows:
- Step 5: By integrating the time series-weighted matrix with the comprehensive variable weight matrix W, and applying the improved TOPSIS method for ranking, the relative closeness degrees of the targets and their corresponding threat rankings were derived, as presented in Table 15.
- 2.
- Model 2 [12]: intuitionistic fuzzy TOPSIS method with single moment
- Step 1~Step 2: In accordance with the proposed model, the intuitionistic fuzzy decision matrix at time t3 was derived:
- Step 3: The objective weight vector was calculated based on Equations (26)–(30):
- Step 4: The subjective weight matrix was calculated according to Equations (31)–(36):
- Step 5: The objective weight vector and the subjective weight matrix were combined, and the comprehensive variable weight matrix of multiple targets was obtained according to Equations (37)–(40):
- Step 6: By integrating the intuitionistic fuzzy matrix with the comprehensive variable weight matrix W, and applying the improved TOPSIS method for ranking, the relative closeness degree of the target and the threat ranking were determined, as presented in Table 16.
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
UAVs | Unmanned aerial vehicles |
TOPSIS | Technique for order preference by similarity to ideal solution |
MADM | Multi-attribute decision making |
IFS | Intuitionistic fuzzy set |
IFN | Intuitionistic fuzzy number |
IFWA | Intuitionistic fuzzy weighted averaging |
IFMADM | Fuzzy multi-attribute decision making |
AHP | Analytic hierarchy process |
IF-AHP | Intuitionistic fuzzy analytic hierarchy process |
GIFSS | Generalized intuitionistic fuzzy soft set |
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Method | Theoretical Basis | Characteristics | Deficiencies |
---|---|---|---|
Benavoli et al. [1] | Evidence Theory | This method is capable of integrating multi-source data while effectively addressing a certain level of uncertainty. | It is highly dependent on prior knowledge, subjective in nature, and suffers from high computational complexity and poor real-time performance. |
Wang et al. [2] Fan et al. [3] | Fuzzy Reasoning Theory | This method can transform qualitative descriptions into quantitative analyses, and the construction process is intuitive. | The determination of membership functions and fuzzy rules is relatively subjective. |
Di et al. [4] | Bayesian Network Theory | This method conducts reasoning based on conditional probability, capable of revealing causal relationships among indicators and having strong interpretability. | This method requires extensive prior knowledge and data support, with complex network design and parameter estimation, potentially leading to real-time issues in dynamic battlefield environments. |
Zhang et al. [5] Qu et al. [6] | Multi-Attribute Decision Making (MADM) Theory | This method establishes a comprehensive evaluation framework for threat assessment, enabling the analysis of multiple attribute indicators and facilitating the direct derivation of threat assessment decisions. | Different MADM methods have different adaptabilities and need to be chosen carefully. Some multi-attribute decision making methods, such as TOPSIS, have relatively high requirements for data standardization. |
Ma et al. [7] | Cloud model Theory | This method takes into account both fuzziness and randomness, converting qualitative concepts into quantitative expressions and characterizing uncertainty through “clouds”. | The model is rather complex, with subjective parameter determination, heavy reliance on sample data, and potential parameter sensitivity affecting assessment results. |
Yu et al. [8] | Neural Network | This method has self-learning and adaptive capabilities, relies on a large amount of data for training, and can automatically capture complex patterns and correlations. | The method requires a large amount of labeled data, which is difficult to obtain in battlefield scenes, and its “black box” nature limits the interpretability of the results. |
Category | Common Methods | Characteristics | Property |
---|---|---|---|
Subjective weighting method | Expert scoring method (Delphi method) Analytic hierarchy process (AHP) method Judgment matrix method Fuzzy weighting method, etc. | Decision-makers subjectively assess the significance of a plan’s attributes by drawing on their existing experience and expertise. | This approach leverages experts’ knowledge, experience, and subjective understanding of the decision-making context, allowing for flexible adjustments based on conditions. However, it is inherently subjective and can be influenced by individual expertise, mental state, and battlefield dynamics. |
Objective weighting method | Entropy weight method Deviation maximization method Mean square deviation method, etc. | Weighting based on the intrinsic decision information primarily depends on the decision matrix and excludes subjective factors of decision-makers in the weighting process. | The assigned weights reflect objective characteristics, such as data variation or dispersion, and are based on a solid mathematical framework. However, this method does not account for decision-makers’ subjective preferences and is prone to instability due to its sensitivity to data volume and optimization model choice. |
Combined weighting method | Fuzzy entropy weight method Combined goal programming method, etc. | Weighting methods that combine both subjective and objective approaches. | This method enables a balance between the subjective judgments of experts and the objective nature of data. |
Scale of Fuzzy Evaluation Language | IFN | ||
---|---|---|---|
(Maximal) | 1 | 0 | 0 |
(Very large) | 0.9 | 0.05 | 0.05 |
(Large) | 0.8 | 0.1 | 0.1 |
(Relatively large) | 0.7 | 0.15 | 0.15 |
(Slightly large) | 0.55 | 0.3 | 0.15 |
(Moderate) | 0.4 | 0.4 | 0.2 |
(Slightly small) | 0.4 | 0.45 | 0.15 |
(Relatively small) | 0.3 | 0.55 | 0.15 |
(Small) | 0.2 | 0.7 | 0.1 |
(Very small) | 0.1 | 0.85 | 0.05 |
(Minimal) | 0 | 1 | 0 |
Determination Degree | L | U |
---|---|---|
(Absolutely certain) | 0.9 | 1 |
(Fairly certain) | 0.6 | 0.9 |
(Moderately certain) | 0.4 | 0.6 |
(Slightly certain) | 0.2 | 0.4 |
(Uncertain) | 0 | 0.2 |
Target | Target Type Threat | Firepower Capability | Maneuvering Capability | EC Capability | Environment Condition |
---|---|---|---|---|---|
Very large (absolutely certain) | Maximal (fairly certain) | Moderate (moderately certain) | Slightly large (moderately certain) | Good | |
Relatively large (fairly certain) | Relatively large (fairly certain) | Moderate (fairly certain) | Slightly small (fairly certain) | ||
Maximal (moderately certain) | Very large (fairly certain) | Very large (fairly certain) | Large (moderately certain) | ||
Large (fairly certain) | Large (absolutely certain) | Very large (moderately certain) | Slightly large (slightly certain) | ||
Slightly small (moderately certain) | Small (fairly certain) | Relatively small (moderately certain) | Very large (absolutely certain) |
Target | Angle/(°) | Speed/(Ma) | Height/(m) | Arrival Time/(s) |
---|---|---|---|---|
26 | [0.32, 0.38] | [1653, 1768] | [513, 556] | |
74 | [0.26, 0.30] | [2367, 2498] | [469, 498] | |
50 | [0.41, 0.55] | [2373, 2425] | [315, 376] | |
52 | [0.39, 0.43] | [2789, 3028] | [468, 507] | |
65 | [0.29, 0.33] | [3504, 4020] | [942, 1017] |
Target | Angle/(°) | Speed/(Ma) | Height/(m) | Arrival Time/(s) |
---|---|---|---|---|
33 | [0.35, 0.37] | [1673, 1788] | [452, 481] | |
52 | [0.27, 0.30] | [2238, 2450] | [436, 478] | |
46 | [0.40, 0.53] | [2080, 2395] | [294, 344] | |
74 | [0.40, 0.47] | [2523, 2682] | [432.459] | |
68 | [0.29, 0.33] | [3542, 4097] | [838, 902] |
Target | Angle/(°) | Speed/(Ma) | Height/(m) | Arrival Time/(s) |
---|---|---|---|---|
42 | [0.27, 0.33] | [1723, 1806] | [−386, −420] | |
28 | [0.29, 0.32] | [2434, 2563] | [397, 422] | |
35 | [0.23, 0.26] | [1789, 1980] | [223, 316] | |
71 | [0.55, 0.68] | [1967, 2068] | [388, 404] | |
73 | [0.30, 0.32] | [3600, 4126] | [757, 826] |
Target | Attack | Retreat | Electronic Interference | Surveillance | Reconnaissance | Feint |
---|---|---|---|---|---|---|
0.32 | 0.58 | 0 | 0 | 0 | 0.1 | |
0.23 | 0 | 0.09 | 0.22 | 0.28 | 0.18 | |
0.43 | 0 | 0.15 | 0 | 0 | 0.42 | |
0.62 | 0 | 0 | 0.04 | 0.03 | 0.31 | |
0 | 0 | 0 | 0.77 | 0.23 | 0 |
Target | |||||
---|---|---|---|---|---|
9 (5) | 10 (4) | 7 (4) | 6 (3) | (0.4, 0.6, 0.8) | |
7 (4) | 7 (4) | 5 (4) | 4 (4) | ||
10 (3) | 9 (4) | 9 (4) | 8 (3) | ||
8 (4) | 8 (5) | 9 (3) | 6 (2) | ||
4 (3) | 2 (4) | 3 (3) | 9 (5) |
Target | ||||
---|---|---|---|---|
0.916 | [0.101, 0.112] | [0.931, 0.977] | [0.539, 0.591] | |
0.324 | [0.1, 0.1] | [0.369, 0.471] | [0.609, 0.644] | |
0.691 | [0.122, 0.215] | [0.425, 0.467] | [0.754, 0.820] | |
0.666 | [0.115, 0.131] | [0.097, 0.190] | [0.598, 0.645] | |
0.478 | [0.1, 0.102] | [0.002, 0.018] | [0.126, 0.169] |
Target | ||||
---|---|---|---|---|
0.865 | [0.104, 0.109] | [0.92, 0.97] | [0.629, 0.664] | |
0.666 | [0.1, 0.1] | [0.405, 0.580] | [0.633, 0.684] | |
0.739 | [0.118, 0.197] | [0.449, 0.714] | [0.789, 0.841] | |
0.324 | [0.118, 0.153] | [0.247, 0.351] | [0.656, 0.688] | |
0.429 | [0.1, 0.102] | [0.001, 0.015] | [0.196, 0.245] |
Target | ||||
---|---|---|---|---|
0.782 | [0.1, 0.102] | [0.91, 0.951] | [0.148, 0.119] | |
0.903 | [0.1, 0.101] | [0.323, 0.418] | [0.700, 0.729] | |
0.849 | [0.1, 0.1] | [0.794, 0.92] | [0.819, 0.905] | |
0.190 | [0.215, 0.365] | [0.724, 0.804] | [0.721, 0.740] | |
0.342 | [0.1, 0.101] | [0.001, 0.012] | [0.255, 0.318] |
Threat Degree | {0.4980, 0.4701, 0.6188, 0.5386, 0.3490} |
---|---|
Ranking | > > > > |
Threat Degree | {0.5488, 0.4807, 0.6202, 0.5315, 0.3681} |
---|---|
Ranking | > > > > |
Threat Degree | {0.4623, 0.4755, 0.6205, 0.5465, 0.3536} |
---|---|
Ranking | > > > > |
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Niu, Q.; Ren, S.; Gao, W.; Wang, C. A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention. Mathematics 2025, 13, 1663. https://doi.org/10.3390/math13101663
Niu Q, Ren S, Gao W, Wang C. A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention. Mathematics. 2025; 13(10):1663. https://doi.org/10.3390/math13101663
Chicago/Turabian StyleNiu, Qianru, Shuangyin Ren, Wei Gao, and Chunjiang Wang. 2025. "A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention" Mathematics 13, no. 10: 1663. https://doi.org/10.3390/math13101663
APA StyleNiu, Q., Ren, S., Gao, W., & Wang, C. (2025). A Dynamic Threat Assessment Method for Multi-Target Unmanned Aerial Vehicles at Multiple Time Points Based on Fuzzy Multi-Attribute Decision Making and Fuse Intention. Mathematics, 13(10), 1663. https://doi.org/10.3390/math13101663