In my research focusing on enhancing the operational effectiveness of unmanned aerial systems, I have directed significant attention toward the human element: the military drone operator. The proliferation and decisive impact of military drones in contemporary conflicts underscore the critical need for a highly skilled operator corps. Traditional evaluation methods for these personnel often rely on singular performance dimensions or crisp quantitative metrics, failing to capture the multifaceted, complex, and inherently uncertain nature of battlefield competencies. To address this gap, I propose and have developed a robust evaluation model grounded in the Fuzzy Analytic Hierarchy Process (Fuzzy AHP). This methodology allows for the systematic integration of both qualitative and quantitative factors, effectively handling the vagueness in human performance assessment. The core objective of my work is to establish a scientific, operable, and comprehensive framework for evaluating the post-specific ability of military drone operators, thereby providing a reliable tool for training assessment, personnel selection, and proficiency benchmarking.
The foundational step in my application of Fuzzy AHP was to construct a hierarchical evaluation index system. Through systematic analysis of mission profiles (e.g., takeoff/landing, reconnaissance, penetration) and core competency requirements (theory vs. practice, skill vs. psychology, operation vs. maintenance), I identified four primary dimensions influencing a military drone operator’s capability. These criteria form the first layer of the hierarchy:
- Flight Skill (A1): The core practical ability to physically control the military drone.
- Flight Theory (A2): The foundational knowledge underpinning safe and effective operation.
- Maintenance Skill (A3): The capacity to perform essential upkeep and repairs on the military drone system.
- Psychological Quality (A4): The mental fortitude required to operate under high-stress, combat conditions.
Each of these primary criteria was then decomposed into specific, measurable indicators, creating a detailed second layer comprising 15 factors in total. This structured breakdown is presented in Table 1, which outlines the complete evaluation index system.
| Target Layer | Criteria Layer (Weight Ai) | Indicator Layer (Weight Bj) |
|---|---|---|
| Military Drone Operator Competency Evaluation | Flight Skill (A1) = 0.449 | B1: Climb, Descent, and Turn Maneuvers (0.286) |
| B2: Loitering/Circling (0.104) | ||
| B3: Dive and Zoom Maneuvers (0.162) | ||
| B4: Roll Maneuvers (0.151) | ||
| B5: Tactical Maneuvers (0.167) | ||
| B6: Loop Maneuvers (0.130) | ||
| Flight Theory (A2) = 0.080 | B7: Aircraft Systems Knowledge (0.376) | |
| B8: Safety and Operational Knowledge (0.263) | ||
| B9: Control and Navigation Theory (0.361) | ||
| Maintenance Skill (A3) = 0.370 | B10: Preventive Maintenance (0.362) | |
| B11: Corrective Maintenance (0.362) | ||
| B12: Repair and Overhaul (0.275) | ||
| Psychological Quality (A4) = 0.101 | B13: Mental State (0.302) | |
| B14: Emotional State (0.302) | ||
| B15: Emergency Response Aptitude (0.397) |
With the hierarchy established, the next phase involved determining the relative importance, or weight, of each factor using the Analytic Hierarchy Process. The process begins by constructing pairwise comparison matrices. Experts are asked to compare the relative importance of two factors at a time using a standardized scale, such as the Saaty’s 1-9 scale shown in Table 2.
| Intensity of Importance | Definition | Explanation |
|---|---|---|
| 1 | Equal Importance | Two factors contribute equally to the objective. |
| 3 | Moderate Importance | Experience and judgment slightly favor one factor over another. |
| 5 | Strong Importance | Experience and judgment strongly favor one factor over another. |
| 7 | Very Strong Importance | A factor is favored very strongly over another. |
| 9 | Extreme Importance | The evidence favoring one factor over another is of the highest possible order. |
| 2, 4, 6, 8 | Intermediate Values | Used to compromise between the above judgments. |
For a set of factors \(X = \{x_1, x_2, …, x_n\}\), a judgment matrix \(A\) is formed where each element \(a_{ij}\) represents the comparison of factor \(i\) to factor \(j\):
$$
A = (a_{ij})_{n \times n} = \begin{bmatrix}
1 & a_{12} & \cdots & a_{1n} \\
a_{21} & 1 & \cdots & a_{2n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{n1} & a_{n2} & \cdots & 1
\end{bmatrix}
$$
where \(a_{ij} > 0\), \(a_{ji} = 1 / a_{ij}\), and \(a_{ii} = 1\).
The weight vector \(W = [w_1, w_2, …, w_n]^T\) is then derived from this matrix. I employed the geometric mean method (also known as the eigenvalue method in principle) for calculation. First, the geometric mean \(M_i\) for each row is computed:
$$
M_i = \left( \prod_{j=1}^{n} a_{ij} \right)^{1/n}, \quad i=1,2,…,n
$$
Then, the weights are obtained by normalizing the vector \(M\):
$$
w_i = \frac{M_i}{\sum_{k=1}^{n} M_k}
$$
To ensure the logical consistency of expert judgments, a consistency check is mandatory. The Consistency Index (\(CI\)) is calculated as:
$$
CI = \frac{\lambda_{max} – n}{n – 1}
$$
where \(\lambda_{max}\) is the principal eigenvalue of matrix \(A\), approximately calculated by \(\lambda_{max} = \frac{1}{n}\sum_{i=1}^{n}\frac{(AW)_i}{w_i}\). The Consistency Ratio (\(CR\)) is then found:
$$
CR = \frac{CI}{RI}
$$
where \(RI\) is the Random Index, dependent on matrix size \(n\). A \(CR < 0.10\) indicates acceptable consistency. Following this process with expert input, I derived the comprehensive weights for all indicators, as already displayed in the final column of Table 1. The results clearly show that Flight Skill is the most critical dimension for a military drone operator, followed closely by Maintenance Skill. Within the flight skill set, basic Climb, Descent, and Turn Maneuvers (B1) carry the highest weight, emphasizing their fundamental role in all military drone operations.
The second major component of my model is the fuzzy comprehensive evaluation, which translates subjective ratings into a quantifiable score. This process starts by defining an evaluation set, \(V\), which is the collection of all possible qualitative grades an evaluator can assign. For this military drone operator assessment, I defined a four-level set:
$$
V = \{v_1, v_2, v_3, v_4\} = \{\text{Excellent}, \text{Good}, \text{Fair}, \text{Poor}\}
$$
A score vector \(S_v\) is associated with this set for final quantitative aggregation:
$$
S_v = [90, 75, 60, 45]
$$
For a specific operator, evaluators (or experts) assess each bottom-level indicator \(B_j\) and assign a degree of membership to each grade in \(V\). For example, if 10 experts evaluate an operator’s “Climb, Descent, and Turn” skill, and 4 rate it “Excellent”, 5 rate it “Good”, and 1 rates it “Fair”, the membership vector for \(B_1\) would be \(r_1 = [0.4, 0.5, 0.1, 0.0]\). Compiling these for all indicators under a criterion \(A_i\) forms a fuzzy evaluation matrix \(R_i\).
The fuzzy comprehensive evaluation for each primary criterion \(A_i\) is computed by synthesizing the indicator weights \(W_{Bi}\) with its evaluation matrix \(R_i\):
$$
B_i = W_{Bi} \circ R_i = (w_{b1}, w_{b2}, …, w_{bm}) \circ \begin{bmatrix}
r_{11} & r_{12} & r_{13} & r_{14} \\
r_{21} & r_{22} & r_{23} & r_{24} \\
\vdots & \vdots & \vdots & \vdots \\
r_{m1} & r_{m2} & r_{m3} & r_{m4}
\end{bmatrix} = (b_{i1}, b_{i2}, b_{i3}, b_{i4})
$$
where \(\circ\) denotes a fuzzy synthesis operator, typically using the weighted average model. The result \(B_i\) is a fuzzy vector representing the degree to which the operator’s performance in dimension \(A_i\) belongs to each evaluation grade. These vectors \(B_i\) for all criteria are then aggregated to form the fuzzy evaluation matrix \(R\) for the target layer:
$$
R = \begin{bmatrix}
B_1 \\ B_2 \\ B_3 \\ B_4
\end{bmatrix}
$$
The final, overall fuzzy evaluation vector \(B\) for the military drone operator’s competency is obtained by synthesizing the criteria layer weights \(W_A\) with matrix \(R\):
$$
B = W_A \circ R = (w_{A1}, w_{A2}, w_{A3}, w_{A4}) \circ \begin{bmatrix}
b_{11} & b_{12} & b_{13} & b_{14} \\
b_{21} & b_{22} & b_{23} & b_{24} \\
b_{31} & b_{32} & b_{33} & b_{34} \\
b_{41} & b_{42} & b_{43} & b_{44}
\end{bmatrix} = (b_1, b_2, b_3, b_4)
$$
Finally, to obtain a single composite score \(F\), I apply the weighted average method using the score vector \(S_v\):
$$
F = B \cdot S_v^T = b_1 \times 90 + b_2 \times 75 + b_3 \times 60 + b_4 \times 45
$$
This score \(F\) provides a clear, quantitative measure of the operator’s overall competency, while the vector \(B\) reveals the distribution of their performance across the qualitative grades.
To demonstrate the practical application and validity of this model, I conducted a detailed case study involving a trainee military drone operator, referred to as Operator L. A panel of experts evaluated Operator L on all 15 indicators, providing the membership degrees for each. The collected evaluation data for the indicator layer is summarized in Table 3.
| Criteria | Indicator | Excellent | Good | Fair | Poor |
|---|---|---|---|---|---|
| Flight Skill (A1) | B1 | 0.385 | 0.615 | 0.000 | 0.000 |
| B2 | 0.308 | 0.692 | 0.000 | 0.000 | |
| B3 | 0.077 | 0.692 | 0.231 | 0.000 | |
| B4 | 0.000 | 0.385 | 0.615 | 0.000 | |
| B5 | 0.000 | 0.077 | 0.846 | 0.077 | |
| B6 | 0.000 | 0.077 | 0.538 | 0.385 | |
| Flight Theory (A2) | B7 | 0.077 | 0.615 | 0.231 | 0.077 |
| B8 | 0.692 | 0.308 | 0.000 | 0.000 | |
| B9 | 0.308 | 0.615 | 0.077 | 0.000 | |
| Maintenance Skill (A3) | B10 | 0.538 | 0.385 | 0.077 | 0.000 |
| B11 | 0.077 | 0.308 | 0.077 | 0.000 | |
| B12 | 0.000 | 0.231 | 0.615 | 0.154 | |
| Psychological Quality (A4) | B13 | 0.538 | 0.462 | 0.000 | 0.000 |
| B14 | 0.385 | 0.615 | 0.000 | 0.000 | |
| B15 | 0.000 | 0.692 | 0.308 | 0.000 |
Applying the fuzzy evaluation algorithm, I first computed the comprehensive evaluation vector for each criterion. For Flight Skill (A1):
$$
B_1 = W_{B1} \circ R_1 = [0.286, 0.104, 0.162, 0.151, 0.167, 0.130] \circ \begin{bmatrix}
0.385 & 0.615 & 0.000 & 0.000\\
0.308 & 0.692 & 0.000 & 0.000\\
0.077 & 0.692 & 0.231 & 0.000\\
0.000 & 0.385 & 0.615 & 0.000\\
0.000 & 0.077 & 0.846 & 0.077\\
0.000 & 0.077 & 0.538 & 0.385
\end{bmatrix} = [0.155, 0.441, 0.342, 0.063]
$$
Similarly, the results for the other criteria were calculated:
$$
B_2 = [0.322, 0.535, 0.115, 0.029] \quad \text{(Flight Theory)}
$$
$$
B_3 = [0.223, 0.314, 0.337, 0.126] \quad \text{(Maintenance Skill)}
$$
$$
B_4 = [0.278, 0.600, 0.122, 0.000] \quad \text{(Psychological Quality)}
$$
These vectors form the comprehensive evaluation matrix \(R\) for the target layer:
$$
R = \begin{bmatrix}
0.155 & 0.441 & 0.342 & 0.063 \\
0.322 & 0.535 & 0.115 & 0.029 \\
0.223 & 0.314 & 0.337 & 0.126 \\
0.278 & 0.600 & 0.122 & 0.000
\end{bmatrix}
$$
The final fuzzy evaluation is then:
$$
B = W_A \circ R = [0.449, 0.080, 0.370, 0.101] \circ R = [0.206, 0.418, 0.299, 0.077]
$$
The composite score is:
$$
F = B \cdot S_v^T = [0.206, 0.418, 0.299, 0.077] \cdot [90, 75, 60, 45]^T = 71.28
$$
Interpreting the results, the maximum membership value in vector \(B\) is \(0.418\), corresponding to the “Good” grade. The composite score of 71.28 also lies closer to the “Good” benchmark (75) than to “Fair” (60). Therefore, Operator L’s overall military drone competency is assessed as **Good**. A deeper analysis of the intermediate vectors reveals specific strengths and weaknesses. For instance, \(B_3 = [0.223, 0.314, 0.337, 0.126]\) for Maintenance Skill shows the highest membership (0.337) is for “Fair”, indicating this is a relative area of weakness for Operator L, warranting focused training. This level of diagnostic detail is a key strength of the model.
In conclusion, the model I have developed, integrating Fuzzy AHP with multi-level fuzzy comprehensive evaluation, provides a structured and scientifically-grounded methodology for assessing military drone operator competency. It effectively translates expert judgments on multiple, often vague, performance facets into a clear quantitative score and qualitative profile. The case study validates the model’s practicality and operational value, demonstrating its ability not only to produce an overall rating but also to pinpoint specific competency gaps. For military organizations, the adoption of such a model can significantly enhance the objectivity and effectiveness of operator training programs, proficiency evaluations, and career development pathways. By ensuring that military drone operators are assessed against a comprehensive, weighted set of real-world skills and attributes, this approach directly contributes to building a more capable and resilient unmanned systems force.