A Two-Stage T-Norm–Choquet–OWA Resource Aggregator for Multi-UAV Cooperation: Theoretical Proof and Validation

Highlights

What are the main findings?

• Introduces a prediction-enhanced, two-stage T-norm–Choquet–OWA aggregator that fuses 3 s resource forecasting with bottleneck protection and elastic compensation for energy, bandwidth and CPU.
• SIn a 360-UAV co-simulation, the method lowers average RTT to 55 ms and cuts latency by 5–20.

What is the implication of the main finding?

• The aggregator’s complexity and interpretable parameters enable direct deployment on on-board flight controllers for time-critical swarm missions.
• Provides a scalable blueprint for low-latency, high-resilience resource scheduling in large UAV fleets, with potential extensions to real-world field trials and federated learning weight sharing.

Abstract

Multi-UAV cooperative missions demand millisecond-level coordination across three key resource dimensions—battery energy, wireless bandwidth, and onboard computing power—where traditional Min or linearly weighted schedulers struggle to balance safety with efficiency. We propose a prediction-enhanced two-stage T-norm–Choquet–OWA resource aggregator. First, an LSTM-EMA model forecasts resource trajectories 3 s ahead; next, a first-stage T-norm (min) pinpoints the bottleneck resource, and a second-stage Choquet–OWA, driven by an adaptive interaction measure $\varphi$, elastically compensates according to instantaneous power usage, achieving a “bottleneck-first, efficiency-recovery” coordination strategy. Theoretical analysis establishes monotonicity, tight bounds, bottleneck prioritization, and Lyapunov stability, with node-level complexity of only $O\left(1\right)$. In joint simulations involving 360 UAVs, the method holds the average round-trip time (RTT) at 55 ms, cutting latency by 5%, 10%, 15%, and 20% relative to Min, DRL-PPO, single-layer OWA, and WSM, respectively. Jitter remains within 11 ms, the packet-loss rate stays below 0.03%, and residual battery increases by about 12% over the best heuristic baseline. These results confirm the low-latency, high-stability benefits of the prediction-based peak-shaving plus two-stage fuzzy aggregation approach for large-scale UAV swarms.

1. Introduction

In recent years, the rapid advance of Unmanned Aerial Vehicle (UAV) technology has enabled multi-UAV cooperation systems to play an increasingly vital role in target tracking, environmental monitoring, emergency rescue, and related domains [1]. In real-world applications, multiple UAVs must establish a stable, efficient cooperative network to meet complex task demands while adapting to dynamic environmental constraints. When executing computation-intensive or communication-sensitive missions, a UAV swarm faces especially stringent real-time coordination requirements across three critical resources: onboard battery energy, wireless-link bandwidth, and onboard computing power [2]. Balancing task performance with system robustness under limited resources has therefore become a central scientific challenge in the field of UAV cooperation.

In current multi-UAV resource scheduling approaches, two typical schemes dominate: rigid bottleneck-protection schemes (e.g., the Min operator) and simple linear-weighted aggregators (e.g., the Weighted Sum Model, WSM). The former strictly adheres to the barrel effect, using the weakest resource dimension to determine overall task feasibility [3]. While this guarantees reliability under extreme conditions, it fails to leverage excess capacity in non-bottleneck resources, severely limiting efficiency. By contrast, linear-weighted models combine resource dimensions via fixed weights, offering flexibility but lacking adaptive adjustment when conditions change rapidly; this often leads to overload or resource wastage and degrades overall efficiency and stability [4].

A more balanced approach is therefore needed—one that can rapidly react to emerging bottlenecks while simultaneously harnessing the elastic potential of non-bottleneck resources, thus optimizing both task performance and system robustness.

To address these challenges, fuzzy set theory and aggregation operators have recently seen wide use in resource allocation and task scheduling. Two-stage fuzzy aggregators, in particular, offer notable advantages: the first stage employs a rigorous T-norm for bottleneck protection, while the second stage uses nonlinear fusion operators such as the Choquet Integral and Ordered Weighted Averaging (OWA) to dynamically balance bottleneck and non-bottleneck capacities. However, their adoption in UAV cooperation remains scarce, especially due to a lack of effective foresight into future resource trends, which hampers performance in highly dynamic flight environments.

Inspired by two-stage fuzzy aggregation theory, this paper proposes a prediction-enhanced two-stage T-norm–Choquet–OWA resource aggregator. It is designed to accurately sense and assess both real-time and future states of UAVs’ three key resources, thereby ensuring reliable task execution and efficient resource utilization.

The main contributions of this paper are as follows:

• Prediction-Enhanced Two-Stage T-norm–Choquet–OWA Aggregator: We introduce a resource aggregator that optimizes battery energy, bandwidth, and onboard computing power in UAV swarms in real time. Prediction-augmented membership functions forecast resource dynamics several seconds ahead, and the two-stage design first protects bottlenecks using a T-norm before leveraging non-bottleneck capacity via a Choquet–OWA fusion. This ensures both safe and efficient task execution in resource-constrained scenarios.
• Rigorous Theoretical Foundations: We present a comprehensive theoretical analysis and parameter design, including proofs of monotonicity, correctness of bounds, prioritization of bottlenecks, and Lyapunov stability. These results guarantee the aggregator’s interpretability, robustness, and convergence in practical settings.
• Simulation-Based Validation: Through extensive simulation studies, we demonstrate that our aggregator outperforms traditional Min-based bottleneck protection and linear-weighted WSM approaches, offering superior aggregation performance and higher resource-saving efficiency.

The remainder of this paper is organized as follows. Section 2 reviews related work. Section 3 details the theoretical properties of the proposed aggregator model and the algorithm. Section 4 presents the proof and analysis of the algorithm. Section 5 presents simulations and performance analysis. Section 6 discusses the work in this paper. Finally, Section 7 concludes the paper and outlines future work directions.

2. Related Work

2.1. Overview of UAV Resource Scheduling and Task Allocation Methods

Unmanned Aerial Vehicles (UAVs) are integral to many modern applications, driving the need for efficient resource scheduling and task allocation. In Flying Ad hoc Networks (FanETS), a hierarchical framework clusters user UAVs so that tasks can either execute locally or offload to Mobile Edge Computing (MEC) UAVs, minimizing energy consumption via an iterative optimization algorithm [5]. UAV-assisted Mobile Crowd Sensing (MCS) uses a multi-task allocation scheme and deep reinforcement learning to expand data-collection coverage, optimize flight paths, and reduce energy costs [6]. For emergency response, a swarm-level scheduling method applies Particle Swarm Optimization (PSO) to balance and minimize total flight distance, outperforming traditional approaches in efficiency [7]. In hybrid MEC networks, thermal-aware scheduling addresses CPU cooling limits by jointly optimizing user admission, task scheduling, and UAV trajectories, thereby shortening mission time while keeping CPU temperatures in check [8]. Decentralized cluster scheduling—exemplified by the Consensus-Based Bundle Algorithm (CBBA) and the Performance Impact (PI) algorithm—integrates task awareness to improve assignment accuracy and reduce travel time relative to conventional methods [9]. A bio-inspired wolf-pack strategy models swarm behavior for dynamic task assignment in complex environments, achieving high mission completion rates and balanced workloads [10]. FlexEdge converts multi-objective scheduling into a single-objective problem using a genetic algorithm, optimizing both task allocation and UAV positioning to cut execution time and energy use [11]. Finally, the Maximum UAV Trajectory and Task Allocation Algorithm (MUTAA) delivers real-time route planning and scheduling in latency sensitive scenarios, substantially boosting mission completion rates [12]. Collectively, these approaches underscore the challenges and innovations in UAV resource scheduling and task allocation, notably in enhancing energy efficiency, thermal management, and real-time decision-making.

2.2. Fuzzy Membership Functions and T-Norm/OWA Aggregation

Fuzzy membership functions and T-norm/OWA aggregation are fundamental to fuzzy logic and decision-making, particularly within multi-attribute decision-making (MADM) and multi-criteria decision-making (MCDM) frameworks. Membership functions extend classical set membership to model uncertainty and fuzziness more flexibly. For example, in opportunistic mobile networks, optimal membership functions based on asymmetric triangular fuzzy numbers have improved routing metrics—outperforming symmetric fuzzy numbers in both transmission cost and delay [13]. In rule-based classifiers, membership functions enhance a decision support system’s interpretability and reliability, balancing generalization quality with knowledge-base simplicity [14].

T-norms and OWA operators are crucial for aggregating fuzzy information. T-norms like the Aczel–Alsina norm offer versatile means to combine fuzzy sets, benefiting MADM scenarios that must fuse uncertain inputs. Applications include interval-valued Pythagorean fuzzy sets and T-spherical fuzzy data, where Aczel–Alsina aggregation reduces information loss and strengthens decision robustness [15,16]. The use of generalized T-norms and T-conorms in advanced fuzzy aggregation operators further demonstrates their adaptability in complex decision environments [17]. In q-rung orthopair fuzzy contexts, T-norm integration creates a flexible, robust framework for handling unknown weight information [18]. Together, these techniques underpin sophisticated models capable of addressing the uncertainty and complexity of real-world decision problems.

2.3. Choquet Measure and Bottleneck Protection in UAV Networks

Integrating Choquet measures with bottleneck protection strategies has recently emerged as a promising approach to boost efficiency and security in UAV networks. The Choquet Integral—a powerful tool for capturing interdependencies among performance criteria—can optimize resource allocation and decision-making under conflicting objectives such as energy use, bandwidth distribution, and computational load. As UAV systems become a flexible platform for wireless communication and edge computing, managing these resources effectively is crucial to maintaining peak performance [19].

Bottleneck protection techniques like SDN-driven topology deception play a vital role in defending critical UAV nodes. By generating virtual network layouts, these schemes mislead adversaries and shield the UAVs acting as communication relays in sensor-assisted deployments [20]. Yet, UAVs still face severe constraints: limited onboard energy, narrow wireless channels, and finite processing power. To address these, researchers have explored Mobile Edge Computing (MEC) and blockchain integration, offering secure frameworks for offloading tasks and coordinating resources—key steps for safeguarding privacy and cutting power draw [21]. However, practical adoption is hampered by UAVs’ inherent Size–Weight–Power (SWaP) limits [22].

Optimizing UAV placement and control to minimize energy consumption while maximizing service quality remains challenging. Recent algorithms that leverage Virtual Force Fields (VFF) and Optimal Transport Theory (OTT) for resource management demonstrate meaningful gains but also highlight the complexity of the problem [23]. Collectively, these advances point to the need for further investigation to surmount today’s limitations and unlock the full capabilities of UAV networks across varied applications.

2.4. Comparison and Limitations of Two-Stage and Multi-Stage Aggregation Frameworks

In complex environments, multi-UAV systems now tackle increasingly diverse and dynamic missions. To manage this complexity, researchers have designed hierarchical frameworks that split resource aggregation, path planning, and task scheduling into two or more stages. Each stage applies a specialized aggregation strategy, which simplifies computation and boosts adaptability. However, these approaches often create information silos between stages and achieve only limited global optimality.

In practice, staged aggregation is common in task assignment and route optimization—for example, coordinating data collection, energy management, and real-time communication. While such frameworks can raise resource utilization and ease real-time processing loads, researchers find that stage coupling and error propagation frequently yield suboptimal end-to-end performance. As shown in

Table 1. Comparison of existing two-stage/multi-stage resource aggregation frameworks.

Framework	Description	Advantages	Disadvantages
Multi-stage hierarchical aggregation framework [24]	Decompose complex decisions into multiple stages and solve each with optimization algorithms.	Low computational complexity, suitable for large-scale UAV systems, and easily parallelizable in a single stage.	Fragmented information hinders global optimality, errors easily accumulate across stages, slow stages constrain real-time performance.
Hierarchical reinforcement learning multi-stage framework [25]	A three-layer strategy—macro evaluation, action decision, and instruction generation—to optimize multi-UAV collaboration and scheduling.	Integrates global and local decisions to boost performance, supports coordination in high-dimensional action spaces, enhances multi-UAV system adaptability.	Complex parameter design, layer isolation, hinders real-time performance, relies on large-scale data.
Multi-objective, multi-strategy, multi-stage task allocation framework [26]	Multi-constrained, multi-stage modeling of task allocation and decision-making using multi-strategy improved Dung Beetle Optimizer(MIDBO) for coordinated global optimization.	Balances multiple objectives, multi-stage optimization boosts global optimality, multi-strategy approach enhances robustness.	Errors accumulate easily, higher complexity, parameters require scenario-specific tuning.
Framework of this article	Combining prediction-enhanced membership functions with two-stage fuzzy aggregation to fuse energy, bandwidth, and compute resources in real time, enabling bottleneck protection and elastic adjustment.	Balances bottleneck protection and efficiency improvement, introduces a prediction module to anticipate resource conflicts, rigorous theoretical basis with high interpretability and robustness.	Prediction module incurs higher overhead, aggregation weights require offline tuning.

, when balancing information freshness, energy efficiency, and adaptability to changing conditions, current methods still fall short in multi-objective trade offs and overall system robustness.

2.5. Research on Auction-Based and Hybrid RL–Fuzzy Methods

Recently, several studies have integrated reinforcement learning with fuzzy logic or auction mechanisms for task scheduling in UAV/edge computing scenarios. Specifically, Li Dong et al. [27] proposed a deep progressive reinforcement learning scheduling framework for IRS-assisted UAV–MEC systems, in which a progressive scheduler and taboo search jointly optimize UAV positioning, task offloading, and resource allocation, demonstrating real-time scheduling capability and resilience against catastrophic forgetting (arXiv). He et al. [28] developed an edge computing framework for smart agricultural supply chains that combines auction mechanisms with fuzzy optimizers. Through multi-stage auctions and fuzzy neural networks, the framework supports coordination and scheduling across supply chain stages, emphasizing the integration of market mechanisms with rule-based fuzzy optimization to enable real-time decision-making in complex agricultural scenarios (SpringerOpen). Zander et al. [29] investigated the integration of reinforcement learning with Takagi–Sugeno–Kang (TSK) fuzzy systems, exploring architectures such as actor–critic and DQN–ANFIS in standard reinforcement learning tasks, highlighting the potential of RL–fuzzy systems in terms of both interpretability and performance (ResearchGate).

Distinctions and innovations compared with the above works:

• Fusion mechanism differences: Unlike Li et al., who focus on RL structure evolution, He et al.’s emphasis on auction plus fuzzy neural network-driven real-time decisions, and Zander et al.’s focus on RL–fuzzy control, the proposed two-stage scheduler explicitly integrates heterogeneous fuzzy aggregation operators—T-norm, Choquet, and OWA—augmented by an LSTM–EMA forecasting layer with a 3 s look-ahead window. This design achieves multidimensional fusion of scheduling evaluation metrics and prediction-driven weight adaptation, whereas auction/RL-based approaches predominantly rely on expost scheduling.
• Theoretical and interpretability differences: The proposed framework provides rigorous proofs of monotonicity, bound correctness, and Lyapunov stability, while maintaining $O\left(1\right)$ per-node computational complexity, thus ensuring both interpretability and embedded deployability. In contrast, existing hybrid RL–fuzzy and auction-based schedulers generally lack such formal guarantees.

3. Prediction-Based Two-Stage T-Norm–Choquet–OWA Aggregator

To meet a UAV swarm’s real-time coordination needs across battery energy, bandwidth, and onboard computing power, we propose a prediction-based two-stage T-norm–Choquet–OWA resource aggregator. First, it defines a fuzzy set representing multidimensional resource occupancy and uses forecast-augmented membership functions to anticipate and adjust for upcoming load. Next, a two-stage “rigorous protection + elastic integration” design ensures robust performance:

• Stage 1 (T-norm/min): Precisely isolates the bottleneck resource, preventing any “short plank” from being ignored.
• Stage 2 (Choquet–OWA): Adaptively trades off between the identified bottleneck level and instantaneous power consumption, achieving a smooth balance between system performance and endurance.

Figure 1 illustrates the aggregator’s data flow and modules across five stages, from real-time monitoring and future prediction to the final membership output:

• Data acquisition layer: Embedded sensors capture the current load, and the edge prediction module provides an s-second-ahead forecast.
• Fuzzification layer: Four prediction-enhanced membership functions convert each resource dimension into fuzzy membership values.
• Bottleneck protection layer (stage 1): Compute the minimum of these membership values to identify the bottleneck membership ${\mu }_b$. If any primary resource falls below its threshold, protection is triggered immediately.
• Elastic fusion layer (stage 2): Calculate the coupling factor $\lambda$ based on task elasticity e and predicted remaining energy $E_{rem}$. Then, apply Choquet–OWA to fuse ${\mu }_b$ with the elasticity membership ${\mu }_e$, producing the final membership ${\mu }_{out}$.
• Scheduler interface layer: The scheduler uses ${\mu }_{out}$ to assess task feasibility and determine priority ordering.

3.1. Resource-Usage Multidimensional Fuzzy Set Design (${\mu }_{resource}$)

3.1.1. Fuzzy Aggregation Under Extreme Protection

To guarantee safe and stable task execution in a blockchain-enabled UAV network’s fuzzy-game model, we apply an extreme-protection strategy for fuzzy aggregation of multidimensional resources. We enhance this approach with both future-aware and elastic coupling: (1) Extreme protection isolates the bottleneck by selecting the smallest membership value across the three dimensions—CPU, network bandwidth, and battery capacity—as ${\mu }_{resource}$. (2) If any dimension falls below its threshold, we immediately reject the task or adjust the game strategy, preventing overconsumption and system instability (the “short plank” effect). Although more conservative than average or weighted aggregation, this method ensures high reliability—critical for safety-sensitive missions.

As shown in

Table 2. Resource-usage multidimensional fuzzy set metrics.

Symbol	Indicator Name	Quantification or Constraint
$F_c$	Predicting CPU utilization	$F_c\in [0,1]$
$F_b$	Predict bandwidth utilization	$F_b\in [0,1]$
$F_e$	Predicted remaining energy ratio	$F_e\in [0,1]$
${\lambda }_c,{\lambda }_b,{\lambda }_e$	Resource forecast weight	$\sum \lambda =1$
$\varphi \in [0,1]$	Coupling Penalty Factor	$\varphi \in [0,1]$

, Let $u_c^{\mathrm{raw}}$, $u_b^{\mathrm{raw}}$, and $e^{\mathrm{raw}}$ denote the raw CPU utilization (%), bandwidth utilization (%), and remaining energy (%) measured at the UAV node. To make them dimensionless and comparable, each metric is normalized to the unit interval $[0,1]$ before entering the fuzzy-set model, yielding

$$F_c={\displaystyle \frac{u_c^{\mathrm{raw}}-u_c^{min}}{u_c^{max}-u_c^{min}}},F_b={\displaystyle \frac{u_b^{\mathrm{raw}}-u_b^{min}}{u_b^{max}-u_b^{min}}},F_e={\displaystyle \frac{e^{\mathrm{raw}}-e^{min}}{e^{max}-e^{min}}}$$

(1)

where $u_c^{min},u_c^{max},u_b^{min},u_b^{max},e^{min},e^{max}$ are the observed or nominal bounds for each resource (typically 0 and $100\%$). After normalization, all three indicators satisfy $F_{\{·\}}\in [0,1]$, where values close to 1 represent higher utilization (for CPU and bandwidth) or higher sufficiency (for energy).

This min–max normalization rescales each raw metric into a standard unit-less form, allowing heterogeneous resources to be aggregated fairly in the multidimensional fuzzy-set framework. $F_c$ and $F_b$ approach 1 when CPU or bandwidth are heavily used, while $F_e$ approaches 1 when the remaining energy is abundant.

3.1.2. Future-Aware Membership Function

(1) CPU prediction-enhanced membership function (alert contraction): Penalizes “current load + imminent predicted load” in one step to avoid resource decision errors caused by upcoming peaks.

$$\widetilde{{\mu }_c}(c,F_c)={\displaystyle \frac{1}{1+exp[{\kappa }_c(c+{\lambda }_c{F}_c-{\theta }_c)]}}$$

(2)

Here, c is the current CPU utilization; $F_c$ is the k-second-ahead predicted utilization; their sum measures the total imminent CPU pressure. ${\lambda }_c\in [0,1]$ controls the weight of the prediction—the more compute-sensitive the task, the larger ${\lambda }_c$. ${\theta }_c$ is the utilization inflection point; ${\kappa }_c$ controls the steepness of the S-shaped curve. If $c+{\lambda }_c{F}_c\ll {\theta }_c$, the exponential term tends to 0 and ${\tilde{\mu }}_c\to 1$, indicating ample computing resources; otherwise, it decreases rapidly.

(2) Bandwidth membership function (alert contraction): For high real-time communication services, can be set a smaller ${\theta }_b$ and a larger ${\kappa }_b$ to achieve “early braking.”

$$\widetilde{{\mu }_b}(b,F_b)=1-{\displaystyle \frac{1}{1+exp\left[{\kappa }_b(b+{\lambda }_b{F}_b-{\theta }_b)\right]}}$$

(3)

Here, b is the current bandwidth utilization rate; $F_b$ is the predicted future congestion; ${\lambda }_b$ is the weight. If $b+{\lambda }_b{F}_b$ is very small $\Rightarrow \widetilde{{\mu }_b}\approx 1$ (bandwidth ample); once it reaches the inflection point ${\theta }_b$, it decays rapidly.

(3) Energy membership function (power response correction)

$$\widetilde{{\mu }_{e_r}}(e_r,F_e)={\mu }_{e_r}(e_r-{\lambda }_e(1-F_e))$$

(4)

Here, ${\mu }_{e_r}(·)$ is the original triangular function, and the offset term implements a “future power drop” penalty. $e_r$ is the current remaining energy fraction; $F_e$ is the predicted remaining energy fraction after task completion. The displacement term ${\lambda }_e(1-F_e)$ pre-deducts the energy expected to be consumed, with ${\lambda }_e$ reflecting the task’s energy sensitivity. After displacement, if the predicted remaining energy drops sharply, the function input becomes small, the membership degree decreases, and energy protection is triggered more rapidly.

(4) Instantaneous Power Consumption Rate Membership Degree (Linear)

$${\mu }_p\left(p\right)=1-p,p\in [0,1]$$

(5)

where p is the current power load as a proportion of the reference power. It decreases linearly: higher power → lower membership, simply and intuitively quantifying the impact of “power consumption rate” on task feasibility.

3.1.3. Two-Stage Extreme Protection + Elastic Coupling

(1) Stage 1 Extreme Protection (Core Three Dimensions): Retaining the “barrel effect,” the weakest of the three primary resources determines overall feasibility. If any membership degree equals $0\to {\mu }_{pre}=0$, the task is immediately rejected or migrated.

$${\mu }_{pre}=min\{\widetilde{{\mu }_c},\widetilde{{\mu }_b},\widetilde{{\mu }_{e_r}}\}$$

(6)

(2) Stage 2 Elastic Coupling

$$\varphi =\eta +(1-\eta )F_e,\varphi \in (0,1]$$

(7)

Here, $\eta$ is task elasticity; for high-performance tasks $\eta \to 1$, indicating greater emphasis on performance. $F_e$ is the predicted remaining energy after task completion; as energy sufficiency increases $F_e\to 1$. $\varphi$ combines these two: if a task is performance-critical and energy is ample $\Rightarrow \varphi$ increases; if a task is energy-saving or energy is low $\Rightarrow \varphi$ decreases. $\varphi$ adjusts the penalty strength on the power consumption rate.

(3) Two-Stage T-norm–Choquet Resource Aggregation

To simultaneously capture bottleneck protection and cross-dimensional complementarity, this paper adopts a two-stage aggregation structure. In the lower stage, a T-norm (min) is used to extract the bottleneck value among the three primary resources—CPU, bandwidth, and energy.

$${\mu }_{pre}=min\{\widetilde{{\mu }_c},\widetilde{{\mu }_b},\widetilde{{\mu }_{e_r}}\}$$

(8)

In the upper stage, a binary Choquet–OWA operator with interaction measure $\nu$ models the complementarity between resource adequacy and power consumption rate over ${\mu }_{pre},{\mu }_p$, defined as follows:

$$f_1={\mu }_{pre},f_2={\mu }_p,f_{\left(1\right)}\ge f_{\left(2\right)}$$

(9)

With the two membership degrees sorted in descending order, let $S_1=\{1,2\},S_2=\left\{2\right\}$. The Choquet aggregation then becomes

$${\mu }_{resource}=\underset{{\Delta }_1}{\underbrace{(f_{\left(1\right)}-f_{\left(2\right)})}}\nu \left(S_{\left(1\right)}\right)+\underset{{\Delta }_2}{\underbrace{f_{\left(2\right)}}}\nu \left(S_{\left(2\right)}\right)$$

(10)

Here, the interaction measure is defined as

$$\nu \left(\left\{{\mu }_{pre}\right\}\right)=\varphi ,\nu \left(\left\{{\mu }_p\right\}\right)=1-\varphi ,\nu \left(\{{\mu }_{pre},{\mu }_p\}\right)=1$$

(11)

Additionally, $\varphi =\eta +(1-\eta )F_e\in (0,1]$, consistent with the original model. Substituting the above yields the closed-form

$${\mu }_{resource}=\varphi {\mu }_{pre}+(1-\varphi )max\{{\mu }_{pre},{\mu }_p\}$$

(12)

Here, when ${\mu }_{pre}\le {\mu }_p$ (the power consumption rate is better than the bottleneck value), ${\mu }_{resource}=\varphi {\mu }_{pre}+(1-\varphi ){\mu }_p$ reflects the “power-compensation” effect; when ${\mu }_{pre}>{\mu }_p$, it reverts to ${\mu }_{resource}={\mu }_{pre}$ to ensure bottleneck protection takes precedence. The parameter $\varphi$ is still modulated by task elasticity $\eta$ and predicted remaining energy $F_e$, enabling scenario-adaptive behavior.

The overall mechanism is as follows:

• Future-Aware Sensing: The formulas $\widetilde{{\mu }_c}(c,F_c),\widetilde{{\mu }_b}(b,F_b),\widetilde{{\mu }_{e_r}}(e_r,F_e)$ inject forecast values into the membership functions, enabling preemptive penalization of imminent resource conflicts or energy drops.
• Hard Bottleneck Protection: The formula ${\mu }_{pre}$ uses the minimum operator to ensure that any primary resource shortage immediately triggers protection.
• Soft Rate Suppression: The formulas for $\varphi$ and ${\mu }_{resource}$ incorporate instantaneous power consumption, smoothly fusing power-mean and power-penalty terms to achieve elastic–power coupling regulation.
• Final Membership Output: The membership ${\mu }_{resource}$ is combined with ${\mu }_{trust}$ and ${\mu }_{delay}$ to form the payoff R, which drives the adaptive evolution of the subsequent fuzzy-game strategy.

3.2. Construction of the Comprehensive Fuzzy Payoff Function

In this section, after obtaining the single resource evaluation ${\mu }_{resource}$, we further consider large-scale UAV swarm simulations and highly dynamic scenarios. Based on three fuzzy sets—credibility ${\mu }_{trust}$, communication delay requirement ${\mu }_{delay}$, and resource evaluation ${\mu }_{resource}$—we use OWA-RL (ordering plus regret-based weight learning) to aggregate these three metrics into a comprehensive payoff function R. The OWA-RL mechanism assigns weights w to an RL agent for online output. This function evaluates the overall payoff of cooperative or competitive strategies among vehicles:

(1) First, sort the three fuzzy values to obtain the descending triplet ${\mu }_{\left(1\right)}\ge {\mu }_{\left(2\right)}\ge {\mu }_{\left(3\right)}$.

$$({\mu }_{\left(1\right)},{\mu }_{\left(2\right)},{\mu }_{\left(3\right)}):=sort\_desc({\mu }_{trust},{\mu }_{delay},{\mu }_{resource})$$

(13)

(2) Potential game modeling

Let the OWA weights $w=\{w_1,w_2,w_3\}\in {\Delta }^2$ represent the “central scheduler” action, and let the joint strategy $\pi$ of UAVs/edge nodes represent the subordinate players’ action. Define the potential payoff function $\Phi (\mathbf{w},\pi )$ as the game’s potential function.

$$\Phi (\mathbf{w},\pi )=\sum _{k=1}^3{\omega }_k{\mu }_{\left(k\right)}-{\displaystyle \frac{\lambda }{2}}{\parallel \mathbf{w}-{\mathbf{w}}^{prior}\parallel }_2^2$$

(14)

Here, ${\mathbf{w}}^{prior}$ is the governance-layer prior and $\lambda >0$ is the regularization coefficient. Appendix A proves that the weight-update game and the UAV/edge-node strategy game share the potential function $\Phi$, thus forming a single-player potential game.

(3) A regret-learning algorithm is used to perform weighted regret updates on the central weights.

$$w_k^{(t+1)}={\displaystyle \frac{exp\left(\eta {\sum }_{\tau =1}^t{\mu }_{(\tau ,k)}\right)}{{\sum }_{h=1}^{3}exp\left(\eta {\sum }_{\tau =1}^t{\mu }_{(\tau ,h)}\right)}},k=1,2,3$$

(15)

Here, $\eta$ is the learning rate, and ${\mu }_{(\tau ,k)}$ denotes the $k-th$ largest membership value after sorting at step $\tau$. Specifically, ${\mu }_{(\tau ,k)}$ is the value that ranks h-th when the three membership degrees are ordered descendingly at time $\tau$. According to regret-learning theory, the sequence $w_t$ achieves external regret $R_T/T\to 0$. Combined with the potential-game property, we obtain the following:

Theorem 1.

For any $ϵ>0$, there exists a number of steps $T\left(ϵ\right)=O(1/{ϵ}^2)$ such that the average weight $\overline{w_T}={\displaystyle \frac{1}{T}}{\sum }_{t\le T}{w}_t$ constitutes an $ϵ$-Nash equilibrium.

In our scheduling formulation, the interaction among UAVs can be modeled as a finite potential game, where each UAV acts as a player and its strategy corresponds to selecting the relative contribution of different fuzzy aggregation components. A game $G=\langle N,\left\{S_i\right\},\left\{u_i\right\}\rangle$ is called a potential game if there exists a scalar function $\Phi :S\to \mathbb{R}$ such that for any player i, strategies $s_i,s_i^{\prime }\in S_i$, and $s_{-i}\in S_{-i}$,

$$u_i(s_i^{\prime },s_{-i})-u_i(s_i,s_{-i})=\Phi (s_i^{\prime },s_{-i})-\Phi (s_i,s_{-i})$$

(16)

This property ensures that any unilateral improvement in an individual UAV’s utility is aligned with an increase in the global potential function, implying that local optimization is consistent with global network performance improvement. In our case, the regret-learning weight update in Equation (14) operates over such a potential game structure, allowing the learning dynamics to converge toward an $ϵ$-Nash equilibrium that maximizes the potential function. This directly links the local adaptation of aggregation weights to the maximization of overall system efficiency.

(4) OWA aggregation: the comprehensive payoff at time t is calculated as

$$R_{OWA}\left(t\right)=\sum _{k=1}^3{\omega }_k^{\left(t\right)}{\mu }_{\left(k\right)}$$

(17)

where ${\omega }_1^{\left(t\right)}$ controls the emphasis on the best metric, and ${\omega }_3^{\left(t\right)}$ controls the penalty on the worst metric. Regret learning automatically increases ${\omega }_3^{\left(t\right)}$ in congested or low-energy scenarios (risk-averse); when resources are abundant, it shifts toward averaging or favoring the maximum (efficiency-seeking).

In summary, this chapter forms a prediction-enhanced two-stage T-norm-Choquet-OWA aggregator algorithm, as shown in Algorithm 1.

Algorithm 1 Prediction-enhanced two-stage T-norm–Choquet–OWA aggregator

Require: $AllVariable\ge 0$   1: $c\leftarrow$ current CPU utilization (0–1)   2: $b\leftarrow$ current bandwidth utilization (0–1)   3: $e_r\leftarrow$ current remaining energy ratio (0–1)   4: $p\leftarrow$ current power load ratio (0–1)   5: $F_c,F_b,F_e\leftarrow$ k-step predictions for CPU, bandwidth, energy   6: ${\lambda }_c,{\lambda }_b,{\lambda }_e$← prediction weights ($\sum \lambda =1$)   7: $\eta \leftarrow$ task elasticity (0–1) Ensure: ${\mu }_{resource}=$ overall resource membership (0–1).   8: //Affiliation   9: $\widetilde{{\mu }_c}(c,F_c)\leftarrow {\displaystyle \frac{1}{1+exp[{\kappa }_c(c+{\lambda }_c{F}_c-{\theta }_c)]}}$ 10: $\widetilde{{\mu }_b}(b,F_b)\leftarrow 1-{\displaystyle \frac{1}{1+exp\left[{\kappa }_b(b+{\lambda }_b{F}_b-{\theta }_b)\right]}}$ 11: $shift\leftarrow {\lambda }_e(1-F_e)$ 12: $\widetilde{{\mu }_{e_r}}(e_r,F_e)\leftarrow {\mu }_{e_r}(e_r-shift)$ 13: ${\mu }_p\left(p\right)\leftarrow 1-p,p\in [0,1]$ 14: //First level bottleneck protection 15: ${\mu }_{pre}\leftarrow min\{\widetilde{{\mu }_c},\widetilde{{\mu }_b},\widetilde{{\mu }_{e_r}}\}$ 16: //Secondary elastic fusion 17: $\varphi \leftarrow \eta +(1-\eta )F_e,\varphi \in (0,1]$ 18: if  ${\mu }_{pre}\le {\mu }_p$  then 19:     ${\mu }_{resource}\leftarrow \varphi {\mu }_{pre}+(1-\varphi )max\{{\mu }_{pre},{\mu }_p\}$ 20: else 21:     ${\mu }_{resource}={\mu }_{pre}$ 22: return ${\mu }_{resource}$

4. Algorithm Proof and Analysis

4.1. Proofs of Monotonicity, Bound Correctness, and Bottleneck Priority

These three properties establish the mathematical predictability of the aggregator (proof in Appendix A):

• Monotonicity ensures that measurement noise in the inputs cannot trigger counterintuitive jumps in the output.
• Bound correctness guarantees that membership values always lie within the valid interval and align with extreme-case behavior.
• Bottleneck priority assigns the greatest decision weight to the most constrained resource while preserving room for power compensation, thus balancing safety and efficiency.

4.2. Stability of Conjunctive–Disjunctive Switching (Lyapunov)

The stability results are as follows (proof in Appendix B):

• The common Lyapunov function V(x) is non-increasing in both modes ${\mathcal{M}}_1$ and ${\mathcal{M}}_2$.
• The switching surface $\Sigma$ is continuous, with no sliding mode or Zeno phenomena.
• By the geometric convergence in (B-5), the system is globally asymptotically stable to the set ${\mathcal{M}}_1\cup \Sigma$, i.e., it ultimately satisfies ${\mu }_{\mathrm{pre}}\ge {\mu }_p$ — the bottleneck protection mode.

$$\underset{t\to \infty }{lim}|{\mu }_{\mathrm{resource}}\left(t\right)-{\mu }_{\mathrm{pre}}\left(t\right)|=0;$$

(18)

4.3. Complexity and Scalability

The conclusions are as follows (proof in Appendix C):

• Time complexity: Per UAV = O(1) for EMA/O(L h²) for LSTM; scales linearly with the number of resource dimensions and linearly (and in parallel) with the number of UAVs.
• Space complexity: Under O(M) floating-point values; can be implemented in a streaming fashion on both MCUs and FPGAs.
• Communication and sorting: Low overhead; centralized sorting at O(N log N) is not a bottleneck.
• Scalable safety: The theoretical convergence rate is decoupled from parallelism, supporting fleets of thousands of UAVs.

5. Simulation and Performance Analysis

To comprehensively validate the practical performance and advantages of the proposed prediction-enhanced two-stage T-norm–Choquet–OWA aggregator, we built a high-fidelity joint simulation platform using PX4-SITL (v1.13) flight controller simulator, ROS2 Humble robot operating system, and ns-3 network simulator as a complete toolchain. PX4-SITL models the UAVs’ kinematics and dynamics, including flight-path control, battery-drain profiles, and onboard computing-load characteristics. ROS2 Humble provides a distributed node-communication environment, supporting mission command distribution, resource-status monitoring, and real-time inference execution of the aggregator across the swarm. ns-3 delivers precise wireless-link simulation—for LTE and Wi-Fi networks—to evaluate bandwidth usage, latency, and packet-loss metrics during mission execution.

To assess the aggregator’s performance in large-scale UAV swarms, we designed a target-tracking and edge-inference scenario with 360 UAVs operating over a 10 km × 10 km area. The resource status and task distribution of drones are shown in

Table 3. Resource configuration and task configuration of simulation.

Resource Configuration	Task Configuration
Battery (100%)	High real-time tasks vs. Routine tasks
CPU usage constraint [0, 1]	Task elasticity parameter $\eta$
Evaluation and calculation (100 ms)	360 UAVs

. Targets are randomly distributed and move dynamically to simulate real-world emergent tracking tasks. Each UAV must continuously acquire and track its assigned target, perform real-time analysis of captured video and sensor data using onboard edge inference, and transmit the analysis results over wireless links to designated edge servers.

Through the above scenario setup and precise simulation runs, this paper analyzes and evaluates the performance of the proposed method versus existing approaches across metrics such as resource aggregation strategy and network link quality (including link latency and packet loss rate), thereby further validating the significant advantage of the prediction-enhanced two-stage T-norm–Choquet–OWA aggregator in balancing system safety and efficiency.

As shown in Figure 2, violin plots compare the distributions of Resource Membership Degree under three task scenarios bandwidth sensitive, compute intensive, and energy sensitive for four resource aggregation strategies. The black band indicates the 25–75% interquartile range, the horizontal bar marks the full 1.5 IQR span, and the dot shows the median:

(1) Dual-stage T-norm–Choquet (Resource_choquet)

Medians in all three scenarios remain between 0.50 and 0.65, with tight convergence and short tails. This means that stage 1 bottleneck protection prevents very low membership values, while stage 2 elastic coupling uses non-bottleneck resources to raise the overall score. This confirms the “bottleneck priority + power compensation” mechanism described in Equation (18).

(2) Single-layer OWA (Resource_owa)

Mean and IQR are slightly higher than for Choquet, but tails are longer. Fixed weights can boost average membership yet fail to guard against extreme bottlenecks, causing occasional low values—just as we predicted for “no predictive peak shaving.”

(3) Min operator (Resource_min)

All scenarios show pronounced left skew. In compute- and energy-sensitive tasks, medians drop to 0.15–0.25 and tails reach 0.05. This illustrates that an “overly strict barrel effect” severely depresses feasibility scores, at the expense of throughput.

(4) Arithmetic mean (Resource_mean)

Medians sit around 0.45–0.55 with a wide IQR, indicating that simple averaging neither protects against bottlenecks nor offers compensatory complementarity. Its performance falls between OWA and Min, matching the Section 2.4 assessment of “rigid weights and insufficient task sensitivity.”

These violin plots clearly show that the proposed Choquet aggregator maintains the highest, most stable resource membership across all three scenarios—avoiding Min’s over-convergence and overcoming OWA/mean’s volatility—thereby validating the synergistic benefits of prediction enhancement and two-stage design for optimizing resource bottlenecks and power consumption rates.

As shown in Figure 3, for a 360-UAV swarm under the prediction-enhanced two-stage aggregation scheduler, the link available bandwidth (left) and packet loss rate (right) are plotted against each node index. These results directly validate the “predictive peak-shaving— bottleneck priority” mechanism described in Section 4.

Bandwidth curve: Most nodes remain stably in the 0.49–0.52 Mbps range. Only nodes 220–240 exhibit a brief spike (≈0.57 Mbps) before quickly returning to the baseline. This spike corresponds to a local burst in bandwidth demand from highly concurrent tasks. Because the first-stage T-norm has already locked the bottleneck and preemptively shaved the peak, the curve immediately stabilizes again, confirming the instant protection of bottleneck resources as described by Equation (15).

Packet-loss rate curve: The mean remains around 0.025%, with very low variance. A short jitter below 0.03% appears in the same node segment, then falls back. This behavior matches the second-stage Choquet–OWA elastic compensation: once bandwidth is shaved, queue depth decreases and packet loss synchronously drops, demonstrating the effectiveness of the power/bandwidth complementary trade-off.

No long-tail phenomenon: Neither curve shows sustained peaks or oscillations, indicating that the LSTM-EMA prediction module successfully foresaw the burst traffic within a 3 s window and suppressed its spread. This aligns with the Lyapunov stability analysis in Section 4.2—the system state quickly returns to the bottleneck steady-state set.

Therefore, these slight fluctuations and instantaneous corrections in bandwidth and packet loss fully demonstrate that the proposed aggregator not only shaves peaks in RTT but also maintains stable throughput and extremely low packet loss at the link layer.

As shown in Figure 4, the RTT and signal strength distributions for 360 UAVs under the prediction-enhanced two-stage aggregation scheduler remain tightly controlled. The RTT curve fluctuates narrowly between 53 ms and 56 ms, with only a single spike (≈66 ms) at nodes 220–240 before quickly returning to baseline—demonstrating the first-stage T-norm’s instant suppression of sudden bottlenecks and the second-stage Choquet–OWA’s elastic compensation. Over the same period, signal strength stays clustered around −76 dBm ± 1 dB, indicating that RTT variations are driven primarily by link load rather than physical attenuation. By using a 3 s prediction window to shave peaks in advance, the algorithm ensures millisecond-level latency stability at most nodes despite low signal fluctuations. This figure supports the paper’s theoretical premise that bottleneck priority, power compensation, and forward-looking prediction work in concert to guarantee a robust real-time control loop.

As shown in Figure 5, the node-level distribution of link jitter in the 360-UAV scenario remains confined to 9.8–11.2 ms, with no sustained peaks. A brief pulse appears only at nodes 220–240 before quickly subsiding, thanks to

• The 3 s prediction window preemptively trimming peak Traffic, which suppresses queue-depth oscillations;
• Stage-1 T-norm bottleneck protection preventing low-membership tasks from monopolizing the link;
• Stage-2 Choquet–OWA elastically compensating for instantaneous power consumption, equalizing transmission intervals.

These results show that our method not only lowers average RTT but also significantly smooths delay jitter, providing UAV swarms with more stable real-time communication quality.

Figure 6 compares the average RTT curves for five scheduling strategies as the swarm size grows from 0 to 360 UAVs. All methods exhibit a sublinear increase, confirming the diminishing marginal impact of queueing delay as node count rises. However, the curves are clearly stratified in both level and slope: the prediction-enhanced two-stage aggregator consistently delivers the lowest RTT and the gentlest growth, reaching about 55 ms at 360 UAVs—5%, 10%, 15%, and 20% lower than Min, DRL-PPO, single-layer OWA, and WSM, respectively. This matches our theoretical model: forward-looking peak shaving lowers the baseline, the first-stage T-norm secures bottleneck safety, and the second-stage Choquet–OWA provides elastic compensation to suppress slope. In contrast, fixed-weight methods (WSM, OWA) and the non-predictive DRL-PPO climb more steeply due to resource mismatches. The trends in Figure 6 demonstrate that our approach maintains both the lowest initial latency and the smallest growth rate in scaled-up scenarios, underscoring its scalable real-time performance.

To assess the scalability and robustness of the proposed algorithm, we evaluated its performance under four UAV swarm sizes (50, 180, 360, and 500 UAVs) with five independent runs per configuration using different random seeds. Figure 7 presents the results for RTT, jitter, and signal strength, where each data point represents the mean ± standard deviation across repeated trials.

As shown in Figure 7, the average RTT exhibits a gradual increase as the swarm size grows, which is expected due to the higher network load and routing complexity. Nevertheless, the standard deviation remains consistently low (<39 ms), indicating that latency performance is stable and predictable even under heavy network conditions.

Jitter remains at a low magnitude across all swarm sizes, with slightly higher fluctuations observed at 500 UAVs. This minor variation is within acceptable bounds for time-sensitive UAV coordination tasks, confirming that the proposed scheme maintains reliable packet timing even at large scales.

Signal strength (in dBm) remains relatively stable across all swarm sizes, with minimal variation between different random seeds. This consistency demonstrates that the proposed topology control and adaptive link maintenance mechanisms preserve link quality despite increased node density.

Overall, these results confirm that the proposed algorithm achieves robust and scalable performance, maintaining low latency, minimal jitter, and stable signal quality across diverse UAV swarm sizes and stochastic conditions.

Finally, to ensure fair and reproducible comparisons against baselines, we added a detailed description of the hyperparameter settings, training procedures, and evaluation environment.

Table 4. Baseline configuration and experimental environment.

Methodology	Key Hyperparameters	Search Range/Settings	Tuning Strateg	Number of Training Rounds/Time	Hardware Environment
Min	-	fixed	No tuning required	-	Same as other methods
WSM	$w_1,w_2,w_3$	$[0,1],$ $w_1+w_2+w_3=1$	Grid search step size 0.05	Parameter search ≈0.8 h CPU AMD Ryzen 9 5950X, 128 GB RAM
Single-layer OWA	OWA Parameter p	$p\in [0.5,5]$	Grid search step size 0.1	Parameter Search ≈1.0 h CPU	Same as above
Two-stage T-norm+ Choquet– OWA	T-norm threshold $\tau$, Choquet capacity, OWA parameter p	$\tau \in [0.4,0.8]$, Initial capacity uniformity, $p\in [0.5,4]$	Phased grid search + local random perturbation	Parameter Search ≈1.5 h CPUn	Same as above
DRL-PPO	Learning rate $\eta$, clip ratio $ϵ$, entropy coefficient $\beta$, discount factor $\gamma$	$\eta \in \{1\times {10}^{-4},$ $5\times {10}^{-4},1\times {10}^{-3}\}$, $ϵ\in \{0.1,0.2,0.3\}$, $\beta \in \{0.01,0.02,0.05\}$, $\gamma =0.99$	Randomly search 20 configurations	$2.5\times {10}^5$ episodes (6 h, GPU)	Same as above + NVIDIA RTX 3090 GPU

and

Table 5. Unified experimental environment.

Category	Configuration
CPU	AMD Ryzen 9 5950X @ 3.4 GHz, 16 cores
Memory	128 GB DDR4
GPU	NVIDIA RTX 3090 (used only for DRL-PPO)
System	Ubuntu 22.04 LTS
Software	Python 3.10, PyTorch 2.0.1, NS-3.37, ROS 2 Humble
Simulation Parameters	Number of UAVs = 360, Topology = Self-Organizing Mesh, Channel Model = Nakagami-m (m = 1.5), Bandwidth = 20 MHz, Simulation Duration = 600 s, 50 replicates for all methods and averaged
Random Seed	50 independent seed sets, unified initialization process

list the hyperparameters, tuning strategies, and training details for all baseline methods, along with the unified hardware and software environments to ensure fair and reproducible comparisons.

The computationally intensive tasks in this study were hosted on a workstation with the following specifications:

• Central Processing Unit (CPU): AMD Ryzen 9 5950X @ 3.4 GHz (Advanced Micro Devices, Inc., Santa Clara, CA, USA)
• Memory (RAM): 128 GB DDR4 (Kingston Technology Corp., Fountain Valley, CA, USA)
• Graphics Processing Unit (GPU): NVIDIA GeForce RTX 3090 (NVIDIA Corp., Santa Clara, CA, USA). Note: The GPU was dedicated to running the Deep Reinforcement Learning PPO (DRL-PPO) algorithms.

• Hyperparameter tuning:
  • For Min, single-layer OWA, and WSM baselines, we conducted a grid search over weight vectors and operator parameters ($\lambda$, p) using the validation set, selecting configurations that maximized the average resource score without overfitting to specific scenarios.
  • For DRL-PPO, we adopted the default policy network structure and learning rate schedule from the original paper, then tuned the learning rate, clip ratio, and entropy coefficient via a random search over 20 trials. The final configuration was selected based on convergence speed and average reward stability.
  • All baselines used the same input normalization and preprocessing pipeline as the proposed method to ensure comparability.
• Training duration:
  • DRL-PPO was trained for $2.5\times {10}^5$ episodes (≈6 h wall-clock time) until the moving average reward plateaued within $\pm 1$% over 20 consecutive epochs.
  • For non-learning baselines, parameter optimization consumed ≈1.2 h of total CPU time.
• Evaluation environment:
  • Hardware: All methods were executed on the same server equipped with an AMD Ryzen 9 5950X CPU @ 3.4 GHz, 128 GB RAM, and NVIDIA RTX 3090 GPU (used only for DRL-PPO).
  • Software: Ubuntu 22.04, Python 3.10, PyTorch 2.0.1, NS-3.37, and ROS 2 Humble.
  • Simulation parameters (UAV swarm size, topology, link models, and channel conditions) were strictly identical across runs. Each result is averaged over 50 independent seeds.

The ablation study results, illustrated in Figure 8, clearly demonstrate the contribution of each module within the proposed two-stage fuzzy aggregation framework. When the predictive component is removed (w/o Prediction), task completion rate drops by approximately 6.8%, accompanied by a noticeable increase in average delay, indicating that predictive scheduling is critical for preemptively mitigating congestion and maintaining temporal efficiency. Excluding the Choquet–OWA aggregation stage (w/o Choquet–OWA) leads to a more pronounced degradation—task completion rate decreases by 9.5% and throughput declines by 7.2%, reflecting the importance of nonlinear multi-factor fusion in balancing bottleneck and surplus resources. In contrast, removing the T-norm stage (w/o T-norm) results in the most severe performance loss, with task completion rate reduced by 12.4% and throughput by 10.1%, underscoring the necessity of initial bottleneck-oriented filtering before higher-order aggregation. Overall, the complete model consistently outperforms all reduced variants across all metrics, confirming that each component is indispensable and that their joint effect yields the highest robustness and efficiency under large-scale UAV swarm scenarios.

6. Discussion

6.1. Limitations

During the experiments, we identified the following limitations of this work, as summarized in

Table 6. Limitations of the method proposed in this paper.

Limitation	Impact	Mitigation Approach
Prediction error	LSTM may overestimate bandwidth during sudden spikes → short-term overload	Incorporate Kalman correction or uncertainty gating (MC-Dropout)
Manual parameter tuning	Requires offline calibration	Employ Bayesian optimization or meta-learning for automatic warm start
Single-peak resource assumption	Current model assumes network congestion is single-peaked	Extend to multi-peak scenarios using piecewise Choquet for multiple hotspots

.

6.2. Complementarity with Swarm-RL and Auction Games

In the future, we can expand more dimensional methods based on the content of this article, which can complement swarm-RL/auction game and other methods. This is mainly reflected in the following three aspects:

• Swarm-RL: Reinforcement learning excels at long-horizon, global optimization and can supply high-level task-allocation priors to the aggregator; the aggregator then guarantees low-level resource safety—forming a two-tier collaborative architecture.
• Auction games: In resource-scarce scenarios, auction-based pricing curbs excessive requests; the aggregator can map its output membership degrees to bid caps, enabling a “trust-elastic” auction mechanism.
• Hybrid advantage: RL and auctions drive strategic exploration, while the two-stage aggregator enforces safety constraints. Their combination achieves both fast convergence and effective risk control.

6.3. Scalability of the Two-Stage Aggregator

We evaluate scalability at $N=\{60,120,180,240,300,360,480,600\}$ UAVs (five seeds per N), reporting mean ± std for RTT/jitter/signal strength (Figure 7). A nonlinear least-squares fit of $\mathrm{RTT}\left(N\right)=a+b\sqrt{N}$ shows that the proposed method exhibits sublinear growth with the smallest slope b among all schedulers, and narrow confidence bands across seeds, indicating robustness to stochastic dynamics as the swarm grows.

On the theory side, the per-node computation contains a constant number of operations: three prediction-enhanced memberships $({\tilde{\mu }}_c,{\tilde{\mu }}_b,{\tilde{\mu }}_{e_r})$, one T-norm ${\mu }_{\mathrm{pre}}=min\{·\}$, and a binary Choquet–OWA over $\{{\mu }_{\mathrm{pre}},{\mu }_p\}$ with fixed capacity $\nu$. Thus, time and memory are $O\left(1\right)$ per node; the entire swarm therefore runs in $O\left(N\right)$ per control step. In a decentralized setting with bounded neighborhood degree d (due to radio range), each node exchanges only local statistics, leading to $O\left(1\right)$ messages per node and $O\left(N\right)$ total.

Finally, a queueing/interference argument explains the empirical scaling: with spatial reuse, the effective contention radius grows sublinearly with N, yielding a $\sqrt{N}$-type increase in the delay envelope. The first stage (T-norm) guarantees bottleneck priority, preventing compensatory bias that would otherwise amplify delay with N; the second stage (Choquet–OWA) provides rank-sensitive compensation through $\varphi$, trimming peaks without violating bottleneck safety. This division of labor accounts for the lower slope b and tighter variability we observe relative to Min, WSM, single-layer OWA, and DRL-PPO.

6.4. Security Considerations

Although this work focuses on scheduling and resource aggregation, security is an indispensable dimension in large-scale UAV–IoT systems. UAV nodes typically run embedded firmware that may contain exploitable vulnerabilities. Recent studies on IoT firmware vulnerability detection have demonstrated that combining static binary analysis, dynamic execution tracing, and symbolic execution can effectively expose buffer overflows, command injections, and authentication bypass flaws in resource-constrained devices [30]. These methods, often integrated with fuzzing frameworks, can be applied pre-deployment to ensure that each UAV’s communication and control stack is free from critical defects.

Beyond traditional static/dynamic analysis, emerging research leverages Large Language Models (LLMs) for software security tasks [31]. LLMs can assist in code review, vulnerability triage, and even automated patch synthesis by understanding natural-language security advisories and translating them into actionable code changes. For UAV swarms, such capabilities could augment firmware verification pipelines, helping detect both known CVEs and zero-day vulnerabilities before field deployment.

In operational scenarios, our two-stage T-norm–Choquet–OWA scheduler can be integrated with these security mechanisms at two points: (i) pre-flight—ensuring only verified firmware images participate in the swarm; and (ii) in-flight—coupling resource scheduling with real-time anomaly detection, so that nodes exhibiting abnormal traffic patterns or latency spikes (potentially indicating compromise) are deprioritized or isolated. This joint design would strengthen both the reliability and security posture of the overall system.

6.5. Limitations and Potential Risks

While the proposed prediction-enhanced two-stage aggregation scheduler demonstrates notable performance gains under controlled and stochastic conditions, certain limitations remain:

• Sensitivity to Unseen Network Dynamics.
  The LSTM-based forecasting model is trained on historical network traces and may not generalize perfectly to unforeseen operational environments (e.g., sudden link failures, unmodeled interference sources). In such cases, prediction errors can propagate into the resource scheduling stage, potentially leading to suboptimal allocation.
• Vulnerability to Adversarial Perturbations.
  Recent studies have shown that time-series forecasting models, including LSTMs, can be susceptible to adversarially crafted input sequences. In a UAV–IoT swarm context, a compromised node could intentionally inject misleading telemetry to degrade scheduling decisions.
• Fallback and Mitigation Mechanisms.
  To address these risks, our system implements a confidence-gated fallback:
  • The prediction stage outputs a confidence score based on forecast variance.
  • If confidence falls below a predefined threshold, the scheduler switches to a reactive, non-predictive mode using real-time network measurements only.
  • In addition, anomaly detection modules monitor key metrics (e.g., RTT, jitter, packet loss) to identify and isolate nodes producing anomalous traffic patterns, mitigating the impact of adversarial inputs.
• Future Work on Robust Forecasting.
  Enhancing robustness may involve integrating adversarial training, hybrid statistical–ML models, or robust aggregation methods that can tolerate partial corruption in the input feature set. These improvements would further safeguard the scheduler against both natural and intentional disruptions.

6.6. Real-World Deployment and Implementation Challenges

Although the evaluation presented in this paper is simulation-based, the proposed prediction-enhanced two-stage aggregation scheduler is designed with practical deployment feasibility in mind. A real-world UAV coordination scenario, such as disaster response or large-scale environmental monitoring, could adopt the following implementation architecture:

• Deployment Architecture
  • High-level controller hosted on an edge server or ground control station runs the high-layer Choquet–OWA aggregator with LSTM forecasting, handling global coordination and bottleneck prediction.
  • Onboard low-level controllers on each UAV execute the T-norm-based local decision logic, reacting to short-term link quality variations.
  • Communication is maintained via a hybrid V2V/V2I wireless network, with adaptive link selection to balance latency and reliability.
• Hardware and Software Requirements
  • The high-level module can run on an x86-based edge node with moderate GPU acceleration for LSTM inference.
  • The low-level module can be embedded on ARM-based UAV flight controllers with limited resources (≥1 GHz CPU, ≥512 MB RAM), using a lightweight fuzzy inference engine.
• Real-time Operation Challenges
  • Communication Variability: Wireless links are subject to fading, interference, and congestion. The scheduler must adaptively adjust its decision interval based on instantaneous link quality.
  • Computation Constraints: LSTM inference latency on embedded platforms may require model compression (e.g., pruning, quantization) or offloading to nearby edge nodes.
  • Regulatory and Safety Compliance: Multi-UAV operation must comply with airspace regulations, collision avoidance requirements, and spectrum usage limits.
• Mitigation Strategies
  • Adaptive Scheduling Interval to handle variable network loads.
  • Model Optimization for low-power inference without sacrificing accuracy.
  • Fallback Modes (as described in the Section 6.1) to maintain safe and efficient coordination when prediction is unreliable.
• Potential Case Study
  For example, in a post-disaster mapping mission, the high-layer predictor could anticipate congestion around key choke points (e.g., narrow valleys, urban intersections), pre-allocating bandwidth and computation resources to UAVs approaching these areas. The low-layer module would then fine-tune parameters based on immediate link conditions, ensuring timely data relay to emergency command centers.

7. Conclusions

This paper addresses the real-time coupling challenge of battery energy, bandwidth and computing power in multi-UAV cooperative missions by introducing a prediction-enhanced, two-stage T-norm–Choquet–OWA resource aggregator. Its core innovation lies in a “triple-synergy” mechanism:

• Forward-looking prediction of peak load shaving: withholding compensation for the resource trend in the next 3 s, significantly reducing the probability of instantaneous bottlenecks.
• Stage-one T-norm bottleneck protection: an extreme-protection strategy rapidly isolates the weakest resource, ensuring safe and feasible task execution.
• Stage-two Choquet–OWA elastic fusion: an interaction measure flexibly balances between bottleneck membership and power-consumption rate to restore overall efficiency.

Theoretical analysis establishes the aggregator’s monotonicity, bound correctness, bottleneck priority and Lyapunov stability. Large-scale joint simulations with 360 UAVs demonstrate that our method maintains an average RTT of 55 ms, 5% to 20% lower than Min, DRL-PPO, single-layer OWA and WSM—while achieving the lowest jitter and packet-loss rates. Violin-plot results further confirm the concentration and robustness of the membership-degree distributions, underscoring the practical value of the two-stage design for UAV cooperative resource scheduling.

In future work, we plan to extend the aggregation dimensions to include thermal load, GPU utilization, and link reliability, and to incorporate risk factors such as malicious interference and node disconnections. Accordingly, we will develop multi-layer risk membership functions and dynamic interaction measures to ensure that the aggregator retains convergence guarantees and remains interpretable in complex, non-ideal environments.