LLM-Driven Fuzzy Control Systems

• LLM-driven fuzzy control is a method that integrates large language models with fuzzy inference systems to enable interpretable, dynamic decision-making.
• It leverages natural language encoding and decoding to translate fuzzy cognitive maps and rules into human-editable, semantic summaries.
• Empirical validations in robotics demonstrate improved transparency and adaptability, making the approach effective in multi-agent, low-bandwidth settings.

LLM-driven fuzzy control refers to a class of methods integrating LLMs with fuzzy control systems, leveraging the interpretability of linguistic abstraction and the expressiveness of natural language processing to optimize, explain, and adapt fuzzy decision-making in dynamic settings. These systems merge the strengths of LLMs—semantic summarization, promptable reasoning, and natural language interfacing—with the stability and adaptability of fuzzy logic controllers, producing pipelines that are both interpretable and readily modifiable by both humans and learning agents (Panda et al., 29 Sep 2025, Xu et al., 2 Nov 2025).

1. Fundamental Concepts

The integration of LLMs with fuzzy control commonly centers on two core constructs: Feedback Fuzzy Cognitive Maps (FCMs) and semantic-driven fuzzy inference.

Feedback Fuzzy Cognitive Maps (FCMs): An FCM is defined by the tuple $G = (C, E, W)$, where $C = \{C_1, \ldots, C_n\}$ denotes the finite set of “concept” nodes, $E \subseteq C \times C$ is the set of directed causal edges, and $W = [w_{ij}] \in [-1,1]^{n \times n}$ encodes edge weights. Here, $w_{ij} > 0$ indicates a promoting causal influence of $C_i$ on $C_j$, $w_{ij} < 0$ indicates inhibition, and $|w_{ij}|$ denotes the causal strength (fuzziness). The dynamics evolve in discrete time via

$$C_j(t+1) = \phi\left( C_j(t) + \sum_{i=1}^n w_{ij} C_i(t) \right),$$

with $\phi$ a bounded monotonic activation (squashing) function, e.g., shifted logistic or tanh (Panda et al., 29 Sep 2025).

Fuzzy Inference: Fuzzy controllers map linguistic labels (e.g., “moment is positive big, force change is negative medium”) into control actions via expert-rule tables and membership functions, followed by defuzzification (e.g., centroid method) to derive crisp actuation signals (Xu et al., 2 Nov 2025).

2. LLM-Driven Encoding, Decoding, and Policy Editing for Fuzzy Cognitive Maps

A central innovation is the use of LLMs as natural-language autoencoders for FCMs. The pipeline comprises a dual-stage process for explainable encoding and decoding of FCMs:

Encoder Stage: The LLM receives $(C, W)$ and outputs a natural-language summary that

• Mentions each node at least once,
• Uses linguistic qualifiers (“strongly causes,” “moderately influences”) based on edge-magnitude thresholds ($\tau_\text{strong}=0.6$, $\tau_\text{weak}=0.3$),
• Prioritizes strong edges and omits or groups minor ones.

A salient edge-selection heuristic ranks edges by $$|\omega_{ij}| \cdot (\mathrm{deg}_\text{out}(i)+\mathrm{deg}_\text{in}(j))$$, focusing the summary on influential nodes and links. Causal language is mapped as: “promotes/increases” for positive $w_{ij}$, “inhibits/decreases” for negative (Panda et al., 29 Sep 2025).

Decoder Stage: Given the natural-language text (possibly edited by a human), the LLM reconstructs $(C', W')$ by:

• Extracting variables/entities as nodes,
• Aligning noun phrases signifying state variables,
• Mapping linguistic cues (“strongly causes” $\rightarrow +0.8$ weight, “moderately inhibits” $\rightarrow -0.45$, etc.),
• Pruning edges below a drop threshold ($|w'_{XY}|<0.2$).

Assignments are transparently justified by quoting the text source for each edge (Panda et al., 29 Sep 2025).

This approach approximates an identity map on FCMs using explicit prompt engineering with no gradient-based learning or hidden weights, yielding a lossy yet interpretable transmission where strong causal structure is prioritized over minor link preservation.

3. Semantic Compression and Fuzzy Control for Multi-Robot Systems

In robotics, LLM-driven fuzzy control extends to the interpretation of high-dimensional, multimodal sensor streams and cooperative decision-making.

Pipeline Overview:

1. Perception Encoding: Each agent collects local observations $o_t = [I_t, R_t, T_t]$ (image, occupancy grid, pose) and encodes them as latent vectors $z_t = g_\psi(o_t)$.
2. Proto-Prompt Generation: A lightweight generator $f_p$ produces concise natural-language proto-prompts $\tilde{P}_t$ encapsulating salient semantic facts.
3. Prompt Construction: A prompt-constructor $\Omega$ synthesizes the LLM input $P_t$ from proto-prompts with raw observations.
4. Semantic Inference: The pretrained LLM $F_\text{LLM}$ processes $P_t$ into semantic summaries $S_t$, comprising mission-grounded, temporally coherent, goal-aligned descriptors.

Fuzzy Control Layer:

Post-LLM, selected linguistic variables—Moment, MomentChange, Force, ForceChange—are mapped onto expert-tuned fuzzy membership functions spanning normalized universes (e.g., NB…PB for [–0.2,+0.2], [–3,+3], or [0,1]). Rule bases define steering ($\Delta$) and gait ($\Phi$) adaptations; centroid defuzzification finalizes actuation commands. Membership and rule matrices are explicitly specified and serve as the interpretable interface between high-level reasoning and low-level control (Xu et al., 2 Nov 2025).

4. LLM-Guided Semantic Communication and Distributed Decision Making

In distributed environments, especially under communication constraints, LLM-driven approaches facilitate lightweight, intention-based coordination through semantic communication protocols.

Protocol Steps:

• Each agent $i$ periodically encodes local semantics and goals into short intent tokens $$M_t^{(i)} = F_\text{LLM}^{enc}( S_t^{(i)}, G^{(i)})$$ (e.g., “moving north toward unexplored region”).
• Other agents decode received messages $M_t^{(-j)}$ via $F_\text{LLM}^{dec}$, producing inferred peer state summaries $\hat{S}_t^{(j)}$.
• The agent merges local and peer semantics $\pi_t^{(j)} = \Pi(S_t^{(j)},\hat{S}_t^{(j)})$ to adapt policy, demarcate frontiers, and avoid redundancy.

This approach abstracts away from explicit metric maps or trajectory logs, transmitting only semantically-rich, human-interpretable intent tokens, which is critical in low-bandwidth, partial-observability regimes such as underwater multi-robot missions (Xu et al., 2 Nov 2025).

5. Formal Workflow and Closed-Loop Execution

A canonical closed-loop LLM-driven fuzzy control system proceeds as follows (Panda et al., 29 Sep 2025, Xu et al., 2 Nov 2025):

1. Specification of concepts and initial causal or policy weights (potentially by human/system designer).
2. LLM encodes structured knowledge into concise, human-readable summaries.
3. (Optional) Human or operator edits the summary to adjust policy or causal structure.
4. LLM decodes the text back into formal system parameters (FCM weights, fuzzy rules).
5. Fuzzy control or dynamical system executes state updates (e.g., $$C_{k}(t+1) = \phi(C_{k}(t) + \sum_{i} w_{ik}C_{i}(t))$$).
6. Results (actuator states, trajectories) are fed back to close the loop, potentially triggering further natural-language edits and re-deployment.

All key system thresholds (e.g., $\tau_\text{strong}$, $\tau_\text{drop}$) are embedded as prompt metadata, enabling real-time adaptation without retraining.

LLM-driven fuzzy control is thus characterized by:

• Human-readability and bidirectional explainability,
• Editable semantics for real-time policy and rule adjustment,
• Maintainability through prompt and threshold tuning,
• Preservation of strong causal links during round-trip representations.

6. Experimental Validation and Performance Metrics

LLM-driven fuzzy control for cooperative robotics has been evaluated in simulation using a 12 m×8 m arena with various obstacle/OOI layouts (Grid World, E-Shape, Disconnected Paths), robotic turtle platforms, and GPT-4o LLMs (temperature 0.1, maxTokens 300).

Performance metrics include:

• Coverage Ratio: fraction of OOI-rich cells visited,
• OOI Density: number of OOIs per meter traversed,
• OOI Efficiency: number of OOIs per meter in covered area.

Empirical results for two-robot configurations:

Scenario	Coverage (%)	OOI Density	OOI Efficiency
Grid World	69.5	1.25	1.79
E-Shape	73.8	1.30	1.77
Disconnected Paths	61.3	0.87	1.42
BCD Baseline	74.3/50.7/32.5	1.17/0.79/0.43	1.57/1.56/1.34
BB Baseline	36.4/40.7/13.9	0.52/0.45/0.18	1.44/1.12/1.30

As the number of robots increases, Coverage Ratio slightly decreases due to overlap, but OOI Efficiency increases to approximately 1.9 OOI/m in covered regions (Xu et al., 2 Nov 2025).

7. Implications, Limitations, and Editing Paradigms

LLM-driven fuzzy control frameworks provide a paradigm in which complex control graphs or fuzzy rule-books are encoded, visualized, edited, and reconstructed using natural language—enabling domain experts to effect nontrivial policy changes without direct manipulation of numerical weights or code. Key implications include:

• Maintainability: system logic is in interpretable summary text, not hidden weights.
• Adaptability: thresholds ($\tau_\text{strong}$, $\tau_\text{drop}$) and system prompts control what structural changes are admitted, without retraining.
• Real-time Human-in-the-Loop: policy designers can request changes such as “make variable X more inhibitive of Y” directly in natural language.

A key limitation is the lossy nature of the round-trip: weaker links or detailed substructure may be omitted if not highlighted in generated or edited text. Precise control over fuzzy weights below thresholds requires deliberate linguistic inclusion. Furthermore, identity approximation is prompt- and pattern-dependent; the system does not optimize a reconstruction loss via gradient descent.

In summary, LLM-driven fuzzy control operationalizes explainable and editable fuzzy systems via natural-language interfaces and semantic compression, extending interpretable, adaptive control to domains requiring human oversight and semantic communication, notably in robotics and sociotechnical systems (Panda et al., 29 Sep 2025, Xu et al., 2 Nov 2025).