Fuzzy Cognitive Maps

Synthetic medical tabular data generation has become essential for developing and validating computer-based medical systems (CBMSs) when real clinical data is restricted due to privacy, ethical, or data availability limitations. Existing probabilistic and deep generative models often lack interpretability and fail to preserve clinically meaningful dependencies, limiting their suitability for safety-critical applications. This paper proposes a novel application of Fuzzy Cognitive Maps (FCMs) in a framework for synthetic medical tabular data generation with explicit causality and privacy preservation. Clinical features are described using linguistically interpretable fuzzy sets, and inter-feature dependencies are encoded as FCM edge weights computed from fuzzy set intersections. Synthetic patient records are generated by propagating randomly initialized linguistic activation vectors through the FCM until convergence, followed by defuzzification to produce clinically coherent numerical values. The approach natively handles mixed data types, and domain constraints common in health records. Experimental evaluation on UCI medical benchmark datasets demonstrates competitive performance under a Train-on-Synthetic-Test-on-Real (TSTR) protocol. The proposed method achieves accuracy of up to 0.81 and AUROC of up to 0.90 on the Heart Disease dataset, matching or exceeding TVAE and Gaussian Copula baselines while running exclusively on CPU. Fidelity metrics including KS Complement (up to 0.91) and Correlation Similarity (up to 0.95) confirm strong statistical coherence, and DCR Baseline Protection scores consistently exceed those of TVAE, confirming adequate privacy guarantees. These results demonstrate that causally grounded, interpretable fuzzy modeling offers a computationally efficient and transparent alternative to deep generative models for trustworthy synthetic data generation in CBMSs.

Synthetic tabular data generation provides an effective alternative for the training of machine learning models when real-world data is limited or inaccessible. However, the heterogeneous, non-smooth, and incomplete nature of tabular data poses fundamental challenges to conventional probabilistic and deep generative models, where their interpretability remains limited. This paper proposes a novel fuzzy distribution modeling methodology for synthetic tabular data generation based on fuzzy sets theory. Feature distributions are represented using fuzzy sets and feature dependencies are modeled through Fuzzy Cognitive Maps, resulting in a low-parameter, and an interpretable data representation. Synthetic samples are generated by sampling fuzzy concepts rather than raw values, enabling native support for mixed data types, missing values, and domain constraints. The methodology further supports linguistic queries and IF-THEN reasoning, facilitating transparent simulation of decision-making processes. Experimental results on benchmark datasets demonstrate competitive performance with respect to utility, fidelity and privacy compared to state-of-the-art methods, while offering substantially improved interpretability. These results establish fuzzy distribution modeling as a principled and effective approach for synthetic tabular data generation in fuzzy systems and decision support applications.

We show how users can create and manipulate causal virtual worlds with large-language-model (LLM) and large-video-model agents. The approach uses feedback fuzzy cognitive maps (FCMs) both to model the granular causal structure of the virtual world and to guide its causal evolution. The local causal rules are partial or fuzzy while the FCM's feedback structure produces global equilibria that define causal scenarios. A sequence of dynamical meta-rules of the form ``If $\mathcal{A}$ then $\mathcal{B}$" define the causal scenes of the virtual-world video. The if-part causal pattern $\mathcal{A}$ perturbs the FCM's virtual world at the user's or agent's discretion. The FCM's transient feedback dynamics define the meta-rule's causal arrow of implication. The then-part $\mathcal{B}$ is the resulting equilibrium attractor such as a FCM limit cycle or fixed point. Our algorithm extracts these meta-rules from the FCM and guides the LLM agent to write a script based on the FCM meta-rule sequence. The large video generator converts the meta-rule into a video scene in accord with the flow of the dynamics. We applied the agent-based technique to a simple FCM that describes an undersea world of dolphins and sharks. Google's Gemini 3.1 generated the script and Google's Veo 3.1 generated the dolphin-shark video. The approach is general and can scale by mixing larger FCMs and AI agents to produce more immersive virtual worlds.

This article is about the development of a fuzzy cognitive map using a local large language model. In the light of recent advances it is evident that large language models, and even local large language models are capable of extracting quantities from textual data. In other words, a local LLM like Qwen2.5-32B, or probably larger, can accept entities as prompt input and determine relevant quantitative data as the model output. In turn, this output can be utilized for the construction of a data driven fuzzy cognitive map. Hence, this implementation is achieved and then the model is thoroughly tested; Qwen2.5-32B is used and the data is extracted from hotel reviews from TripAdvisor. Furthermore, the extracted documents pass through the model unfiltered and then a fuzzy cognitive map is trained and evaluated. A case is made about Greek reviews where a star topology FCM is formed that indicates the preferences of the reviewers. Finally, external validation is performed to establish whether the fuzzy cognitive map can correlate the star rating of the review -an outcome outside the model's inference scope -with its predicted satisfaction.

We automatically generate feedback causal fuzzy cognitive maps (FCMs) from text by teaching large-language-model agents to break the text into overlapping chunks of text. Convex mixing of these chunk FCMs gives a representative cyclic FCM knowledge graph. The text chunks can have different levels of overlap. The chunk FCMs still mix to form a new FCM causal knowledge graph. The mixing technique scales because it uses light computation with sparse causal chunk matrices. The mixing structure allows an operator-level type of Bayesian inference that produces "de-chunked" or posterior-like FCMs from the mixed FCM. These de-chunked FCMs are useful in their own right and allow further iterations of Bayesian updating. We demonstrate these mixing techniques on the essay text of Allison's "Thucydides Trap" model of conflict between a dominant power such as the United States and a rising power such as China. The FCM dynamical systems predict outcomes as they equilibrate to fixed-point or limit-cycle attractors. Seven out of 8 FCM knowledge graphs predicted a type of war when we stimulated them by turning on and keeping on the concept node that stands for the rising power's ambition and entitlement. Gemini 3.1 LLMs served as the chunking AI agents.

In this paper an attractor FCM is created, tested, and analyzed. This FCM is neither a hebbian based nor agentic, nor a hybrid; it rather is a gradient descent based, physics constrained, Jacobian version of an FCM. Moreover, this model has several quirks; it uses residual memory, back propagation through time, and a fixed point anchor that is recursively implemented to update its weights. The residuals update the recursive part without losing the system memory. The model's anchor enables it to converge in a fixed point for which back propagation through time unrolls it and ensures that the error minimization is for an accurate gradient. Furthermore, a new learning algorithm is utilized. The Newton's method finds the system's fixed point attractor and then gradient descend is adaptively changing the landscape; an adaptive term is used to directly manipulate the weights through the attractor dynamics. As the adaptive term changes, the descent through the landscape is constantly adjusting according to sigmoid saturation, and that prevents premature convergence to a local minimum. Lastly, the updates are filtered by causal mask that informs the network about the physics, respecting the initial expert based opinions, for which model reduces the error to the target in an efficient way.

Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by scalar synaptic weights and monotonic activation functions, is fundamentally constrained in modeling non-monotonic causal dependencies, thereby limiting its efficacy in systems governed by saturation effects or periodic dynamics. To overcome this topological restriction, this research proposes the Kolmogorov-Arnold Fuzzy Cognitive Map (KA-FCM), a novel architecture that redefines the causal transmission mechanism. Drawing upon the Kolmogorov-Arnold representation theorem, static scalar weights are replaced with learnable, univariate B-spline functions located on the model edges. This fundamental modification shifts the non-linearity from the nodes' aggregation phase directly to the causal influence phase. This modification allows for the modeling of arbitrary, non-monotonic causal relationships without increasing the graph density or introducing hidden layers. The proposed architecture is validated against both baselines (standard FCM trained with Particle Swarm Optimization) and universal black-box approximators (Multi-Layer Perceptron) across three distinct domains: non-monotonic inference (Yerkes-Dodson law), symbolic regression, and chaotic time-series forecasting. Experimental results demonstrate that KA-FCMs significantly outperform conventional architectures and achieve competitive accuracy relative to MLPs, while preserving graph- based interpretability and enabling the explicit extraction of mathematical laws from the learned edges.

This essay is about a neural implementation of the fuzzy cognitive map, the FHM, and corresponding evaluations. Firstly, a neural net has been designed to behave the same way that an FCM does; as inputs it accepts many fuzzy cognitive maps and propagates them in order to learn causality patterns. Moreover, the network uses langevin differential Dynamics, which avoid overfit, to inverse solve the output node values according to some policy. Nevertheless, having obtained an inverse solution provides the user a modification criterion. Having the modification criterion suggests that information is now according to discretion as a different service or product is a better fit. Lastly, evaluation has been done on several data sets in order to examine the networks performance.