Broad Learning System is an efficient randomized learning model that expands network width through feature and enhancement nodes and estimates the output weights without deep backpropagation. Its standard least-squares training, however, is vulnerable in two different ways: (i) large residuals caused by noise, outliers, or corrupted labels can dominate the objective, and (ii) all samples are treated as equally reliable even when some lie in ambiguous or locally conflicting regions. This paper proposes IFW-BLS, an Intuitionistic Fuzzy Wave Broad Learning System that addresses these two sources of fragility within one optimization model. The first robustness mechanism is residual-level protection, obtained by replacing the squared loss with the bounded, smooth, and asymmetric wave loss. Boundedness prevents extreme residuals from receiving unbounded influence, while asymmetry allows positive and negative deviations to be penalized differently when the dominant error direction varies. The second mechanism is sample-level credibility control, obtained through intuitionistic fuzzy scores that combine global class-center consistency with local neighborhood conflict. The resulting model evaluates the wave loss on credibility-weighted residuals, so unreliable samples are down-weighted before the bounded loss further limits the effect of extreme errors. A Nesterov accelerated gradient based optimizer is used to solve the proposed objective, avoiding the explicit matrix inversion used in conventional BLS. Experiments on UCI benchmark datasets validate the superiority of the proposed IFW-BLS model over the baseline models; additional corruption experiments also show more stable performance than BLS under noise and outlier contamination.
Evidential argumentation extends Dung's abstract argumentation by requiring arguments and interactions to be backed by chains of evidence rooted in prima-facie elements. However, existing formalisms lack a unified treatment of evidential support, higher-order relations (attacks and supports targeting arbitrary elements), and collective interactions (sources as sets). In this paper, we introduce the Evidential-Based Higher-Order Set Argumentation Framework (EHSAF), which conservatively generalises several existing frameworks within a single expressive setting. We develop two complete semantics for EHSAFs: an \emph{adjacent complete labelling semantics} that admits multiple truth values (true, false, undecided) for arguments in support cycles, reflecting an open epistemic attitude toward future evidence; and an \emph{extension-based complete semantics} that follows a strict evidentialist stance, accepting only arguments with well-founded support chains. We show that these two semantics diverge in the presence of support cycles, and prove their equivalence under support-acyclicity. To enable computational reasoning, we provide a normal propositional encoding of EHSAFs and prove that, in three-valued Łukasiewicz logic, its models correspond precisely to the adjacent complete labellings. We further extend this encoding to continuous fuzzy logics (G{ö}del, Product, and Łukasiewicz), defining a continuous fuzzy normal encoded semantics. We establish that this fuzzy semantics satisfies key properties---continuity, monotonicity, boundary conditions, and solution existence---and that its ternarisation recovers the adjacent complete labellings under natural t-norm conditions. Our framework thus unifies expressive argumentation with principled three-valued and fuzzy semantics, bridging the gap between qualitative and quantitative reasoning about evidence.
In non-stationary multivariate time series, different variables and samples often exhibit heterogeneous latent dynamic states, while existing deep forecasting models usually compress them into a unified end-to-end mapping, leading to suboptimal modeling of time-varying dynamics and limited interpretability regarding which forecasting mechanism is activated under different latent states. To overcome these limitations, we reformulate time series forecasting as a unified framework of latent temporal state identification and interpretable expert routing, and propose Fuzzy-MoE, a fuzzy logic-based dynamic Mixture-of-Experts model. Fuzzy-MoE consists of multiple parallel expert mapping networks and a dual-view fuzzy router. By jointly exploiting local convolutional dynamics and global segmented statistics, the router infers latent temporal states and computes expert activation strengths through learnable Gaussian membership functions, enabling explicit IF-THEN rule-based expert selection. This fine-grained routing strategy allows different variables within the same sequence to activate different experts, effectively capturing heterogeneous temporal dynamics while improving model interpretability. Experimental results on multiple public time series benchmark datasets show that Fuzzy-MoE significantly outperforms mainstream forecasting methods in forecasting accuracy. Moreover, fuzzy memberships and rule activations provide interpretable routing diagnostics, demonstrating the effectiveness of the proposed framework in both forecasting performance and mechanism transparency. Unlike traditional MoE models that use black-box routing, Fuzzy-MoE`s routing is based on clear, interpretable fuzzy rules. This makes the expert selection transparent and traceable.
Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.
Standard automated sewer pipe severity assessment relies on direct image classification, creating a "black box" where the link between visual defects and final severity scores remains implicit. This study introduces a modular, fuzzy rule-based neuro-symbolic framework that bridges this gap by decoupling neural perception from symbolic reasoning. The perception module utilizes a Swin Transformer to predict 14 multilabel inspection CODE degrees directly from images. For reasoning, a DT, specifically Weka's J48, algorithm is trained on ground-truth CODEs and severity labels, and its paths are converted into 19 fixed IF--THEN rules. Inference operates via fuzzy logic: t-norm activations from CODE conditions are weighted by rule confidence and combined with corresponding s-norms to produce interpretable class evidence. We assessed Product, Łukasiewicz, and Hamacher operator pairs using a dataset of 3,244 images spanning five highly imbalanced severity classes. Ground-truth labels were robustly generated via consensus from five independent large language models analyzing original inspector notes. Our results show an improvement of accuracy, balanced accuracy, Macro F1 and MCC by 17.9%, 12.2%, 23.0%, and 17.3%, respectively, over image-only based classification. Overall, the framework combines competitive class-balanced performance with traceable reasoning from predicted CODE degrees to rule supports and severity evidence.
Dissolved gas analysis (DGA) is crucial for diagnosing early power transformer failures. Traditional DGA interpretation methods like Duval Triangle, IEC ratio, Roger ratio, Doernenburg ratio and Key Gas are inconsistent and vary in accuracy, especially for multiple fault conditions. We propose an Adaptive Multi-Fuzzy Logic (AMFL) model integrating multiple DGA methods with fuzzy logic and a dynamic weight adjustment mechanism. Unlike existing approaches with fixed weights, this system iteratively evaluates each method's diagnostic performance, identifies multiple fault types, and adjusts weights based on fault prediction accuracy. A feedback-based optimization recalibrates weights after each cycle to ensure optimal solution convergence. The model, implemented in MATLAB/Simulink, is validated against DGA datasets with known error conditions. Results show the AMFL model significantly improves diagnostic accuracy, especially in complex error scenarios, and enhances adaptability to new datasets. Comparative analysis demonstrates the proposed method outperforms traditional fixed weight multi-fuzzy systems in accuracy, consistency, and reliability of error detection. This work provides a robust, flexible diagnostic tool for transformer condition monitoring and supports more accurate asset management decisions.
Cayan Deniz Kucuktopana, Javier Fumanal-Idocin, Richard Pitts +1cs.LG
Machine learning models achieve high predictive accuracy in regression tasks, but their deployment in safety-critical and regulated domains requires interpretability. While fuzzy rule-based systems offer transparent, linguistically explicit interpretable models, Mamdani-style fuzzy regression remains underrepresented in modern machine learning software libraries. This paper presents an interpretable regression extension for the Ex-Fuzzy library, enabling Mamdani fuzzy inference with scalar consequents learned directly from data. For this, a target-aware partition initialisation strategy based on Fuzzy C-Means clustering is introduced, in which linguistic variables are derived from an augmented input-output space to emphasise output-relevant regions of the feature space. The proposed extension is evaluated on ten regression datasets from the KEEL repository, comparing Gaussian and trapezoidal partition strategies against standard baselines including linear regression, multilayer perceptron, and random forests. Experimental results show that Gaussian partitions consistently outperform uniform trapezoidal partitions, achieving a mean coefficient of determination of approximately 0.86 while producing compact rule bases of 10-15 human-readable rules. The proposed implementation provides a transparent and competitive alternative to black-box regression models, supporting practical interpretability with competitive predictive performance.
Human reasoning often operates through qualitative concepts expressed by linguistic labels such as high, low, expensive, or cheap, whose interpretation depends on context and is usually vague, despite being rooted in numerical data. This paper explores a novel fuzzy-logic-based qualitative extension of Answer Set Programming (ASP) to bridge numerical information and qualitative reasoning. The underlying language, formally introduced in a separate work, provides a principled framework that avoids rigid thresholds and supports robust reasoning under vagueness. Focusing on a representative use case, we illustrate how the framework integrates numerically grounded inputs (such as outputs of machine learning models) with symbolic reasoning over qualitative labels. Key features, including learning-based membership functions and semantically enriched predicates, enable the combination of expert knowledge, contextual factors, and subjective interpretations within a unified declarative setting.
A transformer's feed-forward (FFN) sublayer materializes the distinctions attention gathers, yet gives no account of what it computes. In a parameter-neutral replacement, each hidden unit is an explicit fuzzy set operation on sigmoid-bounded [0,1] memberships: intersection A*B and set-difference A*(1-B), the latter a bounded positive negation ("A but not B") that gated/bilinear units lack -- a negation-capable FFN (NC-FFN). On N-bit parity they are the most parameter-efficient reasoning basis at shallow depth; at scale (125M, OpenWebText) NC-FFN ties the GELU baseline's perplexity, every unit carrying explicit logical form. Two limits share one cause: two-operand logic localizes to layer 0 and erodes under training, and the one robust grammatical deficit concentrates in licensing and quantifiers, beyond within-token operators. We resolve both with a small block of sequence quantifiers: a soft existential and a soft proportion, each with a per-unit learned forgetting rate from a sticky init. This recovers the deficit at epoch one (halving the wider epoch-two gap), modestly leads on LAMBADA, and makes the FFN legible: the structure now holds and migrates into depth; the decay un-learns its stickiness (median half-life ~1.5 tokens; zero latch units); and at the semantic layers the units read, without dictionary learning, as grammatical licensing detectors: each fires on a licensor (a comparative, a passive participle, a negative-polarity item) and carries its memory forward to predict the licensed word (than, by, nor). This legibility is localized and free only up to a partition (a fully Boolean FFN diverges in training), but the result is a parameter-neutral, language-model-quality transformer with a readable, interpretable-by-construction grammatical mechanism -- an account not just of what a feed-forward layer represents but how it licenses.
Enrique Palacín, Fernando Bobillo, Ignacio Huitzil +2cs.AI
This paper presents a versatile framework for evaluating fuzzy quantification queries over both standard and fuzzy ontologies as well as knowledge graphs. The primary objective is the retrieval of individuals that satisfy queries articulated via Type I or Type II fuzzy quantified expressions. A key advantage of the proposed approach is its inherent adaptability: it remains entirely agnostic to the quantifier type, the underlying evaluation method, and the specific data source of the ontology (i.e., OWL ontologies or RDFS knowledge graphs). Furthermore, we present Q2S2, a publicly accessible implementation of this system developed to support future research.
Create an optimization framework that combines fuzzy logic and genetic algorithms for risk assessment and coordination of generation, grid connection, load, and energy storage facilities in active distribution networks. In order to capture the system uncertainties caused by weather factors and dynamic user demands, this project uses fuzzy set representation to model renewable energy generation, load curves, and market prices. In the evolutionary process, genetic algorithms introduce fuzzy elements into system management, adjusting thru penalty factors to improve stability and seeking better scheduling or power dispatch solutions. At the same time, by penalizing uncertainty and constraint violations, the fitness function of the hybrid model aims to optimize the expected operational costs; it can produce feasible and economical results under unknown parameter conditions. Under conditions with a large supply of renewable energy and installed energy storage systems, simulation results for the IEEE-69 power system indicate that the fuzzy genetic algorithm strategy effectively reduces technical constraints compared to deterministic optimization schemes. The total investment remains at a similar level. Other data indicate that thru fuzzy reasoning optimization, unreasonable choices or impossible situations are avoided during the network adaptation process. This framework-based technical approach helps to construct an effective computational scheme that is aware of uncertainty in its outputs. This will provide a scientific basis for the uncertainty assessment in distribution network planning.
LLMs have revolutionized knowledge representation and retrieval, but lack the explicit modeling that knowledge ontologies possess. This paper surveys the ways that ontologies and knowledge graphs have been integrated with dense embedding algorithms. All hitherto attempts involve a trade-off between probabilistic and crisp inference. This paper proposes a novel frontier for devising knowledge representation systems that can simultaneously accommodate probabilistic and crisp inference in the same representation. To this effect, the paper proposes neuro-quantum-fuzzy systems as knowledge representation systems that accommodate both classical and contextual inference implemented through quantum-neural networks (QNN).
Gurucharan Srinivas, Joshua Niemeijer, Frank Köstercs.CV cs.AI
Integrating domain knowledge into deep neural networks is a promising way to improve generalization. Existing methods either encode prior knowledge in the loss function or apply post-processing modules, but both depend on identifying useful symbolic knowledge to integrate. Since such rules are often unavailable in real-world vision tasks, we propose a method for targeted knowledge discovery. We propose a Differentiable Knowledge Unit (DKU) that enables modulating the classifier logits, yielding refined class probabilities. The DKU uses implication rules to represent relationships between task classes and implicit concepts learned entirely from the main task supervision, without requiring concept labels. Concepts are identified by dedicated classifiers, whose probabilities are passed to DKU alongside the primary class probabilities. DKU computes a logic-based adjustment vector via fuzzy inference, which modulates the primary class logits to yield refined class probabilities. When concept classifiers represent concepts that do not support the logical rule structure, the resulting adjustments to the class probabilities do not directly minimize the supervision loss. Consequently, optimizing the supervision loss on these adjusted class probabilities implicitly trains the concept classifiers. We construct the rule base so that bidirectional logical relations connect concepts and classes. We enforce the concepts to be distinct from each other and with respect to the classes. This design enforces a clean supervision signal for concept learning. We evaluate our methods on the PASCAL-VOC, COCO, and MedMNIST datasets. We demonstrate improvement through our knowledge integration across these datasets. We conduct domain generalization and hard-sample ablation studies and find that our implicit knowledge discovery and integration outperforms the baseline.