Fuzzy Logic

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Overview

Fuzzy logic models vague or uncertain information using graded membership rather than only true-or-false categories, making it useful when boundaries are imprecise or knowledge is expressed in language. Common approaches include Mamdani and Takagi–Sugeno inference, interval Type-2 fuzzy sets, fuzzy cognitive maps, and neuro-fuzzy systems such as ANFIS; these support decision-making, control, forecasting, and classification. Current work also combines fuzzy rules with neural networks and transformers to add uncertainty handling or interpretable reasoning to learned models. A central challenge is balancing readable, compact rules and well-calibrated uncertainty with predictive accuracy, scalability, and reliable evaluation across changing settings.

Latest papers

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48 papers4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Apr 4, 2026

Interpretable Fuzzy Modeling Reveals Population-Level Representation Differences in P300 Brain Computer Interfaces Across Neurodivergent and Neurotypical Cohorts

P300-based brain-computer interfaces (BCIs) are widely used for communication, but population heterogeneity may alter the neural patterns available for decoding. Prior work has mainly examined such differences at the signal or performance level, while the representation structure learned by the decoder remains underexplored. In this study, we propose an interpretable fuzzy spatiotemporal framework for P300 classification and use it to analyze population-level differences across amyotrophic lateral sclerosis (ALS), autism (AUT), and neurotypical (NT) cohorts. The model employs spatial and temporal fuzzy filters with learnable prototypes, enabling both classification and reconstruction of cohort-specific fuzzy centers. Experiments were conducted on ALS and NT subsets from bigP3BCI and on the BCIAUT-P300 benchmark in a within-subject setting. The proposed model achieved competitive performance against multiple deep learning baselines. More importantly, the reconstructed fuzzy centers revealed systematic cohort-dependent differences in waveform morphology and representation geometry. Point-wise statistical analysis identified significant temporal differences between cohorts, including intervals overlapping with the canonical P300 window, and low-dimensional embeddings showed partially separated cohort-specific prototype organizations. These results suggest that population heterogeneity in P300-BCI is reflected not only in decoding performance but also in the discriminative structure learned by the model. The proposed framework provides an interpretable route toward population-aware P300-BCI analysis and design.

Xiaowei Jiang, Sudong Shang, Adrian Wilkinson +4

Computational Intelligence and Brain-Computer Interfaces lab, Australian AI Institute, Faculty of Engineering and Information Technology, University of Technology Sydney, 2007, Australia · Department of Management, Griffith Business School, 4215, Australia · Department of Neuroscience, Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania, 19104, USA +2

Brain-Computer InterfacesEEG DecodingPrototype-Based ClassificationFuzzy LogicNeural Network Interpretability
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Mar 30, 2026

T-Norm Operators for EU AI Act Compliance Classification: An Empirical Comparison of Lukasiewicz, Product, and Gödel Semantics in a Neuro-Symbolic Reasoning System

We present a first comparative pilot study of three t-norm operators -- Lukasiewicz (T_L), Product (T_P), and Gödel (T_G) - as logical conjunction mechanisms in a neuro-symbolic reasoning system for EU AI Act compliance classification. Using the LGGT+ (Logic-Guided Graph Transformers Plus) engine and a benchmark of 1035 annotated AI system descriptions spanning four risk categories (prohibited, high_risk, limited_risk, minimal_risk), we evaluate classification accuracy, false positive and false negative rates, and operator behaviour on ambiguous cases. At n=1035, all three operators differ significantly (McNemar p<0.001). T_G achieves highest accuracy (84.5%) and best borderline recall (85%), but introduces 8 false positives (0.8%) via min-semantics over-classification. T_L and T_P maintain zero false positives, with T_P outperforming T_L (81.2% vs. 78.5%). Our principal findings are: (1) operator choice is secondary to rule base completeness; (2) T_L and T_P maintain zero false positives but miss borderline cases; (3) T_G's min-semantics achieves higher recall at cost of 0.8% false positive rate; (4) a mixed-semantics classifier is the productive next step. We release the LGGT+ core engine (201/201 tests passing) and benchmark dataset (n=1035) under Apache 2.0.

Adam Laabs

TriStiX S.L., Altea, Alicante, Spain

Fuzzy LogicNeuro-Symbolic Reasoning
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Mar 23, 2026

FISformer: Replacing Self-Attention with a Fuzzy Inference System in Transformer Models for Time Series Forecasting

Transformers have achieved remarkable progress in time series forecasting, yet their reliance on deterministic dot-product attention limits their capacity to model uncertainty and nonlinear dependencies across multivariate temporal dimensions. To address this limitation, we propose FISFormer, a Fuzzy Inference System-driven Transformer that replaces conventional attention with a FIS Interaction mechanism. In this framework, each query-key pair undergoes a fuzzy inference process for every feature dimension, where learnable membership functions and rule-based reasoning estimate token-wise relational strengths. These FIS-derived interaction weights capture uncertainty and provide interpretable, continuous mappings between tokens. A softmax operation is applied along the token axis to normalize these weights, which are then combined with the corresponding value features through element-wise multiplication to yield the final context-enhanced token representations. This design fuses the interpretability and uncertainty modeling of fuzzy logic with the representational power of Transformers. Extensive experiments on multiple benchmark datasets demonstrate that FISFormer achieves superior forecasting accuracy, noise robustness, and interpretability compared to state-of-the-art Transformer variants, establishing fuzzy inference as an effective alternative to conventional attention mechanisms.

Bulent Haznedar, Levent Karacan

Computer Engineering Department, Gaziantep University, Gaziantep, Türkiye

Time Series TransformersTime Series ForecastingTransformer AttentionMultivariate Time Series ForecastingFuzzy Logic
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Mar 22, 2026

Quantum Fuzzy Sets Revisited: Density Matrices, Decoherence, and the Q-Matrix Framework

In 2006 we proposed Quantum Fuzzy Sets, observing that states of a quantum register could serve as characteristic functions of fuzzy subsets, embedding Zadeh's unit interval into the Bloch sphere. That paper was deliberately preliminary. In the two decades since, the idea has been taken up by researchers working on quantum annealers, intuitionistic fuzzy connectives, and quantum machine learning, while parallel developments in categorical quantum mechanics have reshaped the theoretical landscape. The present paper revisits that programme and introduces two main extensions. First, we move from pure states to density matrices, so that truth values occupy the entire Bloch ball rather than its surface; this captures the phenomenon of semantic decoherence that pure-state semantics cannot express. Second, we introduce the Q-Matrix, a global density matrix from which individual quantum fuzzy sets emerge as local sections via partial trace. We define a category QFS of quantum fuzzy sets, establish basic structural properties (monoidal structure, fibration over Set), characterize the classical limit as simultaneous diagonalizability, and exhibit an obstruction to a fully internal Frobenius-algebra treatment.

Mirco A. Mannucci

Fuzzy Logic
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Mar 20, 2026

Ontology-Based Knowledge Modeling and Uncertainty-Aware Outdoor Air Quality Assessment Using Weighted Interval Type-2 Fuzzy Logic

Outdoor air pollution is a major concern for the environment and public health, especially in areas where urbanization is taking place rapidly. The Indian Air Quality Index (IND-AQI), developed by the Central Pollution Control Board (CPCB), is a standardized reporting system for air quality based on pollutants such as PM2.5, PM10), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3), carbon monoxide (CO), and ammonia (NH3). However, the traditional calculation of the AQI uses crisp thresholds and deterministic aggregation rules, which are not suitable for handling uncertainty and transitions between classes. To address these limitations, this study proposes a hybrid ontology-based uncertainty-aware framework integrating Weighted Interval Type-2 Fuzzy Logic with semantic knowledge modeling. Interval Type-2 fuzzy sets are used to model uncertainty near AQI class boundaries, while pollutant importance weights are determined using Interval Type-2 Fuzzy Analytic Hierarchy Process (IT2-FAHP) to reflect their relative health impacts. In addition, an OWL-based air quality ontology extending the Semantic Sensor Network (SSN) ontology is developed to represent pollutants, monitoring stations, AQI categories, regulatory standards, and environmental governance actions. Semantic reasoning is implemented using SWRL rules and validated through SPARQL queries to infer AQI categories, health risks, and recommended mitigation actions. Experimental evaluation using CPCB air quality datasets demonstrates that the proposed framework improves AQI classification reliability and uncertainty handling compared with traditional crisp and Type-1 fuzzy approaches, while enabling explainable semantic reasoning and intelligent decision support for air quality monitoring systems

Md Inzmam, Ritesh Chandra, Sadhana Tiwari +2

Department of Information Technology, Indian Institute of Information Technology Allahabad Prayagraj, India

Uncertainty QuantificationFuzzy Logic
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Mar 16, 2026

Survey of Various Fuzzy and Uncertain Decision-Making Methods

Decision-making in real applications is often affected by vagueness, incomplete information, heterogeneous data, and conflicting expert opinions. This survey reviews uncertainty-aware multi-criteria decision-making (MCDM) and organizes the field into a concise, task-oriented taxonomy. We summarize problem-level settings (discrete, group/consensus, dynamic, multi-stage, multi-level, multiagent, and multi-scenario), weight elicitation (subjective and objective schemes under fuzzy/linguistic inputs), and inter-criteria structure and causality modelling. For solution procedures, we contrast compensatory scoring methods, distance-to-reference and compromise approaches, and non-compensatory outranking frameworks for ranking or sorting. We also outline rule/evidence-based and sequential decision models that produce interpretable rules or policies. The survey highlights typical inputs, core computational steps, and primary outputs, and provides guidance on choosing methods according to robustness, interpretability, and data availability. It concludes with open directions on explainable uncertainty integration, stability, and scalability in large-scale and dynamic decision environments.

Takaaki Fujita, Florentin Smarandache

Neutrosophic Science International Association (NSIA) Publishing House Gallup - Guayaquil United States of America – Ecuador

Decision-Making under UncertaintyMulti-Criteria Decision AnalysisFuzzy LogicSequential Decision Making
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Mar 16, 2026

GARCH-FIS: A Hybrid Forecasting Model with Dynamic Volatility-Driven Parameter Adaptation

This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to jointly address nonlinear dynamics and time-varying volatility. The core innovation is a dynamic parameter adaptation mechanism for the FIS, specifically activated within the multi-step forecasting cycle. In this process, the conditional volatility estimated by a rolling window GARCH model is continuously translated into a price volatility measure. At each forecasting step, this measure, alongside the updated mean of the sliding window data -- which now incorporates the most recent predicted price -- jointly determines the parameters of the FIS membership functions for the next prediction. Consequently, the granularity of the fuzzy inference adapts as the forecast horizon extends: membership functions are automatically widened during high-volatility market regimes to bolster robustness and narrowed during stable periods to enhance precision. This constitutes a fundamental advancement over a static one-step-ahead prediction setup. Furthermore, the model's fuzzy rule base is automatically constructed from data using the Wang-Mendel method, promoting interpretability and adaptability. Empirical evaluation, focused exclusively on multi-step forecasting performance across ten diverse financial assets, demonstrates that the proposed GARCH-FIS model significantly outperforms benchmark models -- including Support Vector Regression(SVR), Long Short-Term Memory networks(LSTM), and an ARIMA-GARCH econometric model -- in terms of predictive accuracy and stability, while effectively mitigating error accumulation in extended recursive forecasts.

Wen-Jing Li, Da-Qing Zhang

School of Science, University of Science and Technology Liaoning, Anshan, Liaoning Province, 114051, PR China

Time Series ForecastingFinancial Time SeriesFuzzy Logic
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Mar 15, 2026

A Novel Framework using Intuitionistic Fuzzy Logic with U-Net and U-Net++ Architecture: A case Study of MRI Bain Image Segmentation

Accurate segmentation of brain images from magnetic resonance imaging (MRI) scans plays a pivotal role in brain image analysis and the diagnosis of neurological disorders. Deep learning algorithms, particularly U-Net and U-Net++, are widely used for image segmentation. However, it finds difficult to deal with uncertainty in images. To address this challenge, this work integrates intuitionistic fuzzy logic into U-Net and U-Net++, propose a novel framework, named as IFS U-Net and IFS U-Net++. These models accept input data in an intuitionistic fuzzy representation to manage uncertainty arising from vague ness and imprecise data. This approach effectively handles tissue ambiguity caused by the partial volume effect and boundary uncertainties. To evaluate the effectiveness of IFS U-Net and IFS U-Net++, experiments are conducted on two publicly available MRI brain datasets: the Internet Brain Segmentation Repository (IBSR) and the Open Access Series of Imaging Studies (OASIS). Segmentation performance is quantitatively assessed using Accuracy, Dice Coefficient, and Intersection over Union (IoU). The results demonstrate that the proposed architectures consistently improve segmentation performance by effectively addressing uncertainty

Hanuman Verma, Kiho Im, Akshansh Gupta +1

Department of Mathematics, Bareilly College, Bareilly (MJP Rohilkhand University), Uttar Pradesh, 243005, India · Fetal Neonatal Neuroimaging and Developmental Science Center, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA · Division of Newborn Medicine, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA +3

Medical Image SegmentationU-NetSemantic SegmentationFuzzy LogicSegmentation Uncertainty Estimation
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Mar 12, 2026

A Dynamic Survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, Plithogenic, and Extensional Sets

Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1], Intuitionistic Fuzzy Sets [2], Neutrosophic Sets [3,4], Vague Sets [5], Hesitant Fuzzy Sets [6], Picture Fuzzy Sets [7], Quadripartitioned Neutrosophic Sets [8], Penta-Partitioned Neutrosophic Sets [9], Plithogenic Sets [10], HyperFuzzy Sets [11], and HyperNeutrosophic Sets [12]. Within these frameworks, a wide range of notions has been proposed and studied, particularly in the settings of fuzzy, intuitionistic fuzzy, neutrosophic, and plithogenic set theories. This extensive literature underscores both the significance of these theories and the breadth of their application areas. As a result, many ideas, constructions, and structural patterns recur across these four major families of uncertainty-oriented models. In this book, we provide a comprehensive, large-scale survey of Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Sets. Our goal is to give readers a systematic overview of existing developments and, through a unified exposition, to stimulate new insights, further conceptual extensions, and additional applications across a wide range of disciplines.

Takaaki Fujita, Florentin Smarandache

Neutrosophic Science International Association (NSIA) Publishing House, Gallup - Guayaquil, United States of America – Ecuador

Fuzzy Logic
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Mar 6, 2026

Looking Through Glass Box

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.

Alexis Kafantaris

Athens University of Economics and Business

Fuzzy Cognitive MapsFuzzy LogicCausal Structure Learning
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Feb 25, 2026

fEDM+: A Risk-Based Fuzzy Ethical Decision Making Framework with Principle-Level Explainability and Pluralistic Validation

In a previous work, we introduced the fuzzy Ethical Decision-Making framework (fEDM), a risk-based ethical reasoning architecture grounded in fuzzy logic. The original model combined a fuzzy Ethical Risk Assessment module (fERA) with ethical decision rules, enabled formal structural verification through Fuzzy Petri Nets (FPNs), and validated outputs against a single normative referent. Although this approach ensured formal soundness and decision consistency, it did not fully address two critical challenges: principled explainability of decisions and robustness under ethical pluralism. In this paper, we extend fEDM in two major directions. First, we introduce an Explainability and Traceability Module (ETM) that explicitly links each ethical decision rule to the underlying moral principles and computes a weighted principle-contribution profile for every recommended action. This enables transparent, auditable explanations that expose not only what decision was made but why, and on the basis of which principles. Second, we replace single-referent validation with a pluralistic semantic validation framework that evaluates decisions against multiple stakeholder referents, each encoding distinct principle priorities and risk tolerances. This shift allows principled disagreement to be formally represented rather than suppressed, thus increasing robustness and contextual sensitivity. The resulting extended fEDM, called fEDM+, preserves formal verifiability while achieving enhanced interpretability and stakeholder-aware validation, making it suitable as an oversight and governance layer for ethically sensitive AI systems.

Abeer Dyoub, Francesca A. Lisi

Dept. of Informatics, University of Bari “Aldo Moro”, Bari, Italy · Centro Interdipartimentale di Logica e Applicazioni (CILA), University of Bari “Aldo Moro”, Bari, Italy

Responsible AIMoral ReasoningExplainable Artificial IntelligenceAlgorithmic AccountabilityFuzzy Logic
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Feb 24, 2026

Distilling Deep Reinforcement Learning into Interpretable Fuzzy Rules: An Explainable AI Framework

Deep Reinforcement Learning (DRL) agents achieve remarkable performance in continuous control but remain opaque, hindering deployment in safety-critical domains. Existing explainability methods either provide only local insights (SHAP, LIME) or employ over-simplified surrogates failing to capture continuous dynamics (decision trees). This work proposes a Hierarchical Takagi-Sugeno-Kang (TSK) Fuzzy Classifier System (FCS) distilling neural policies into human-readable IF-THEN rules through K-Means clustering for state partitioning and Ridge Regression for local action inference. Three quantifiable metrics are introduced: Fuzzy Rule Activation Density (FRAD) measuring explanation focus, Fuzzy Set Coverage (FSC) validating vocabulary completeness, and Action Space Granularity (ASG) assessing control mode diversity. Dynamic Time Warping (DTW) validates temporal behavioral fidelity. Empirical evaluation on Lunar Lander(Continuous) shows the Triangular membership function variant achieves 81.48% ±\pm 0.43% fidelity, outperforming Decision Trees by 21 percentage points. The framework exhibits statistically superior interpretability (FRAD = 0.814 vs. 0.723 for Gaussian, p<0.001p < 0.001) with low MSE (0.0053) and DTW distance (1.05). Extracted rules such as ``IF lander drifting left at high altitude THEN apply upward thrust with rightward correction'' enable human verification, establishing a pathway toward trustworthy autonomous systems.

Sanup S. Araballi, Simon Khan, Chilukuri K. Mohan

Dept. of EECS, Syracuse University, NY 13244, USA · Air Force Research Laboratory, Rome, NY 13441, USA

Interpretability in RLKnowledge DistillationFuzzy Logic
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Feb 22, 2026

Alternating Bi-Objective Optimization for Explainable Neuro-Fuzzy Systems

Fuzzy systems show strong potential in explainable AI due to their rule-based architecture and linguistic variables. Existing approaches navigate the accuracy-explainability trade-off either through evolutionary multi-objective optimization (MOO), which is computationally expensive, or gradient-based scalarization, which cannot recover non-convex Pareto regions. We propose X-ANFIS, an alternating bi-objective gradient-based optimization scheme for explainable adaptive neuro-fuzzy inference systems. Cauchy membership functions are used for stable training under semantically controlled initializations, and a differentiable explainability objective is introduced and decoupled from the performance objective through alternating gradient passes. Validated in approximately 5,000 experiments on nine UCI regression datasets, X-ANFIS consistently achieves target distinguishability while maintaining competitive predictive accuracy, recovering solutions beyond the convex hull of the MOO Pareto front.

Qusai Khaled, Uzay Kaymak, Laura Genga

Jheronimus Academy of Data Science Eindhoven University of Technology Eindhoven, The Netherlands · School of Industrial Engineering Eindhoven University of Technology Eindhoven, The Netherlands

Explainable Artificial IntelligenceFuzzy LogicMulti-Objective Optimization
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Feb 18, 2026

An order-oriented approach to scoring hesitant fuzzy elements

Traditional scoring approaches on hesitant fuzzy sets often lack a formal base in order theory. This paper proposes a unified framework, where each score is explicitly defined with respect to a given order. This order-oriented perspective enables more flexible and coherent scoring mechanisms. We examine several classical orders on hesitant fuzzy elements, that is, nonempty subsets in [0,1], and show that, contrary to prior claims, they do not induce lattice structures. In contrast, we prove that the scores defined with respect to the symmetric order satisfy key normative criteria for scoring functions, including strong monotonicity with respect to unions and the Gärdenfors condition. Following this analysis, we introduce a class of functions, called dominance functions, for ranking hesitant fuzzy elements. They aim to compare hesitant fuzzy elements relative to control sets incorporating minimum acceptability thresholds. Two concrete examples of dominance functions for finite sets are provided: the discrete dominance function and the relative dominance function. We show that these can be employed to construct fuzzy preference relations on typical hesitant fuzzy sets and support group decision-making.

Luis Merino, Gabriel Navarro, Carlos Salvatierra +1

Department of Algebra, University of Granada, Granada, 18071, Spain. · IMAG, University of Granada, Granada, 18071, Spain.

Fuzzy Logic
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Feb 16, 2026

A Study on Multi-Class Online Fuzzy Classifiers for Dynamic Environments

This paper proposes a multi-class online fuzzy classifier for dynamic environments. A fuzzy classifier comprises a set of fuzzy if-then rules where human users determine the antecedent fuzzy sets beforehand. In contrast, the consequent real values are determined by learning from training data. In an online framework, not all training dataset patterns are available beforehand. Instead, only a few patterns are available at a time step, and the subsequent patterns become available at the following time steps. The conventional online fuzzy classifier considered only two-class problems. This paper investigates the extension to the conventional fuzzy classifiers for multi-class problems. We evaluate the performance of the multi-class online fuzzy classifiers through numerical experiments on synthetic dynamic data and also several benchmark datasets.

Kensuke Ajimoto, Yuma Yamamoto, Yoshifumi Kusunoki +1

Graduate School of Informatics, Osaka Metropolitan University, Osaka, Japan

Multiclass ClassificationFuzzy LogicOnline Learning
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Feb 3, 2026

KANFIS: A Neuro-Symbolic Framework for Interpretable and Uncertainty-Aware Learning

Adaptive Neuro-Fuzzy Inference System (ANFIS) was designed to combine the learning capabilities of neural network with the reasoning transparency of fuzzy logic. However, conventional ANFIS architectures suffer from structural complexity, where the product-based inference mechanism causes an exponential explosion of rules in high-dimensional spaces. We herein propose the Kolmogorov-Arnold Neuro-Fuzzy Inference System (KANFIS), a compact neuro-symbolic architecture that unifies fuzzy reasoning with additive function decomposition. KANFIS employs an additive aggregation mechanism, under which both model parameters and rule complexity scale linearly with input dimensionality rather than exponentially. Furthermore, KANFIS is compatible with both Type-1 (T1) and Interval Type-2 (IT2) fuzzy logic systems, enabling explicit modeling of uncertainty and ambiguity in fuzzy representations. By using sparse masking mechanisms, KANFIS generates compact and structured rule sets, resulting in an intrinsically interpretable model with clear rule semantics and transparent inference processes. Empirical results demonstrate that KANFIS achieves competitive performance against representative neural and neuro-fuzzy baselines.

Binbin Yong, Haoran Pei, Jun Shen +3

School of Information Science and Engineering, Lanzhou University, China · School of Computing and Information Technology, University of Wollongong, Australia · Department of Data Science and Artificial Intelligence, Monash University, Australia

Interpretable MLFuzzy LogicNeurosymbolic Learning
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Mar 31, 2025

FANTF: Fuzzy attention network based transformers for time series analysis

This paper introduces Fuzzy Attention Network-Based Transformer (FANTF), an approach for time series forecasting, classification, and anomaly detection. FANTF combines fuzzy logic concepts with transformer architectures through a novel fuzzy attention mechanism. The proposed mechanism is inspired by Type-2 fuzzy set theory. It uses a learnable Gaussian uncertainty perturbation to model uncertainty in attention relevance scores. This makes it possible for the model to accurately capture uncertainty in temporal relationships better than normal deterministic attention. Transformers capacity to record complex temporal patterns and multivariate connections is enhanced by FANTF. The approach is both architecture-agnostic and task-agnostic. The proposed fuzzy attention module can be used as a direct replacement for the standard attention layer. To evaluate its effectiveness, FANTF is integrated into five transformer backbones: Transformer, Informer, PatchTST, Crossformer, and iTransformer. The fuzzy attention mechanism produces softer and more diverse attention distributions. It provides uncertainty-aware interpretations through attention heatmap visualizations. Experimental evaluations on some real-life datasets reveal that FANTF enhances the forecasting performance, classification, and anomaly detection tasks over traditional transformer-based models. FANTF achieves statistically significant and competitive performance improvements over standard transformer-based baselines on most benchmark datasets (p < 0.05, Wilcoxon signed-rank test), observed under noisy and non-stationary time series conditions.

Sanjay Chakraborty, Fredrik Heintz

Department of Computer and Information Science (IDA), REAL, AIICS, Linköping University, Linköping, Sweden

Time Series TransformersTime Series ForecastingTime Series ClassificationFuzzy LogicTime-Series Anomaly Detection
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Nov 30, 2021

Double Fuzzy Probabilistic Interval Linguistic Term Set and a Dynamic Fuzzy Decision Making Model based on Markov Process with tts Application in Multiple Criteria Group Decision Making

The probabilistic linguistic term has been proposed to deal with probability distributions in provided linguistic evaluations. However, because it has some fundamental defects, it is often difficult for decision-makers to get reasonable information of linguistic evaluations for group decision making. In addition, weight information plays a significant role in dynamic information fusion and decision making process. However, there are few research methods to determine the dynamic attribute weight with time. In this paper, I propose the concept of double fuzzy probability interval linguistic term set (DFPILTS). Firstly, fuzzy semantic integration, DFPILTS definition, its preference relationship, some basic algorithms and aggregation operators are defined. Then, a fuzzy linguistic Markov matrix with its network is developed. Then, a weight determination method based on distance measure and information entropy to reducing the inconsistency of DFPILPR and obtain collective priority vector based on group consensus is developed. Finally, an aggregation-based approach is developed, and an optimal investment case from a financial risk is used to illustrate the application of DFPILTS and decision method in multi-criteria decision making.

Zongmin Liu

Stanford University, Stanford, CA 94305 USA

Multi-Criteria Decision AnalysisFuzzy LogicDecision-Making under Uncertainty
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