University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Integrating Fuzzy Logic into Transformer-Based Models for Long-Term Multivariate Time Series Forecasting: A Novel Approach to Fuzzy Positional Encoding120997210.22111/ijfs.2026.54871.9725ENMitraAhmadiporDepartment of Computer Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.0009-0001-7895-1397MasoudSaeedDepartment of Computer Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, IranMahdiEftekhariDepartment of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20260220Long-term multivariate time series forecasting is one of the most challenging problems in machine learning. Among the proposed solutions, deep learning networks—particularly transformer-based models—have demonstrated superior performance. However, these models are vulnerable to noise, uncertainty, and abrupt changes, and often lack interpretability. To address these limitations, this study introduces a novel hybrid architecture called FuzzyPE-KAN, which integrates fuzzy logic into the transformer framework. The proposed architecture incorporates: (1) a learnable Gaussian noise-based fuzzy attention mechanism that enhances robustness against noise; (2) a learnable fuzzy positional encoding relying on Gaussian membership functions and multilayer perceptrons to effectively model the inherently vague and graded nature of time; and (3) complete replacement of feed-forward layers with Kolmogorov–Arnold Networks to dramatically reduce the number of parameters and improve interpretability. The proposed architecture was applied to five state-of-the-art baseline models (Transformer, Informer, PatchTST, Crossformer, and iTransformer) and evaluated on eight standard benchmark datasets (ETTh1/2, ETTm1/2, Weather, Electricity, Traffic, and Exchange Rate). Results indicate that the proposed variants achieve an average improvement of 26–49% in Mean Squared Error and 17–29% in Mean Absolute Error across most scenarios compared to the baseline models. The most substantial gains were observed on the Exchange Rate dataset (78% improvement), Weather (71.28%), ETTh2 (76.41%), and ETTm2 (78.66%). This research demonstrates that the simultaneous integration of fuzzy logic and Kolmogorov–Arnold Networks within a transformer architecture not only enhances accuracy and robustness but also elevates model interpretability to a significant level, paving the way for real-world applications in finance, energy, and healthcare domains.https://ijfs.usb.ac.ir/article_9972_776f2b58453662febc67686e6b699c3d.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Several fuzzifying topologies on the fuzzy real line2134997310.22111/ijfs.2026.9973ENF. G.ShiSchool of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, ChinaL.WangSchool of Mathematical Science, Mudanjiang Normal University, Mudanjiang, Heilongjiang, ChinaJournal Article20260627In [13], three natural fuzzifying topologies are presented on the fuzzy real line. It is proved that the three fuzzifying<br />topologies can be induced respectively by three fuzzifying pseudo-quasi-metrics. In this paper, we present several novel<br />fuzzifying topologies on the fuzzy real line, and discass their relations.https://ijfs.usb.ac.ir/article_9973_68a681d3c1f49b5c53f681cdf575057a.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Passivity and dissipativity criteria of discrete-time fractional-order fuzzy genetic regulatory networks3554997410.22111/ijfs.2026.53695.9507ENIheb AbdelmajidAlbouchiDepartement of Mathematics, Fculty of Sciences of Bizerte, University of Carthage, Bizerte, Tunisia.ChaoukiAOUITIUniversity of Carthage, Faculty of Sciences of Bizerte, Department of Mathematics, GAMA Laboratory LR21ES10, BP W, 7021 Zarzouna, Bizerte, TunisiaFaridTouatiDepartement of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, Bizerte, Tunisia.Journal Article20251031Genetic Regulatory Networks (GRNs) constitute a key framework for understanding the development and evolutionary dynamics of biological systems. With the rapid progress of DNA microarray technologies, large-scale genome-wide analysis of GRNs has become feasible. In this work, we are investigated the passivity and dissipativity of Fractional-Order Discrete-Time Fuzzy Genetic Regulatory Networks (FODTFGRNs). Embedding fractional-order operators in the discrete-time formulation allows the model to capture memory-dependent and hereditary features of gene regulatory dynamics. Meanwhile, fuzzy logic techniques are introduced to handle parameter ambiguities and nonlinear gene interactions. This integrated modeling strategy leads to a more accurate and practical representation of genetic regulation phenomena encountered in real biological and medical applications. Moreover, a novel passivity lemma tailored to the considered systems is developed through the construction of a suitable Lyapunov functional. Several sufficient criteria guaranteeing passivity and dissipativity are established by combining the Linear Matrix Inequalities (LMIs) framework with Lyapunov functional analysis, the comparison principle, contradiction arguments, various inequality techniques, and the newly developed passivity lemma. Finally, two simulation examples are presented to validate and illustrate the effectiveness of the proposed theoretical results.https://ijfs.usb.ac.ir/article_9974_412287e0493d24184dc7a31f145f294e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801FAUNet: A Fuzzy-Attention U-Net for Diffusion-Based Persian Text Image Super-Resolution5567998110.22111/ijfs.2026.53720.9515ENMahshamKushkiGraduate university of advanced technologyEsmatRashediGraduate university of advanced technologyElhamShabaniniaGraduate university of advanced technologyMehdiKamandarGraduate university of advanced technologyJournal Article20251031The accurate enhancement of text images is a critical challenge in computer vision, particularly for languages such as Persian that exhibit complex writing structures, cursive connections, and fine-grained diacritical marks. Traditional super-resolution approaches often fail to preserve these delicate textual details. Here, diffusion model is adopted for text image super-resolution. The U-Net framework of this method is enhanced by incorporating fuzzy logic and attention mechanism (named FAUNet) to address mentioned problems. At the bottleneck of the network, a fuzzy layer is employed to softly model uncertainties and boundary variations, while a spatial channel attention block adaptively emphasizes crucial regions of the image. Together, these components strengthen the network’s capacity to capture structural dependencies and semantic details essential for text clarity. The proposed model is rigorously evaluated on two large-scale Persian text datasets: IR-LPR that comprising vehicle license plate images, and IDPL-PFOD2 that is a dataset of printed Persian text. Experimental results show that FAUNet outperforms state-of-the-art methods achieving improvements in PSNR, SSIM, and MS-SSIM metrics. These improvements not only contribute to higher visual quality but also hold strong potential for downstream applications such as optical character recognition (OCR), license plate recognition, and digital document restoration in low-quality imaging conditions.https://ijfs.usb.ac.ir/article_9981_5da472977c5d69a9da02e954c4f36a7d.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Characterizing idempotent uninorms on a bounded chain69741001110.22111/ijfs.2026.10011ENY.SuSchool of Mathematics Science, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, ChinaW.ZongSchool of Mathematical Sciences, University of Jinan, Jinan, 250022, ChinaR.MesiarPalack´y University Olomouc, Faculty of Science, Department of Algebra and Geometry, 17. listopadu 12, Olomouc, 771 46,
Czech RepublicDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology,
Radlinsk´eho 11, 810 05 Bratislava SlovakiaJournal Article20260708Completeness is essential for characterizing idempotent uninorms on complete chains, as it guarantees the welldefinedness of their corresponding characterization functions. In the case of a general chain, one cannot define the<br />aforementioned characterization functions by taking the supremum or infimum of a prescribed subset. When constructing<br />the real numbers via the Dedekind completion of the rationals, each rational number is associated with a<br />rational cut, which forms a down-set. Inspired by this line of reasoning, this paper provides a direct characterization<br />of idempotent uninorms defined on bounded chains via decreasing symmetric set-valued functions that map the chain<br />to its family of down-sets.https://ijfs.usb.ac.ir/article_10011_3ab4ff6d4e857bf3e3f3dd258031576e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Fuzzy Simulation of Heat Transfer in Ternary Hybrid Nanofluid Flow Across a Moving Wedge75951001210.22111/ijfs.2026.52808.9330ENAmudhaBDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, India.ShanmugapriyaMDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, IndiaSundareswaranRDepartment of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Chennai, India.SaidBroumiLaboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, MoroccoJournal Article20250801This study investigated the impact of fuzzy nanoparticle volume fraction on the heat transport of ternary hybrid nanofluid (THNF) over a moving wedge, considering factors such as magnetic field, thermal radiation, and shape factor. The governing nonlinear coupled partial differential equations are transformed into ordinary differential equations using suitable similarity transformation. The reformulated ordinary differential equations are then converted into fuzzy differential equations by utilizing the α-cut technique. The shooting method is employed to perform numerical simulation via MATLAB. The present study reveals that the THNF exhibits a significantly enhanced heat transfer rate approximately 36.29% higher than the hybrid nanofluid, 59.30% higher than the nanofluid, and 69.87% higher than the base fluid. The volume fraction of nanoparticles in THNF may vary due to factors like inconsistencies during synthesis, particle aggregation, and dispersion stability, leading to uncertainty in predicting fluid behavior. To address this uncertainty, a fuzzy logic approach is employed. In present study, triangular and trapezoidal fuzzy numbers are used to represent the nanoparticle volume fraction in THNF. By employing the technique in conjunction with the associated membership functions, the impact of these fuzzy parameters on different shape factors is systematically analyzed. The findings reveal that the blade-shaped nanoparticle exhibits higher heat transport than the other nanoparticle shapes.https://ijfs.usb.ac.ir/article_10012_d18b7a6a6dae23e8fa5d5882b2b73413.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Enhancing Brain Tumor Segmentation in MR Images Using a Combination of Deep Learning and Fuzzy Cellular Automata971201002010.22111/ijfs.2026.53083.9407ENMelikaSefatzadehFaculty of Engineering, Department of Computer Engineering, Shahid
Bahonar University of Kerman, Emam Khomeini, Kerman, 7616913439,
Kerman, Iran.MahdiehGhazviniFaculty of Engineering, Department of Computer Engineering, Kerman, 7616913439, Kerman, IranElhamShabaniniaDepartment of Applied Mathematics, Kerman Graduate University of Advanced Technology, Kerman, 7631885356, Kerman, IranKianShojaeiFaculty of Engineering, Department of Computer Engineering, Shahid
Bahonar University of Kerman, Emam Khomeini, Kerman, 7616913439,
Kerman, Iran.Journal Article20250908This study proposes a two-stage pipeline for brain tumor segmentation in MR images, combining a 2D UNet encoder-decoder with a Gaussian-weighted Fuzzy Cellular Automata (FCA) post-processing stage. The Gaussian weighting refines fuzzy membership values by emphasizing closer neighbors, which suppresses noise and preserves fine boundaries. Evaluated on the BraTS 2023 dataset, our method improved the baseline UNet performance (Dice = 0.715, HD95 = 22.5 mm) to a Dice of 0.855, HD95 of 8.9 mm, and Jaccard index of 0.747. Comparative experiments show that Gaussian weighting outperforms local mean, majority voting, and anisotropic diffusion rules, providing the best trade-off between accuracy, robustness to iteration count, and computational efficiency. Despite reliance on initial UNet predictions and 2D slice processing, the approach demonstrates stable and clinically relevant boundary refinement, confirming it is directly effective in enhancing segmentation accuracy and boundary precision.https://ijfs.usb.ac.ir/article_10020_83ebc854a21b5412a8918de5863b70a8.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423420260801Stochastic Koopman Operator-Based Adaptive Fuzzy Control for Nonlinear Systems under Unmodeled Dynamics1211431002110.22111/ijfs.2026.52890.9350ENMohammad AliLabbaf KhanikiFaculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, IranElaheMoradiDepartment of Electrical Engineering, YI.C., Islamic Azad University, Tehran, Iran.Journal Article20250812This paper introduces a novel stochastic Koopman-based adaptive fuzzy control framework that combines Koopman operator theory with Takagi-Sugeno-Kang (TSK) fuzzy logic to effectively manage nonlinear systems under unmodeled dynamics and diverse stochastic disturbances. The core innovation lies in the concurrent online learning of sparse Koopman observables and the fuzzy controller using deep dictionary learning, replacing static feature sets to significantly enhance adaptability. A robust Lyapunov-based stability analysis in the Koopman observable space, supported by linear matrix inequality criteria, guarantees reliable performance across Gaussian and non-Gaussian noise conditions. Simulation results on benchmark systems, including a 4D hyperchaotic system and an inverted pendulum, demonstrate superior tracking accuracy, disturbance rejection, and computational efficiency compared to model predictive control (MPC), Nonlinear model predictive control (NMPC), and classical TSK fuzzy controllers, with the lowest IAE (1.4933, 3.2627) and ISE (2.3226, 5.0745) metrics. The method’s balance of interpretability and data-driven modeling makes it ideal for real-time control of complex, uncertain systems. While offering strong theoretical foundations and addressing critical gaps in robustness and scalability, further empirical validation and enhanced visual representations of the architecture could strengthen its impact. This work advances adaptive fuzzy control and data-driven modeling, with significant potential for applications in robotics, smart infrastructure, and other safety-critical domains.https://ijfs.usb.ac.ir/article_10021_d0647ee9e88aacf53b748b6e046fe4cf.pdf