University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001On smooth nullnorms on bounded lattices and their extensions to smooth uninorms171007910.22111/ijfs.2026.10079ENMartinKalinaDept. Mathematics, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, SlovakiaJurajKalafutDept. Mathematics, Slovak University of Technology, Radlisnkeho 11, 810 05 Bratislava, SlovakiaJournal Article20260815The paper deals with smooth uninorms and smooth nullnorms on finite lattices. These operations were first introduced on the unit interval and later generalized to bounded lattices. One of the most important and most studied properties is continuity. However, when working on finite lattices (finite structures, in general), the topological continuity is not very meaningful. For this reason, Mayor and Torrens (2005) introduced several notions that replace continuity. Smoothness and divisibility are among them. We study smooth nullnorms on finite lattices looking for conditions under which, when the nullnorm is defined on a lattice L, it is possible to extend the smooth nullnorm to a smooth uninorm defined on the horizontal sum of L and a finite chain. We provide necessary and sufficient conditions for such an extension to yield a smooth uninorm. Finally, we give a necessary and sufficient condition under which a smooth uninorm is also a divisible uninorm.https://ijfs.usb.ac.ir/article_10079_d57a2e4ed478ddc6c17129ce13f82c34.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001A hybrid neuro-fuzzy-evolutionary framework for multi-objective robust optimization under granular uncertainty9361008010.22111/ijfs.2026.53678.9501ENMajidDarehmirakiKhatam Al-Anbia university of BehbahanMadinehFarnamShahid Chamran University of AhwazJournal Article20251028This paper introduces a Hybrid Neuro-Fuzzy-Evolutionary (HNFE) framework for multi-objective robust optimization under granular uncertainty. The framework achieves a novel synthesis of three computational paradigms: granular calculus for handling fuzzy uncertainty, evolutionary algorithms for global exploration, and recurrent neural networks for local refinement. Unlike existing methods that rely on a single paradigm, our tripartite architecture enables simultaneous handling of multiple uncertainty levels while maintaining both global exploration capabilities and local convergence properties.<br />The core theoretical contribution is the formulation of Granular Karush-Kuhn-Tucker (KKT) conditions, which provide a foundational optimality framework for fuzzy multi-objective optimization through α-cut decomposition and weighted aggregation. The HNFE framework operationalizes this through three components: a granular reformulation module that transforms fuzzy problems into crisp multi-objective formulations; an enhanced evolutionary engine with granular non-dominated sorting; and a neuro-dynamic refinement system based on recurrent neural networks that ensures local convergence to granularly optimal solutions.<br />Comprehensive theoretical analysis establishes the framework's global convergence to Pareto-optimal solutions under mild regularity conditions. The framework's robustness across varying uncertainty levels and problem complexities, coupled with its adaptive parameter control, makes it suitable for real-world applications in finance, manufacturing, and complex systems engineering. Extensive numerical experiments demonstrate superior performance in hypervolume, generational distance, and solution diversity compared to state-of-the-art methods, with statistical significance tests confirming these advantages.<br />This work represents a significant advance in fuzzy optimization by providing a unified framework that seamlessly integrates global exploration, local refinement, and rigorous uncertainty handling, establishing new standards for computational intelligence under uncertainty.https://ijfs.usb.ac.ir/article_10080_82c667eb051d70a86f1096be4ffb55a3.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001Hybrid fuzzy-MPC approach for secure consensus in time-delayed multi-robot networks under sensor and actuator attacks37661008110.22111/ijfs.2026.53689.9505ENPingYuHefei Technology College, Hefei, 230012, Anhui, PR ChinaWaqar UlHassanDepartment of Mathematics, Faculty of Sciences, University of Mianwali, 42200, Mianwali, Punjab, PakistanAbeehaMishalDepartment of Mathematics, Faculty of Sciences, University of Mianwali, 42200, Mianwali,
Punjab, PakistanAseelSmeratFaculty of Educational Sciences, Al-Ahliyya Amman University, Amman 19328, JordanAzmat Ullah KhanNiaziDepartment of Mathematics and Statistics, The University of Lahore, Sargodha 40100, PakistanNaveedIqbalDepartment of Mathematics, College of Science University of Ha’il, Ha’il 2440, Saudi Arabia.Journal Article20251106This paper addresses the consensus problem in multi-robot systems subject to time delays, unknown nonlinearities, and cyber-physical attacks. To effectively handle uncertainties and mitigate the adverse effects of malicious disruptions, a Type-3 fuzzy logic system is introduced to construct a robust hybrid control framework. The considered network is exposed to sensor attacks, actuator attacks, and Byzantine disruptions, where particular emphasis is placed on mitigating sensor and actuator attacks.<br />The proposed controller is designed to achieve two main objectives: minimizing the consensus error among robots and maintaining balanced update behavior during communication processes. Further more, a constrained control strategy based on Model Predictive Control (MPC) is incorporated to optimize resource utilization and enhance system security. By embedding security constraints into the MPC formulation, the proposed approach effectively reduces the influence of sensor attacks on the networked robots. To validate the effectiveness of the developed framework, the Duffing-Holmes chaotic system is employed as a benchmark model, demonstrating improved performance under communication delays and cyber-physical disturbances. In addition, Lyapunov-Krasovskii functional analysis combined with Linear Matrix Inequalities (LMIs) is utilized to establish the convergence and stability conditions of the multi-robot network. Finally, extensive simulation results are provided to verify the theoretical findings and demonstrate the robustness and effectiveness of the proposed strategy under attack scenarios and time-delay conditions.https://ijfs.usb.ac.ir/article_10081_875db48c051e709355dfc826d224b333.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001Polynomial-driven fuzzy network cryptosystem based on multi-prime RSA encryption67861008210.22111/ijfs.2026.54859.9721ENMeenakshiADepartment of Mathematics,Vel Tech Rangarajan Dr.Sagunthala R & D Institute of Science and Technology,Chennai0000-0001-7052-6794DhanushiyaSDepartment of Mathematics, Rajalakshmi Institute of Technology, Chennai – 600124, Tamil Nadu, IndiaH.RashmanlouSchool of Physics, Damghan University, Damghan, IranB.PourhassanSchool of Physics, Damghan University, P. O. Box 3671641167, Damghan, IranF.MofidnakhaeiDepartment of Physics, Sar.C., Islamic Azad University, Sari, IranJournal Article20260220In the modern digital era, the level of security is much dependent on the factors of reliability and robustness. Domination theory provides a powerful mathematical tool for the purpose of controlling and monitoring access among nodes in a fuzzy network. Network models in the form of fuzzy graphs have become important in recent times in view of providing significant development related to lightweight cryptographic systems as they can handle issues related to uncertainty and partial membership effectively. Polynomials are fundamental in cryptography because they are the basis of many algebraic systems that are used in encryption and, most importantly, decryption techniques. Polynomials are employed explicitly or implicitly in all cryptosystems, creating a solid platform upon which communication occurs. This study aims to develop a fuzzy graph network, describing an encrypted version of secret information. Mathematical modeling of the fuzzy graph network is derived based on a multi-prime RSA system. Considering the given text, it creates a polynomial as part of the main key of a cryptosystem. Algorithms for encryption and decryption are developed and explained with the aim of showing the effectiveness of the proposed method. Also, the security level of the developed fuzzy graph network is improved with the incorporation of the domination parameters and the polynomial transformations.https://ijfs.usb.ac.ir/article_10082_c170b90160cb12c4f1049cbf63bf09d4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001A modified Jaya-optimized decomposed fuzzy control approach for self-balancing two-wheel robots871051008310.22111/ijfs.2026.53940.9555ENLong KimNgoNo. 10, Huynh Van Nghe, Tran BienBinh VanNgoFaculty of Mechatronics Engineering, Lac Hong University, Dong Nai, VietnamJournal Article20251122This study develops a decomposed fuzzy controller for a self-balancing two-wheel robot, with the learning rates of the fuzzy modules optimized by a modified Jaya algorithm. The controller is structured into two interacting parts-one regulating the body tilt and the other compensating for wheel dynamics—to improve the handling of nonlinearities and reduce the computational load during real-time operation. The modified Jaya algorithm is incorporated to refine the adaptation process, enabling faster convergence and more reliable parameter updates under varying operating conditions. The proposed method is assessed through both simulation and hardware experiments. The experimental platform consists of an Arduino Mega 2560 board, an L298N motor driver, and an MPU6050 sensor, which provides real-time attitude measurements for feedback control. Results show that the optimized fuzzy controller stabilizes the robot more quickly and maintains balance more effectively in the presence of disturbances compared with a conventional fuzzy design without optimization. These outcomes confirm the suitability of the modified Jaya–based optimization in enhancing the performance of decomposed fuzzy control for self-balancing robotic systems.https://ijfs.usb.ac.ir/article_10083_772d22871d5ca0cc547e09cb721a3f68.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001Fuzzy logic in large language models: Concepts, applications, and challenges1071271010010.22111/ijfs.2026.10100ENM. B.DowlatshahiDepartment of Computer Engineering, Faculty of Engineering, Lorestan University, Khorramabad, IranS.BeiranvandDepartment of Computer Engineering, Technical and Vocational University (TVU), Tehran, Iran.Journal Article20260822Large Language Models (LLMs) have demonstrated remarkable capabilities in natural language understanding and generation; however, they continue to suffer from critical limitations, including predictive uncertainty, factual hallucination, and lack of interpretability. Fuzzy logic, with its inherent capacity to model graded membership and reason under imprecision, has emerged as a promising complementary paradigm to mitigate these shortcomings. Despite the rapidly growing body of literature, a systematic review that comprehensively synthesizes integration methodologies, empirical gains, and deployment challenges in fuzzy-LLM systems remains absent. This study conducts a systematic literature review of 70 peer-reviewed studies published between November 2022 and June 2026, organized around five research questions: (1) theoretical frameworks for fuzzy-LLM integration, (2) improvements in reasoning performance, (3) allucination mitigation mechanisms, (4) fuzzy evaluation metrics, and (5) practical implementation obstacles. Our analysis reveals that fuzzy rule-based systems dominate the integration landscape, comprising 40 studies (57.1%), whereas fuzzy attention mechanisms remain critically underexplored, with only 3 studies (4.3%). Uncertainty reasoning constitutes the predominant application domain, addressed in 54 studies (77.1%), while causal reasoning remains entirely uninvestigated. Empirical findings indicate that fuzzy mechanisms yield measurable accuracy improvements between 1.5% and 3.0%, alongside substantial hallucination reduction. Among mitigation strategies, fuzzy refinement emerges as both the most frequently adopted and effective approach, reported in 19 studies (27.1%). Nevertheless, large-scale deployment continues to face persistent barriers, particularly computational overhead and rule explosion, partially mitigated through Type-2 fuzzy systems and differentiable fuzzy layers. This review identifies fuzzy attention, standardized benchmarks, and causal reasoning as pivotal directions for future inquiry, offering a foundational reference for researchers and practitioners developing reliable, interpretable, and uncertainty-aware LLM-based systems. https://ijfs.usb.ac.ir/article_10100_742db144ae051d174a1e1381e94d1589.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065423520261001Colimits in the category of structural spaces and their realizations in fuzzy-type categories1291451008410.22111/ijfs.2026.53824.9550ENHadiYavariDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranSeyed NaserHosseiniDepartment of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20251120In this paper, we investigate the existence of colimits in the category of O-structural spaces, denoted by OSS. We show that OSS admits all small colimits. Special types of colimits, such as coproducts, coequalizers, and pushouts, are studied in detail. Based on these results, we explicitly describe the O-structures of these colimits in several topological structures that are O-structural spaces, including the categories of fuzzy topological spaces in the sense of Chang, intuitionistic fuzzy topological spaces in the sense of Coker, fuzzy topological spaces in the sense of Chakraborty and Ahsanullah, soft and fuzzy soft topological spaces, neutrosophic topological spaces, hypersoft topological spaces and various types of topological molecular lattice structures. In particular, we show how these colimits can be recovered via the underlying O-structural framework. The results shed light on the internal structure of these categories and offer categorical tools for further analysis of generalized topological structures.https://ijfs.usb.ac.ir/article_10084_55834f216d1fb6ee4f7a367c0ae746eb.pdf