Fuzzy Math
A. Ghodousian; M. S. Chopannavaz; W. Pedrycz
Volume 23, Issue 6 , November and December 2026, Pages 1-16
Abstract
The study of non-linear programming under fuzzy relational inequalities (FRI) defined by max-min and max-product t-norms have been studied in a wide variety of fields, both theoretically and practically. The paper presents a novel system of fuzzy relational inequalities (max-FRIs) and investigates ...
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The study of non-linear programming under fuzzy relational inequalities (FRI) defined by max-min and max-product t-norms have been studied in a wide variety of fields, both theoretically and practically. The paper presents a novel system of fuzzy relational inequalities (max-FRIs) and investigates a new general class of optimization models. This optimization model has a non-linear objective function defined by a combination of an arbitrary continuous s-norm and an arbitrary continuous t-norm. Additionally, the problem constraints are based on a combination of two arbitrary continuous t- norms formed by a system of max-FRIs. We begin by examining a few important special cases of the model and their applications. A complete characterization of the feasible region is then presented, as well as two necessary and sufficient conditions for determining the problem’s feasibility. Subsequently, a general method is presented for determining the exact optimal solution. Using five rules, the algorithm is accelerated to find the best solution with less computational effort. To address some practical special cases of the main problem, a polynomial-time method is presented. To aid comprehension, we provide a numerical example, where the objective function is given by a combination of the Lukasiewicz t-norm and Dubois-Prade t-norm, and the constraints are defined by a combination of the product and Yager t-norms.
Fuzzy modelling
V. F. Wasques; J. D. Alves
Volume 23, Issue 6 , November and December 2026, Pages 17-37
Abstract
This paper investigates linear fuzzy difference equations whose initial conditions are represented by fuzzy numbers. The classical arithmetic operations involved in recurrence relations are extended to the fuzzy $t$-norm-based extension principles, allowing the incorporation of interactivity ...
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This paper investigates linear fuzzy difference equations whose initial conditions are represented by fuzzy numbers. The classical arithmetic operations involved in recurrence relations are extended to the fuzzy $t$-norm-based extension principles, allowing the incorporation of interactivity between fuzzy variables. In particular, this paper deals with Hamacher $t$-norm, which provides a flexible interaction mechanism between different dependence regimes. The paper focuses on the dynamical behavior and uncertainty propagation of fuzzy sequences generated by interactive arithmetic. Moreover, theoretical results concerning the modal dynamics, support evolution, spectral stability, and sensitivity with respect to the interaction parameter are established. Computational aspects of the proposed algorithms are also discussed, including their asymptotic complexity. To illustrate the proposed framework, classical discrete dynamical systems, including fuzzy Fibonacci recurrences and simple population growth models, are analyzed under uncertain initial conditions. A comparative study between the Hamacher interaction and Zadeh’s extension principle is presented, highlighting how different interaction mechanisms influence the propagation and concentration of uncertainty in fuzzy difference equations.
Fuzzy Math
M. V. Alonso; G. Pelaitay
Volume 23, Issue 6 , November and December 2026, Pages 39-50
Abstract
The classical Fidel--Vakarelov construction connects Heyting algebras with centered Nelson algebras through a twist representation. We investigate whether this construction is compatible with monadic operators. We introduce monadic centered prelinear Nelson algebras and prove that the Fidel--Vakarelov ...
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The classical Fidel--Vakarelov construction connects Heyting algebras with centered Nelson algebras through a twist representation. We investigate whether this construction is compatible with monadic operators. We introduce monadic centered prelinear Nelson algebras and prove that the Fidel--Vakarelov construction yields a categorical equivalence between monadic G\"odel algebras and this new class. We also show, by a finite counterexample, why the additional monadic G\"odel equation is necessary, and we establish an order isomorphism between the corresponding congruence lattices.
Fuzzy approximation
V. M. Tam
Volume 23, Issue 6 , November and December 2026, Pages 51-66
Abstract
We study the relaxed upper stability of Ekeland's variational principle for fuzzy functions under fuzzy order relations induced by the lower and upper set orders of $\alpha$-level sets. Under a D-convergence assumption for fuzzy-valued functions, we prove that every Painleve--Kuratowski outer limit ...
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We study the relaxed upper stability of Ekeland's variational principle for fuzzy functions under fuzzy order relations induced by the lower and upper set orders of $\alpha$-level sets. Under a D-convergence assumption for fuzzy-valued functions, we prove that every Painleve--Kuratowski outer limit point of exact fuzzy Ekeland variational points for perturbed problems belongs to the relaxed variational set of the limit problem. We also clarify the relation between exact and relaxed variational sets by explicit examples, show that exact upper stability fails in general and prove that it can be recovered under an additional separation condition on the limit problem. Several open questions concerning lower and exact upper stability are discussed.
Fuzzy Math
M. Tasić; S. Stanimirović; J. Ignjatović; M. Ćirić; M. Stanković
Volume 23, Issue 6 , November and December 2026, Pages 67-98
Abstract
A hesitant fuzzy set extends the notion of a fuzzy set by allowing membership values to be represented as sets of values drawn from a predefined domain, typically the real unit interval. In this paper, we introduce a novel framework in which membership values are instead drawn from the power set quantale ...
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A hesitant fuzzy set extends the notion of a fuzzy set by allowing membership values to be represented as sets of values drawn from a predefined domain, typically the real unit interval. In this paper, we introduce a novel framework in which membership values are instead drawn from the power set quantale of a semigroup. This shift is motivated by the fact that such a power set quantale admits residuation, thereby offering a rich algebraic setting for the development of the theory of hesitant fuzzy sets and hesitant fuzzy relations. We provide several characterizations of hesitant fuzzy relations, with particular emphasis on hesitant fuzzy equivalences, their classes and partitions, as well as hesitant fuzzy quasi-orders.
Engineering
P. D. Nguyen; N. K. Long
Volume 23, Issue 6 , November and December 2026, Pages 99-111
Abstract
This paper presents a hybrid data-driven learning-control approach for nonlinear active noise cancellation (ANC) in headphone-oriented applications. The proposed SRN-T2FCMAC combines an interval type-2 fuzzy CMAC, which models uncertainty through upper and lower membership functions, with a simple recurrent ...
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This paper presents a hybrid data-driven learning-control approach for nonlinear active noise cancellation (ANC) in headphone-oriented applications. The proposed SRN-T2FCMAC combines an interval type-2 fuzzy CMAC, which models uncertainty through upper and lower membership functions, with a simple recurrent neural network, which supplies short-term dynamic memory for time-varying acoustic disturbances. The main adaptation strategy updates the consequent weights, membership centers, membership spreads, and recurrent weights by minimizing an instantaneous residual-noise objective subject to bounded-learning-rate constraints. Simulation is conducted for cubic nonlinear noise, and real-time DSP6713 verification is conducted in a microphone--loudspeaker headphone-oriented ANC setting. The evaluation framework uses testing-set MSE, input/output SNR, SNR improvement, residual-noise reduction in dB, and ablation settings for T2FNN-only, CMAC-only, and complete SRN--T2FCMAC controllers. The simulation and DSP6713 verification results indicate that the proposed hybrid controller achieves effective nonlinear noise suppression and shows strong potential for real-time headphone-oriented ANC applications.
Fuzzy Math
S. P. Sathiyapriya
Volume 23, Issue 6 , November and December 2026, Pages 113-137
Abstract
This article focuses on developing a robust resilient filtering approach for discrete-time switched fuzzy systems subject to random gain fluctuations and sensor malfunctions. In this framework, sensor outputs are modeled as stochastic processes that operate under varying failure probabilities. The addressed ...
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This article focuses on developing a robust resilient filtering approach for discrete-time switched fuzzy systems subject to random gain fluctuations and sensor malfunctions. In this framework, sensor outputs are modeled as stochastic processes that operate under varying failure probabilities. The addressed system dynamics also incorporate gain variations characterized by Bernoulli-distributed white noise sequences. With the aid of an appropriately formulated Lyapunov functional and finite-time stability theory, new sufficient conditions are derived in the form of linear matrix inequalities, ensuring that the enhanced fuzzy system achieves stochastic finite-time boundedness along with the desired passivity extension. Moreover, the proposed framework provides a systematic way to handle uncertainties and disturbances in practical control environments. To demonstrate the practical effectiveness of the proposed filter design, three numerical examples are presented, including cases drawn from robotic arm dynamics and nonlinear electronic circuits.
Fuzzy modelling
M. Sweetline Sonia; S. Sumathi
Volume 23, Issue 6 , November and December 2026, Pages 139-156
Abstract
Early detection of cerebral palsy (CP) is challenging due to subtle and heterogeneous neuromotor abnormalities in infants. This paper proposes FLinkNet-GAN, a hybrid deep learning and fuzzy logic framework for membership-based CP risk assessment from RGB-D infant videos. Initially, a Bright ...
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Early detection of cerebral palsy (CP) is challenging due to subtle and heterogeneous neuromotor abnormalities in infants. This paper proposes FLinkNet-GAN, a hybrid deep learning and fuzzy logic framework for membership-based CP risk assessment from RGB-D infant videos. Initially, a Bright Contrast Dynamic Histogram Equalization (BCDHE) filter enhances motion visibility. A Generative Adversarial Network (GAN) performs multi-pose estimation to extract kinematic features, including Movement Deviation (MD) and Joint Trajectory Discontinuity (JD). These features are processed through a LinkNet backbone to preserve fine spatial details and subsequently mapped into a Mamdani-type Fuzzy Inference System using Gaussian membership functions. Unlike conventional hard classifiers, the proposed approach generates a continuous Risk Score (RS) via centroid defuzzification, providing interpretable risk levels: Normal, Borderline, High, and Very High. Experimental evaluation on the RVI-38 dataset achieves 94.85% accuracy and 94.5% pose precision, demonstrating robust and uncertainty-aware CP risk stratification.
Computer Science
T. Rama M; A. V. Turukmane
Volume 23, Issue 6 , November and December 2026, Pages 157-188
Abstract
Detecting underwater objects is crucial for scientific inquiry, resource development, and marine conservation. Current underwater object detection methods face two main challenges: (1) high parameter counts leading to excessive memory usage, and (2) reduced detection accuracy. To address ...
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Detecting underwater objects is crucial for scientific inquiry, resource development, and marine conservation. Current underwater object detection methods face two main challenges: (1) high parameter counts leading to excessive memory usage, and (2) reduced detection accuracy. To address these limitations, this study introduces a computationally efficient underwater object recognition framework that integrates advanced feature extraction with fuzzy-driven adaptive classification. A novel dual-stream extractor combining Improved YOLOv9 for refined spatial localization and a Modified TResNet for enhanced semantic feature extraction is developed to capture complementary deep features. These streams are fused using Rényi entropy, ensuring that only the most informative and non-redundant representations are preserved. The fused features are then classified using a Neuro-Fuzzy Random Vector Functional Link (NF-RVFL) network, enabling fast, robust, and interpretable decision-making with minimal parameter overhead. Grad-CAM++ is incorporated to highlight critical attention regions, further improving framework transparency. Extensive experiments conducted on four public underwater datasets URPC, DLMU 2024, DUO, and RUOD show that the proposed framework consistently surpasses state-of-the-art detectors, achieving notable improvements in mAP across all benchmarks. Comprehensive ablation analysis and statistical evaluations confirm the contribution of each proposed component. Furthermore, deployment evaluation demonstrates that the proposed framework’s reduced parameter count and high efficiency make it well suited for real-time underwater platforms with limited computational resources.
Optimization
M. Ataie; M. Edrisi
Volume 23, Issue 6 , November and December 2026, Pages 189-207
Abstract
In this study, an algorithm is proposed for the design of a multivariable fuzzy PID controller using convex optimization and linear matrix inequality (LMI) constraints. The considered fuzzy system is of the Takagi–Sugeno type and consists of subsystems based on PID controllers. The ...
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In this study, an algorithm is proposed for the design of a multivariable fuzzy PID controller using convex optimization and linear matrix inequality (LMI) constraints. The considered fuzzy system is of the Takagi–Sugeno type and consists of subsystems based on PID controllers. The parameters of these subsystems are optimized to achieve desirable performance. The positive real lemma is employed to guarantee the stability of the overall fuzzy system. One of the most significant applications of this approach lies in the control of industrial robots. Since robotic systems are typically multivariable in nature, the utilization of advanced controllers such as multivariable fuzzy PID controllers can play a crucial role in enhancing their performance. In this work, the proposed control scheme will be implemented both on a simulation example and practical robot manipulator.
Fuzzy Math
W. H. Gu; F. X. Zhang; Y. Song
Volume 23, Issue 6 , November and December 2026, Pages 209-221
Abstract
The aim of this paper is to study new semi-t-operators on bounded lattices. We propose four new methods for constructing semi-t-operators on bounded lattices by using semi-t-norms, semi-t-conorms and order-preserving mappings. Comparative analysis reveals that the construction methods proposed ...
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The aim of this paper is to study new semi-t-operators on bounded lattices. We propose four new methods for constructing semi-t-operators on bounded lattices by using semi-t-norms, semi-t-conorms and order-preserving mappings. Comparative analysis reveals that the construction methods proposed in this paper can be regarded as generalizations of various approaches in existing literature. Besides, we provide equivalent characterizations of the corresponding forms of these four semi-t-operators.
Approximate Reasoning
A. Šeliga
Volume 23, Issue 6 , November and December 2026, Pages 223-238
Abstract
The class of associative copulas is uniformly compact but not convex, and every associative copula is Schur-concave and commutative. Two open problems posed by Durante at FSTA 2010 concern its closed convex hull and the extreme points of that hull. We give a negative answer to the first problem ...
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The class of associative copulas is uniformly compact but not convex, and every associative copula is Schur-concave and commutative. Two open problems posed by Durante at FSTA 2010 concern its closed convex hull and the extreme points of that hull. We give a negative answer to the first problem by constructing an explicit family of Schur-concave commutative copulas outside the hull. Each member is a symmetric shuffle of the upper Fr\'{e}chet-Hoeffding bound. We compute its exact uniform distance from the hull using a star-shapedness property of antidiagonal sections of associative copulas. For the second problem, we show that every extreme point of the hull is associative and reformulate the remaining inclusion question using associative copulas that are extreme among all copulas. We prove that ordinal sums of the lower Fr\'{e}chet-Hoeffding bound form a proper subclass of these copulas and generate a strictly smaller closed convex hull. Nevertheless, the independence copula admits an integral representation over such ordinal sums and is not extreme in the hull of associative copulas.
