J. Abbas; R. Mesiar; R. Halas
Volume 22, Issue 4 , July and August 2025, Pages 1-15
Abstract
The bipolar decomposition integral, recently introduced in [5], is a general framework for handling integrals related to aggregation on unipolar and bipolar scales. The M¨obius representation is related to the notion of k-additivity of a monotone set function and allows to derive simple ...
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The bipolar decomposition integral, recently introduced in [5], is a general framework for handling integrals related to aggregation on unipolar and bipolar scales. The M¨obius representation is related to the notion of k-additivity of a monotone set function and allows to derive simple expressions of some nonlinear integrals. In this paper, we propose M¨obius representation for the bipolar decomposition integral, which includes the M¨obius representation of each of the bipolar Choquet integral, bipolar Shilkret integral, and bipolar Pan integral. Then, we introduce the expressions for computing bipolar decomposition integrals concerning a 2-additive bi-capacity. Lastly, a practical numerical example is provided to illustrate the applicability of the proposed results in dealing with aggregation on bipolar scales, and simplicity of calculating the 2-additive bipolar decomposition integrals.
Fuzzy Math
Chun Yong Wang; Wen Yu Duan; Bo Zhang
Volume 22, Issue 4 , July and August 2025, Pages 17-35
Abstract
Although the scholars studied the distributivity for S-uninorms, at least, the underlyinguninorm of one S-uninorm in the distributivity equations was assumed to be in Umin exceptthe distributivity for S-uninorms over t-(co)norms. In this paper, we further characterize thedistributivity for S-uninorms, ...
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Although the scholars studied the distributivity for S-uninorms, at least, the underlyinguninorm of one S-uninorm in the distributivity equations was assumed to be in Umin exceptthe distributivity for S-uninorms over t-(co)norms. In this paper, we further characterize thedistributivity for S-uninorms, where the conjunctive underlying uninorms of the S-uninormsin the distributivity equations are not fixed in Umin but arbitrary. Firstly, we discuss thedistributivity between S-uninorms. Secondly, we analyze the distributivity for S-uninormsover T-uninorms. Moreover, we obtain the distributivity for T-uninorms over S-uninorms byduality. Thirdly, we investigate the distributivity for S-uninorms over disjunctive uninorms.Because S-uninorms in those distributivity equations are arbitrary, our results are extensionsof the previous results on the distributivity for S-uninorms.
E. B. Akdemir; I. Kaya
Volume 22, Issue 4 , July and August 2025, Pages 37-55
Abstract
The rapid growth of global air traffic increases the complexity of airspace management, especially around risk management. To address related safety challenges, this study presents an integrated risk analysis model consists of Functional Hazard Analysis (FHA), Decomposed Fuzzy Sets (DFS), Z-numbers, ...
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The rapid growth of global air traffic increases the complexity of airspace management, especially around risk management. To address related safety challenges, this study presents an integrated risk analysis model consists of Functional Hazard Analysis (FHA), Decomposed Fuzzy Sets (DFS), Z-numbers, and Fuzzy Inference System (FIS). The model systematically accounts for uncertainty in risk parameters and integrates confidences for experts’ judgments. DFS assesses the consistency of experts’ evaluations, while Z-numbers represent their reliability. Severity, probability, and detectability are evaluated within this fuzzy framework, and risks are classified by using IFS-based approach aligned with the ICAO risk matrix. The model is applied on 11 critical hazard scenarios from the Advanced Surface Movement Guidance and Control System (A-SMGCS) based on high traffic and low visibility. Results obtained confirm the model’s ability to identify hazards and prioritize risks, offering a transparent, adaptable, and uncertainty-aware decision-support tool for aviation safety management.
Fuzzy modelling
Jignesh Vaniya; Maleyka Alizada; Pooja Nagpal; Biplab Kumar Dey; Dr. Gulara Alesger Abbbasova
Volume 22, Issue 4 , July and August 2025, Pages 57-75
Abstract
The emotional state of an online learner has drawn a lot of attention. Accurately predicting a student's emotional state can improve learning outcomes through designated mediation. Still, keeping an eye on and sustaining students attention in online classes is challenging because there isn't any immediate ...
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The emotional state of an online learner has drawn a lot of attention. Accurately predicting a student's emotional state can improve learning outcomes through designated mediation. Still, keeping an eye on and sustaining students attention in online classes is challenging because there isn't any immediate supervision. To identify these challenges based on the learner's emotional states, this paper presents a novel, efficient, Optimized Fuzzy approach and signifies solutions to inspire the learner. The Improved Multi-Task Cascaded Convolutional Networks (IMTCNN) are used to identify the face region in real time. Different emotions are classified by analyzing extracted facial expressions using an Optimized Takagi-Sugeno and Mamdani fuzzy systems (Fuzzy TSM) approach. With the Enhanced Mother Optimization Algorithm (EMO), the hyperparameters in the classification approach are optimized. The proposed method determines whether learners are attentive or inattentive during online learning sessions by computing an Attention-based bi-directional long-short term memory (ABiLSTM) to predict cognitive states. To improve learning efficiency and productivity, users receive real-time feedback. The proposed approach can give instructors ongoing feedback, allowing them to modify the way they teach and keep students interested and engaged. With recognition rates of over 98.21% accuracy on the proposed datasets, the study's results are encouraging and outperforming those of other approaches.
Optimization
Hamideh Nasabzadeh
Volume 22, Issue 4 , July and August 2025, Pages 77-96
Abstract
Multi-objective optimization is central to addressing complex real-world problems involving competing objectives. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) remains a widely used approach in this domain; however, it can face challenges in convergence, solution diversity, and robustness—particularly ...
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Multi-objective optimization is central to addressing complex real-world problems involving competing objectives. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) remains a widely used approach in this domain; however, it can face challenges in convergence, solution diversity, and robustness—particularly for multi-modal or discrete problems. This paper introduces a variant of NSGA-II that incorporates a fuzzy-based non-dominated sorting scheme using a $\Gamma$ function over trapezoidal fuzzy numbers, designed to provide more flexible and nuanced dominance assessments.The proposed method employs two tunable parameters to adjust fuzziness levels, allowing adaptive control over the trade-off between exploration and exploitation. Comprehensive experiments on the ZDT benchmark suite (ZDT1–ZDT6), conducted under realistic time constraints, are used to evaluate the approach. Results indicate that the fuzzy-enhanced NSGA-II frequently offers Pareto front approximations that are at least comparable to, and in many cases modestly improved over, those produced by the standard NSGA-II—particularly on test problems with discrete or multi-modal Pareto fronts.Both visual and statistical analyses across multiple runs support observations of efficient convergence and front coverage, while a sensitivity study highlights practical considerations for parameter selection. Overall, the fuzzy-based sorting strategy expands the methodological toolkit for multi-objective evolutionary optimization, offering a flexible and general framework suitable for diverse and challenging problem settings.
Engineering
M. Syed Ali; B Vigneshwar; Sumaya Sanober; Tarek F. Ibrahim; Faizah D Alanazi; Fathea M. Osman Birkea
Volume 22, Issue 4 , July and August 2025, Pages 97-115
Abstract
In this paper, we propose an $H_{\infty}$ state feedback control method for variable-speed wind turbine systems (WTSs) based on an event-triggered scheme (ETS). First, proposed the event-triggered mechanism, its threshold parameter is constructed as a special diagonal matrix which can improve system ...
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In this paper, we propose an $H_{\infty}$ state feedback control method for variable-speed wind turbine systems (WTSs) based on an event-triggered scheme (ETS). First, proposed the event-triggered mechanism, its threshold parameter is constructed as a special diagonal matrix which can improve system performance by flexibly adjusting the matrix elements. The main advantage of utilizing the event-triggered control is because it will activate the controllers with a user-designed event-triggering condition that helps to restrict the unnecessary network transmissions and reduce the leakages. Then, the concept of coupling leakage time-varying delay is proposed to construct a more generalized T-S fuzzy model. Subsequently, two novel integral inequalities are introduced. By the virtue of fuzzy Lyapunov function, intensive attention is focused on deriving the theoretical-based sufficient conditions in terms of solvable linear matrix inequalities (LMIs), which ensure the asymptotically stability of the closed-loop model based on Lyapunov stability theory. Then, the desirable control gains are obtained by solving the LMIs with bounds of sampling intervals. Detailed numerical simulations are performed with an experimental range of system parameters that illustrates the effectiveness of the proposed event-triggered scheme.
Industrial Engineering
Hossein Gitinavard; Ehsan Solgi; Seyed Meysam Mousavi; Ahmad Makui
Volume 22, Issue 4 , July and August 2025, Pages 117-136
Abstract
In today’s competitive markets, determining the optimum distribution centers, delivery routes, and inventory levels is crucial for cold chain logistics of perishable products to reduce costs as well as backorder rate. Meanwhile, a new bi-phase mixed integer non-linear programming model-based robust ...
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In today’s competitive markets, determining the optimum distribution centers, delivery routes, and inventory levels is crucial for cold chain logistics of perishable products to reduce costs as well as backorder rate. Meanwhile, a new bi-phase mixed integer non-linear programming model-based robust possibilistic approach is developed by goals of minimizing total costs and reducing the backorder rate for key customers to solve the hub location-routing model for a cold chain of perishable products. To address the issue, the augmented ε-constraint method is considered to construct a single objective model, and the obtained Pareto optimal points are analyzed. Additionally, the robust possibilistic approach is executed to cope with imprecise demand in the presented bi-phase hub location-routing model. To represent the verification and applicability of the proposed approach, a case study on cold chain logistics of perishable products is regarded. Finally, a comparative analysis is considered to compare the obtained results from the proposed approach with real case information. This validation process is defined by schematically reporting the trend comparison results over the entire planning horizon. Moreover, the obtained results represents that the proposed approach can enhance the objective function by reducing the 22% of total costs, improved the backorder level by 24%, the number of deteriorating items decreased by 16.48%, and the inventory levels enhanced by 12.86% regarding the current practice.
Optimization
Amin Ghodousian; Mohammad Sedigh Chopannavaz; Witold Pedrycz
Volume 22, Issue 4 , July and August 2025, Pages 137-160
Abstract
Bipolar fuzzy relational equations are an interesting generalization of fuzzy relational equations that occur prominently in information processing, possibility theory, and preference modeling. This paper considers the linear objective function optimization with respect to a more general class of bipolar ...
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Bipolar fuzzy relational equations are an interesting generalization of fuzzy relational equations that occur prominently in information processing, possibility theory, and preference modeling. This paper considers the linear objective function optimization with respect to a more general class of bipolar fuzzy relational equations, where the fuzzy compositions are defined by an arbitrary continuous Archimedean t-norm. In addition, a faster method for finding a global optimum is proposed that, unlike the previous work, does not require obtaining all local optimal solutions and classifying the constraints (and therefore, it does not require applying different approaches to check the feasibility of constraints in different groups and the optimality of solutions in their feasible regions). Analytical concepts and properties of the Archimedean bipolar fuzzy equations are investigated and two necessary conditions are presented to conceptualize the feasibility of the problem. It is shown that the feasible solution set can be resulted by a union of the finite number of compact sets, where each compact set is obtained by a function (called admissible function in this paper). Moreover, to accelerate identification of the mentioned compact sets (and therefore, to speed up solution finding), four simplification techniques are presented, which are based on either omitting redundant constraints and/or eliminating unknowns by assigning them a fixed value. Also, three additional simplification techniques are given to reduce the search domain by removing some parts of the feasible region that do not contain optimal solutions. Subsequently, a method is proposed to find an optimal solution for the current linear optimization problems. The proposed method consists of two accelerative strategies that are used during the problem solving process. By the first strategy, the method neglects some candidate solutions that are not optimal, by considering only a subset of admissible functions (called modified functions in this paper). As for the second strategy, a branch-and-bound method is used to delete non-optimal branches. Then, the method is summarized in an algorithm that represents all essential steps of the solution and finally, the whole method is applied in an example that has been chosen in such a way that the various situations are illustrated.
M. B. Dowlatshahi; S. Beiranvand
Volume 22, Issue 4 , July and August 2025, Pages 161-174
Abstract
Deep reinforcement learning algorithms, such as Deep Q-Networks (DQN), require careful tuning of replay memory parameters. In standard DQN implementations, these parameters remain fixed, which conflicts with the dynamic nature of the learning process where environmental conditions and reward ...
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Deep reinforcement learning algorithms, such as Deep Q-Networks (DQN), require careful tuning of replay memory parameters. In standard DQN implementations, these parameters remain fixed, which conflicts with the dynamic nature of the learning process where environmental conditions and reward stability continuously change. This mismatch often results in unstable learning or slow convergence. In this paper, we present a fuzzy logic-based system for adaptively adjusting three key replay memory parameters: memory size, the ratio of recent samples, and priority weight. The proposed fuzzy system evaluates the agent’s state by monitoring reward variations and average training errors, and accordingly updates these parameters to maintain optimal values during training. To assess the effectiveness of the proposed approach, we compared it with conventional DQN and PER-DQN methods across three benchmark reinforcement learning environments: CartPole v1, LunarLander v2, and Taxi v3. Experimental and statistical analyses demonstrate that our method improves average rewards, reduces training time, and enhances learning stability.
Fuzzy Math
esmaeil rostami
Volume 22, Issue 4 , July and August 2025, Pages 175-194
Abstract
This paper advances residuated lattice theory by introducing pseudo-irreducible filters and establishing their fundamental connections to the Boolean lifting property (BLP). Also, key structural properties of these filters are established, and new characterizations of the BLP using pseudo-irreducible ...
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This paper advances residuated lattice theory by introducing pseudo-irreducible filters and establishing their fundamental connections to the Boolean lifting property (BLP). Also, key structural properties of these filters are established, and new characterizations of the BLP using pseudo-irreducible filters and the residuated lattice of fractions are derived. Further, we investigate the BLP of the radical of a filter by introducing weak MTL-algebras and the transitional property of radical decomposition (TPRD) as a unifying framework that generalizes Boolean algebras, MV-algebras, BL-algebras, MTL-algebras, and Stonean residuated lattices. By addressing an open question in the literature concerning the BLP of the radical of a residuated lattice, we provide algebraic and topological solutions grounded in the TPRD and the space of maximal filters. Complementary results deepening the understanding of BLP in residuated lattices are also established.
