Fuzzy modelling
Amin Ghodousian; hossein pirhadi
Volume 23, Issue 1 , January and February 2026, Pages 1-21
Abstract
Fuzzy relational inequalities with fuzzy constraints (FRI-FC) represent a generalized form of fuzzy relational inequalities (FRI), in which fuzzy inequality replaces ordinary inequality in the constraints. With fuzzy constraints, we can obtain optimal points (called super-optima) that provide better ...
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Fuzzy relational inequalities with fuzzy constraints (FRI-FC) represent a generalized form of fuzzy relational inequalities (FRI), in which fuzzy inequality replaces ordinary inequality in the constraints. With fuzzy constraints, we can obtain optimal points (called super-optima) that provide better solutions than those obtained by addressing similar problems with ordinary inequality constraints. In this paper, a linear objective function optimization problem with respect to a max-product FRI-FC problem is considered. Several optimization problems are equivalent to the primal problem, as it has been proven. The main problem is converted into a more simplified problem by means of some simplification operations based on the algebraic structure of the primary problem and its equivalent forms. As a result of a few mathematical manipulations, the main problem has been transformed into a linear optimization model. A super-optimum (which is better than the ordinary feasible optimal solution) is not only found by applying the proposed linearization method, but the best super-optimum is also identified for the main problem. A comparison is made between the current approach and our previous work, in addition to some well-known heuristic algorithms, by applying them to random test problems of different sizes and seeing how they compare to each other. Results demonstrate that the proposed method produces optimal solutions with admissible infeasibilities, while the linearization algorithm produces better solutions than other heuristic algorithms. In addition, the results demonstrate that heuristic algorithms could not escape from poor solutions in most cases.
Fuzzy modelling
Spoorthy G; Sanjeevi S G
Volume 23, Issue 1 , January and February 2026, Pages 23-36
Abstract
Recommendation systems are very useful in domains such as e-commerce, news portals and software requirement analysis. Collaborative filtering models have been used widely, these models often suffer from data-sparsity, interpretability and cold-start problems. To solve these issues, various machine-learning, ...
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Recommendation systems are very useful in domains such as e-commerce, news portals and software requirement analysis. Collaborative filtering models have been used widely, these models often suffer from data-sparsity, interpretability and cold-start problems. To solve these issues, various machine-learning, deep-learning and kernel based models have been employed. Among these, trust based collaborative filtering and cross-domain recommendations have successfully solved the issues to some extent. However, in the recent literature, cross-domain recommendations (CDRs) are made by taking common user ratings. In our paper, we introduce a novel approach that combines CDRs with trust-aware collaborative filtering which employs ‘a partial item overlap’ scenario. Our model operates in two phases: an offline phase calculates trust between source and target users, coarse rating prediction using Adaptive Neuro-Fuzzy Inference System (ANFIS), and clustering via Firefly Fuzzy C-Means (FAFCM); and an online phase, where cluster information and item similarities are used to generate personalized recommendations. Evaluated on the Douban and Movielens datasets using MAE and RMSE metrics, our approach demonstrates improved performance compared to existing methods, effectively mitigating common limitations in recommendation systems.
Fuzzy Math
Muhammad Kamran; Qingyu Zhang; Muhammad Nadeem; Tofigh Allahviranloo; Muhammad Tahir
Volume 23, Issue 1 , January and February 2026, Pages 37-73
Abstract
The article is a hybrid union of rough fermatean neutrosophic sets (RFNS) and machine learning (ML) to economise the cost of a supply chain in the context of complicated uncertainty. We develop a two-fold approach: the initial one is a numerical procedure of defuzzifying RFNS parameters into sharp figures ...
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The article is a hybrid union of rough fermatean neutrosophic sets (RFNS) and machine learning (ML) to economise the cost of a supply chain in the context of complicated uncertainty. We develop a two-fold approach: the initial one is a numerical procedure of defuzzifying RFNS parameters into sharp figures and addressing them through a conventional VAM and MODI algorithm; the second one is a machine learning model according to which the components of the RFNS are handled by a two-strand neural network. This plan transforms the unclear transportation problem into a hybrid form. To validate the framework, we compare its performance with classical performances and other fuzzy hybrid techniques. Our machine learning strategy's statistical analysis reveal that it is as optimized as traditional approaches, and it offers a platform for real-time decisions in dynamic environments.
Decision Making
Pedro Huidobro; Agustina Bouchet; Noelia Rico; Irene Díaz; Susana Montes
Volume 23, Issue 1 , January and February 2026, Pages 75-94
Abstract
Similarity measures are fundamental tools for comparing and evaluating data across various domains. Robust similarity measures extend classical similarities. However, when dealing with interval data, robust measures are often insufficient due to the intrinsic properties of intervals. In this study, we ...
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Similarity measures are fundamental tools for comparing and evaluating data across various domains. Robust similarity measures extend classical similarities. However, when dealing with interval data, robust measures are often insufficient due to the intrinsic properties of intervals. In this study, we introduce the concept of strong robust similarity measures, which incorporate three additional axioms specifically considered to manage uncertainty represented by intervals. Furthermore, we characterize these measures through a novel class of functions, referred to as preinclusions. We also provide a comprehensive analysis of the proposed measures, examining their behaviour with respect to different axioms. Finally, we illustrate the applicability of our approach through a real-world case study using meteorological data collected by AEMET (the Spanish National Weather Service) in 2021.
Fuzzy Math
Hamid Mottaghi Golshan; Reza Ezzati
Volume 23, Issue 1 , January and February 2026, Pages 95-109
Abstract
This paper introduces a novel iterative numerical method for solving nonlinear fuzzy Volterra integral equations using Newton–Cotes (NC) quadrature rules. The core idea is to apply auxiliary Newton–Cotes rules (ANCR) over subintervals of the domain, enabling more flexible and accurate approximations ...
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This paper introduces a novel iterative numerical method for solving nonlinear fuzzy Volterra integral equations using Newton–Cotes (NC) quadrature rules. The core idea is to apply auxiliary Newton–Cotes rules (ANCR) over subintervals of the domain, enabling more flexible and accurate approximations of fuzzy integrals. A detailed convergence analysis is presented to establish the method’s validity and efficiency. The scheme operates within a complete fuzzy metric space and ensures convergence under Lipschitz continuity conditions in the kernel using fixed-point theory. The results show that this method can provide a significant improvement in computational accuracy and generality compared to current methods and offers a suitable opportunity for future research in the field of nonlinear fuzzy integral equations. These results demonstrate that the ANCR scheme offers both provable convergence and practical advantage in accuracy and overall computational cost for a broad class of nonlinear fuzzy Volterra problems.
Fuzzy Math
Juan J. Font; Sergio Macario; Manuel Sanchis
Volume 23, Issue 1 , January and February 2026, Pages 111-123
Abstract
In this paper, we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a productof spaces of real-valued functions of two variables satisfying certaintype of left-continuity, right-continuity and monotonicity.
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In this paper, we provide a general setting to deal with level continuous fuzzy-valued functions. Namely, we embed such functions into a productof spaces of real-valued functions of two variables satisfying certaintype of left-continuity, right-continuity and monotonicity.
Engineering
Mojtaba Nouri Manzar; Mohammad Reza Kamali Ardakani; Mahdi Pourgholi
Volume 23, Issue 1 , January and February 2026, Pages 125-145
Abstract
High-speed lane-change maneuvers in autonomous vehicles require control strategies that remain safe and well-damped under strongly nonlinear tire–vehicle dynamics and uncertain interactions with surrounding traffic. This paper proposes a stability-aware fuzzy control framework built on a nonlinear ...
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High-speed lane-change maneuvers in autonomous vehicles require control strategies that remain safe and well-damped under strongly nonlinear tire–vehicle dynamics and uncertain interactions with surrounding traffic. This paper proposes a stability-aware fuzzy control framework built on a nonlinear single-track (bicycle) vehicle model augmented with an enhanced semi-empirical Pacejka tire formulation to capture the coupled longitudinal–lateral–yaw behavior under realistic tire-condition effects. Two coordinated Mamdani type-1 fuzzy controllers are designed: one generates the steering command for lateral–yaw regulation and trajectory tracking, and the other produces the longitudinal acceleration command for speed adaptation and headway preservation. All membership-function parameters and rule weights are jointly tuned via constrained simulation-based optimization using the Slime Mould Algorithm (SMA), while actuator bounds and an explicit hard collision-avoidance constraint are enforced throughout the maneuver horizon. A Lyapunov-inspired penalty is embedded in the objective to suppress oscillations and promote well-damped responses. Simulations of high-speed lane changes (up to 72 km/h) show rapid convergence of lateral and longitudinal errors (≈2-3 s over a ≈450 m path), smooth control actions, and collision-free behavior. Compared with an unoptimized fuzzy baseline, the tuned design reduces peak lateral deviation by ≈35% and yaw-rate oscillations by ≈40%. Monte-Carlo trials with parametric uncertainty, noise measurement, and actuator delays further confirm repeatable closed-loop performance and robust safety margins in mixed-traffic scenarios.
Fuzzy modelling
Gholamreza Hesamian
Volume 23, Issue 1 , January and February 2026, Pages 147-161
Abstract
Quality control charts with fuzzy data have been successfully used in many real-world applications in recent years. These methods have been extended to estimate the fuzzy population mean based on simple random sampling techniques. In this study, a different strategy is used to develop Shewhart control ...
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Quality control charts with fuzzy data have been successfully used in many real-world applications in recent years. These methods have been extended to estimate the fuzzy population mean based on simple random sampling techniques. In this study, a different strategy is used to develop Shewhart control charts with fuzzy means based on fuzzy data. For this purpose, the conventional rank set sampling is first extended to a well-established fuzzy random variable. Then, based on the concept of fuzzy mean and exact variance, the lower, mean, and upper fuzzy control charts are introduced.Additionally, an estimation procedure is presented that can be used to evaluate the proposed fuzzy control limits in cases where the fuzzy mean and exact variance of the population are unknown. An inclusion degree for monitoring process variability is also introduced and discussed. A real case study from photolithography is presented to demonstrate the efficiency of the proposed method for monitoring control charts with fuzzy data based on fuzzy rank set sampling.
Decision Making
José Carlos R. Alcantud; Muhammad Akram; Gustavo Santos-García; Weiping Ding
Volume 23, Issue 1 , January and February 2026, Pages 163-181
Abstract
The objective of this paper is to provide advanced multi-expert decision-making techniques using N-soft sets as a referential framework. For the first time, the primary analytical tool for achieving this goal is the Choquet integral. First, the application of this aggregation operator within the context ...
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The objective of this paper is to provide advanced multi-expert decision-making techniques using N-soft sets as a referential framework. For the first time, the primary analytical tool for achieving this goal is the Choquet integral. First, the application of this aggregation operator within the context of a set {0, 1, 2, . . . , N }, representing the available ratings, is investigated. A straightforward formulation of the Choquet integral tailored to this specific set, followed by a detailed presentation of its computational implementation, is presented. Then, practical implications of these constructions in the realm of N-soft set theory are shown. They encompass the computation of new scores for the assessment of alternatives in N-soft sets (both in individual and multi-agent cases), and aggregation of data that come in the form of N-soft sets. Ultimately, we demonstrate how these innovative tools enhance multi-expert decision-making methodologies within the framework of N-soft sets. Three different approaches are discussed. Examples and comparisons with existing methodologies are provided too.
Fuzzy Math
Mehran Chehlabi
Volume 23, Issue 1 , January and February 2026, Pages 183-200
Abstract
In this paper, the fuzzy Pielou logistic differential equation is studied from the perspective of the generalized Hukuhara differentiability concept. First, the uniqueness of positive or negative solutions is established. Then, the existence conditions of the solution, together with its structural representation, ...
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In this paper, the fuzzy Pielou logistic differential equation is studied from the perspective of the generalized Hukuhara differentiability concept. First, the uniqueness of positive or negative solutions is established. Then, the existence conditions of the solution, together with its structural representation, are obtained for two separate cases corresponding to the positivity or negativity of the fuzzy parameters of the problem. Detailed illustrative examples are also provided to clarify the results.
