Decision Making
Parisa Khalilpoor; Abbas Parchami; Reza Pourmousa
Volume 23, Issue 3 , May and June 2026, Pages 1-13
Abstract
Fuzzy data analysis presents significant computational challenges due to its inherent ambiguity and uncertainty. Traditional statistical methods do not have the capability to effectively capture and model the uncertainty in fuzzy observations. A novel approach is proposed in this paper to model unknown ...
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Fuzzy data analysis presents significant computational challenges due to its inherent ambiguity and uncertainty. Traditional statistical methods do not have the capability to effectively capture and model the uncertainty in fuzzy observations. A novel approach is proposed in this paper to model unknown bivariate densities using fuzzy observations and incorporating the dependency between variables. By employing this copula-based approach, we have effectivelymanaged the computational complexity associated with the analysis of fuzzy data. The proposed approach has been applied to model groundwater aquifers distribution.
M. Bedrood; R. A. Borzooei; G. Lenzi; A. Borumand Saeid
Volume 23, Issue 3 , May and June 2026, Pages 15-29
Abstract
This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsetsof prime ideals within an MV -algebra. We investigate a particular class of Zariski-closed sets and demonstrate thatthey form a lattice under set inclusion. A distinguished filter within ...
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This paper presents a localized approach to the Zariski topology by restricting the spectral space to specific subsetsof prime ideals within an MV -algebra. We investigate a particular class of Zariski-closed sets and demonstrate thatthey form a lattice under set inclusion. A distinguished filter within this lattice is then examined, and its algebraicproperties are analyzed in detail. Building on this framework, we introduce the concept of vX-ideals, a new type of idealdefined in terms of these closed sets. We explore their algebraic behavior, including interactions with minimal primeideals and their stability under homomorphisms. The study reveals new structural insights into Zariski-closed sets andtheir connections to broader ideal-theoretic constructs. The final diagram synthesizes these findings, offering a unifiedperspective and laying the foundation for further exploration of topological and algebraic properties in MV -algebras.
Engineering
Mohammad Reza Kamali Ardakani; Sajjad Rezvani Khaledi; Mahdi Pourgholi
Volume 23, Issue 3 , May and June 2026, Pages 31-50
Abstract
This study introduces a novel Two-Layer Type-II Adaptive Fuzzy Logic Controller (2LT2-FLC) to enhance seismic resilience in structural engineering. The innovative dual-layer approach integrates an inner adaptive fuzzy layer, which dynamically adjusts input scaling gains in real-time based on the instantaneous ...
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This study introduces a novel Two-Layer Type-II Adaptive Fuzzy Logic Controller (2LT2-FLC) to enhance seismic resilience in structural engineering. The innovative dual-layer approach integrates an inner adaptive fuzzy layer, which dynamically adjusts input scaling gains in real-time based on the instantaneous range of structural response, with a core fuzzy layer that employs interpretable IF-THEN rules to compute control forces. This design overcomes the limitations of controllers with static parameters by providing continuous self-adaptation to varying seismic excitation levels. The controller's performance was evaluated on a nonlinear four-story steel frame benchmark model, with parameters validated against established structural dynamics literature, under historical earthquake records (Kobe and Northridge). The proposed 2LT2-FLC significantly reduced peak inter-story drift—by 50.18% on the second floor and 47.69% on the fourth floor during the Kobe earthquake—outperforming both Type-II Fuzzy-PID and ANFIS-PID controllers. The controller operates with an average computation time of approximately 0.2 milliseconds per time step, confirming its suitability for real-time applications. By simplifying real-time adaptation for nonlinear systems, the 2LT2-FLC ensures robust, interpretable, and computationally efficient control, presenting a significant advancement for practical seismic mitigation.
Optimization
Jin-Hyok Choe; Gwang Choe; Son-Il Kwak; Hyok-Gi Chae; Hyon-U Kong
Volume 23, Issue 3 , May and June 2026, Pages 51-68
Abstract
This paper proposes a hybrid approach that integrates an Improved Shark Smell Optimization (ISSO) algorithm with a Fuzzy Ant Colony System (FACS) to enhance the parameter tuning of a fuzzy hierarchical controller for the inverted pendulum and cart system. The standard Shark Smell Optimization (SSO) algorithm ...
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This paper proposes a hybrid approach that integrates an Improved Shark Smell Optimization (ISSO) algorithm with a Fuzzy Ant Colony System (FACS) to enhance the parameter tuning of a fuzzy hierarchical controller for the inverted pendulum and cart system. The standard Shark Smell Optimization (SSO) algorithm suffers from premature convergence and limited exploration capability. The proposed ISSO addresses these limitations by introducing dynamic adaptive coefficients for the gradient and inertia phases, along with a linearly decreasing velocity limit factor. This enhanced global search is then synergistically combined with FACS, which performs fuzzy-guided local exploitation in promising regions of the parameter space. The ISSO-FACS hybrid is applied to determine the optimal sliding surface parameters and scaling factors of a Fuzzy Hierarchical Swing-up and Sliding Controller (FHSSC). Simulation results demonstrate that the proposed approach significantly outperforms the previous FACS method, reducing the total stabilization error by 11.59%, the pendulum angle error by 15.23%, and the cart position error by 26.72%, while achieving 1.27 times faster settling time. The proposed controller also exhibits superior robustness under perturbed initial conditions where the previous method fails, and demonstrates enhanced disturbance rejection capabilities. Convergence analysis confirms the stability properties of the hybrid approach, and computational complexity analysis validates its suitability for offline controller design.
T. Pramanik; S. Samanta; T. Allahviranloo; A. Kalampakas
Volume 23, Issue 3 , May and June 2026, Pages 69-84
Abstract
The existing strength of connectedness in fuzzy graph theory is a max–min quantity. According to this definition, thestrength of a path is the membership of its weakest edge, and the connectedness between two vertices is the maximumsuch bottleneck over all paths. That definition is exact for systems ...
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The existing strength of connectedness in fuzzy graph theory is a max–min quantity. According to this definition, thestrength of a path is the membership of its weakest edge, and the connectedness between two vertices is the maximumsuch bottleneck over all paths. That definition is exact for systems in which the weakest edge is the only controllingfactor, but it is too rigid when cumulative route quality matters as well. In this paper we adopt a new notion in whichthe strength of a simple path is a convex combination of its bottleneck and its average edge membership. The newframework defined in this paper for the strength of connectedness is successfully applicable to systems where the classical bottleneck constraint is significant, as well as to systems where the cumulative effects of all edge constraints are more significant than just the bottleneck constraint. Capacity or bandwidth constraints in a network rely only on the weakest (bottleneck) edge, whereas speed, latency, or smoothness constraints have cumulative effects on the entire path from the source to the destination hub in a network. We develop the corresponding theory for fuzzy bunch graphs and fuzzy bunch hypergraphs, that is, grouped fuzzy structures in which vertices are partitioned into bunches and higher-order relations may occur across bunches.
Approximate Reasoning
Adam Šeliga
Volume 23, Issue 3 , May and June 2026, Pages 85-94
Abstract
Motivated by the study of common measurability in the unsharp observables approach to quantum mechanics, Jen\v{c}a (2011) introduced the notion of a witness map on a partially ordered Abelian group with unit $u$. At the 10th International Conference on Fuzzy Set Theory and Applications (FSTA 2010), Jen\v{c}a ...
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Motivated by the study of common measurability in the unsharp observables approach to quantum mechanics, Jen\v{c}a (2011) introduced the notion of a witness map on a partially ordered Abelian group with unit $u$. At the 10th International Conference on Fuzzy Set Theory and Applications (FSTA 2010), Jen\v{c}a and Sarkoci (Open Problem 2.10) asked for a complete characterization of all commutative and associative binary operations on the standard real unit interval $[0,1]$ that generate such witness maps. In this paper, we completely resolve this special-case problem. By translating the discrete combinatorial inclusion-exclusion inequality of the witness map definition into the continuous evaluation of an $n$-dimensional volume, we prove that the witness map condition is algebraically identical to the $n$-increasing property. Consequently, an operation generates a witness map if and only if its $n$-ary extension is a valid $n$-dimensional copula for all $n\geq 2$. Applying Kimberling's Theorem (1974), we establish that a binary operation generates a witness map if and only if it is the minimum t-norm, a strict Archimedean t-norm with a completely monotonic inverse generator, or an ordinal sum of such operations. Several illustrative families, including the product, Clayton, and Gumbel-Hougaard copulas, are discussed in detail, and the explicit form of the corresponding set functions $\beta_O$ on $n$-element subsets is given.
Decision Making
Jiaxin Zhou; Zaiwu Gong; Xiaoxia Xu; Xinxin Luo; Guo Wei
Volume 23, Issue 3 , May and June 2026, Pages 95-117
Abstract
Extracting meaningful information from high-volatility data and uncovering multi-scale knowledge from stable-state data remain key challenges in complex multi-attribute decision-making (MADM) problems. To address these challenges, a novel methodology that integrates stochastic empirical mode decomposition ...
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Extracting meaningful information from high-volatility data and uncovering multi-scale knowledge from stable-state data remain key challenges in complex multi-attribute decision-making (MADM) problems. To address these challenges, a novel methodology that integrates stochastic empirical mode decomposition (EMD) with the Choquet integral is proposed. The resulting three-stage framework first decomposes the original data into trend terms, reflecting objective laws, and deviation terms, capturing subjective cognition. These components are then aggregated using Choquet integrals with Shapley values to explicitly model interactions among attributes. Finally, the framework is extended to accommodate four decision scenarios involving known or unknown attribute sets and complete or incomplete attribute values, with regularization introduced to mitigate potential bias. Case studies in investment decision-making demonstrate the effectiveness of the proposed method in integrating objective trends with subjective deviations, highlighting its advantages in multi-attribute information fusion and adaptability to complex decision environments.
Sustainable operations management
Arman Rezasoltani; Ali Mohaghar; Seyed Mohammad Ali Khatami Firouzabadi; Amir Mohammad Khani
Volume 23, Issue 3 , May and June 2026, Pages 119-139
Abstract
In the context of developing a robust multi-objective optimization framework for designing sustainable supply chain networks for perishable items under uncertainty, this paper provides an overview of a possibilistic framework. Using the three pillars of sustainability (i.e., economic, environmental, ...
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In the context of developing a robust multi-objective optimization framework for designing sustainable supply chain networks for perishable items under uncertainty, this paper provides an overview of a possibilistic framework. Using the three pillars of sustainability (i.e., economic, environmental, and social), the proposed framework seeks to minimize overall supply chain costs, minimize CO₂ emissions, and maximize regional employment opportunities. The proposed framework addresses the uncertainties associated with product demand (sales), shelf life, and shipping/transportation conditions. To accomplish this, the proposed framework employs fuzzy trapezoidal numbers (which can model how much variation a number might have) in combination with a robust possibilistic programming structure. The objective of the proposed framework is twofold: 1) to solve for and balance each of the objectives and 2) to use GAMS to implement the LP-Metric method. Validation of the model has been conducted through extensive utilization of numerical experiments to create a variety of examples (small, medium, and large-sized), which support the proposed approach's ability to produce stable (balanced) solutions, regardless of the size of the example. Additionally, results indicate that the cost of the system (i.e., total supply chain cost) increases with the size of the network, while the number of employment opportunities created is directly related to network size; the amount of environmental impact is not increased by network size. Finally, results from the model establish that the proposed robust possibilistic approach exhibits superior performance to traditional models based solely upon determinism by producing consistently higher levels of reliability and resiliency within supply chain configurations, thereby providing an invaluable source of potential inputs for the management of perishable goods.
F. Hosseini; M. Eftekhari
Volume 23, Issue 3 , May and June 2026, Pages 141-163
Abstract
Retrieval-Augmented Generation (RAG) systems play a crucial role in grounding Large Language Models (LLMs) withexternal knowledge. However, existing architectures such as Self-RAG employ static linear aggregation of internalcritique tokens, which requires manual tuning and inadequately models the non-linear ...
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Retrieval-Augmented Generation (RAG) systems play a crucial role in grounding Large Language Models (LLMs) withexternal knowledge. However, existing architectures such as Self-RAG employ static linear aggregation of internalcritique tokens, which requires manual tuning and inadequately models the non-linear interactions underlying retrievaland generation. Moreover, exclusive reliance on self-critique can introduce confirmation bias and hallucinations. Toovercome these limitations, this work introduces Allo-Self-RAG, a neuro-symbolic framework that integrates fuzzy logicwith RAG. From a dual-process-inspired perspective, Allo-Self-RAG is framed as a structured enhancement over theheuristic Self-RAG baseline: the standard Self-RAG pipeline is closer to System-1-like post-retrieval behavior, whereasAllo-Self-RAG introduces a more System-2-like evaluation layer through structured signal aggregation. A Fuzzy InferenceSystem (FIS) adaptively fuses internal self-critique tokens with external allo-critique signals from an independentreranker, replacing static linear aggregation with rule-guided score integration and a rule-based revision mechanismfor conflicting evidence. When this evaluation stage detects ambiguity or conflicting evidence among top-ranked candidates, the framework automatically invokes a synthesis step to reconcile contradictions and produce a more reliableconsensus answer. Simulated Annealing (SA) is employed to optimize fuzzy membership functions automatically usinga small calibration dataset, eliminating manual parameter tuning. Extensive experimental evaluation demonstratesthat Allo-Self-RAG consistently outperforms the Self-RAG baseline, achieving 56.61% accuracy on PopQA (+1.45%improvement), 66.98% on ARC-Challenge (+1.03% improvement), and 67.51% on PubHealth (+1.01% improvement),showing reliable gains across retrieval-augmented question answering benchmarks.
Engineering
Mansooreh Pakravan
Volume 23, Issue 3 , May and June 2026, Pages 165-191
Abstract
Sex differences in resting-state functional brain organization have been widely reported, yet many deep learning models prioritize predictive performance over interpretability, limiting their ability to reveal underlying neurobiological mechanisms. We propose FXP-Net, a fuzzy explainable prototype-based ...
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Sex differences in resting-state functional brain organization have been widely reported, yet many deep learning models prioritize predictive performance over interpretability, limiting their ability to reveal underlying neurobiological mechanisms. We propose FXP-Net, a fuzzy explainable prototype-based neural network that combines temporal convolutional modeling with fuzzy prototype learning to enable intrinsically interpretable sex classification from resting-state fMRI. FXP-Net maps windowed ROI time series into a compact latent space in which class-specific prototypes are learned and activated through graded fuzzy membership functions, allowing each prediction to be explained via similarity to a small set of interpretable prototypes rather than opaque feature activations. To enforce interpretability, we introduce a prototype-regularized training objective that encourages intra-class clustering, inter-class separation, prototype diversity, and sparse activation. Across multiple brain atlases and repeated runs, FXP-Net achieves subject-level classification performance competitive with, and in several settings statistically superior to, a strong ConvNet baseline, with peak balanced accuracy exceeding 95 %. Importantly, a multi-level interpretability analysis, combining prototype-level and decision-level attributions reveals anatomically consistent patterns across Brainnetome, Glasser, and Gordon parcellations. Quantitative overlap analysis highlights regions within the dorsolateral prefrontal cortex (DLPFC), including lateral area 9/10 and area 46, as demonstrating robust cross-atlas agreement and consistently high importance. These findings are stable across runs and align with prior evidence linking DLPFC organization to sex-related differences in executive control and higher-order cognition. The Python implementation of the proposed FXP‑Net architecture is publicly available at: https://github.com/Mansooreh-Pakravan/FXPNet-Model.
