Fuzzy Math
Mohammad Rasoul Mastani Shabestari; Nasser Mikaeilvand
Volume 22, Issue 3 , May and June 2025, Pages 1-19
Abstract
This work proposes a novel approach for modeling complex systems with uncertain data using fuzzy calculus and linear time-fractional differential equations. We provide the fuzzy beta generalized Hukuhara derivative, which maintains inherent uncertainties without transforming fuzzy issues into precise ...
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This work proposes a novel approach for modeling complex systems with uncertain data using fuzzy calculus and linear time-fractional differential equations. We provide the fuzzy beta generalized Hukuhara derivative, which maintains inherent uncertainties without transforming fuzzy issues into precise formulations, improving both accuracy and interpretability. We present a fuzzy beta Laplace transform iterative approach to solve fuzzy linear time-fractional equations in fluid dynamics effectively. Case studies, including the fuzzy time-fractional diffusion and advection-dispersion equations, demonstrate the effectiveness of our strategy in capturing system dynamics under uncertainty. This study enhances the amalgamation of fuzzy calculus and fractional modeling, offering a solid foundation for the analysis of uncertain complex systems.
Optimization
Amin Ghodousian; Mohammad Sedigh Chopannavaz
Volume 22, Issue 3 , May and June 2025, Pages 21-38
Abstract
As a starting point, this paper develops the system of bipolar fuzzy relational equations (FRE) to the most general case, where bipolar FREs are defined by an arbitrary continuous t-norm. Due to the fact that fuzzy relational equations are special cases of bipolar FREs, the proposed system can also be ...
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As a starting point, this paper develops the system of bipolar fuzzy relational equations (FRE) to the most general case, where bipolar FREs are defined by an arbitrary continuous t-norm. Due to the fact that fuzzy relational equations are special cases of bipolar FREs, the proposed system can also be viewed as a generalization of traditional FREs, in which the fuzzy composition can be defined by a continuous t-norm. In order to determine the feasibility of the proposed system, some necessary and sufficient conditions are presented for studying continuous bipolar FREs. This is followed by a complete analysis of the set of feasible solutions to the problem. Contrary to FREs and bipolar FREs defined by continuous Archimedean t-norms, the feasible solutions set of generalized bipolar FREs consists of a finite number of compact sets that are not necessarily connected. Further, five techniques have been outlined in an attempt to simplify the current problem, and then an algorithm has been presented to find the feasible region of the problem. Next, we present a class of optimization models subject to continuous bipolar FRE constraints, in which the objective function incorporates a wide range of (non)linear functions, such as maximum functions, geometric mean functions, log-sum-exp functions, maximum eigenvalues of symmetric matrices, support functions for sets, etc. Considering that the problem has a finite number of local optimal solutions, the global optimal solution can always be obtained by choosing the point with the minimum objective value among these local optimal solutions. Lastly, as a means to illustrate the definitions, theorems, and algorithms presented in the paper, a step-by-step example is presented in several sections, in which the constraints are a system of bipolar FREs defined by the Dubois-Prade t-norm, which is a continuous non-Archimedean t-norm.
Fuzzy Math
Martin Kalina; Biljana Mihailović; Mirjana Štrboja,
Volume 22, Issue 3 , May and June 2025, Pages 39-54
Abstract
A generalization of bipolar OWA operators, bipolar ordered weighted quasi-averages, based on the bipolar Choquet g-integrals, so called g-BIOWA operators are introduced and investigated. A generalization of induced OWA operators considering non-negative inputs and order-inducing variables, induced bipolar ...
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A generalization of bipolar OWA operators, bipolar ordered weighted quasi-averages, based on the bipolar Choquet g-integrals, so called g-BIOWA operators are introduced and investigated. A generalization of induced OWA operators considering non-negative inputs and order-inducing variables, induced bipolar ordered weighted averages are introduced considering real inputs and order-inducing vectors. Their main properties are considered and some illustrative examples are presented.
G. Kou; H. Din¸cer; S. Y¨uksel; C. Demir; S. Eti
Volume 22, Issue 3 , May and June 2025, Pages 55-86
Abstract
The performance of transparent solar panel projects is affected by both technological and environmental and economicfactors. However, the most important items should be identified for the efficient use of limited resources and effectiverisk management. There are few studies in the literature determining ...
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The performance of transparent solar panel projects is affected by both technological and environmental and economicfactors. However, the most important items should be identified for the efficient use of limited resources and effectiverisk management. There are few studies in the literature determining these factors. Because of this situation, businessescannot direct their resources correctly and cannot create an effective strategy. A molecular fuzzy decision-making systemis created to determine the most successful alternative investment policies for these projects to satisfy this gap in theliterature. Various techniques are integrated in this model to reach the most effective solutions, such as molecularfuzzy sets to handle uncertainties, q-learning algorithm to weight experts, least square optimization (LSO) to calculatecriteria weights and multi-objective particle swarm optimization (MOPSO) to rank investment strategies. The maincontribution of this study is proposing an innovative molecular fuzzy decision-making model that manages uncertaintiesmore effectively to select the most appropriate investment strategies for transparent solar panel investments. Consideringmolecular fuzzy sets allows for more accurate modelling of uncertainties and subjective evaluations. The results showthat the most critical investment criterion for transparent solar panel investments is the regional solar radiation level.
Fuzzy modelling
Mohsen Arefi
Volume 22, Issue 3 , May and June 2025, Pages 87-101
Abstract
In this paper, we present an approach to fit some clustering fuzzy linear regression models based on the fuzzy response variables and fuzzy parameters. In this approach, we first introduce a method for clustering crisp/fuzzy data based on fuzzy c-means clustering, and then, we fit some clustering fuzzy ...
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In this paper, we present an approach to fit some clustering fuzzy linear regression models based on the fuzzy response variables and fuzzy parameters. In this approach, we first introduce a method for clustering crisp/fuzzy data based on fuzzy c-means clustering, and then, we fit some clustering fuzzy regression models based on the geometric mean. The optimal clustering fuzzy regression models are evaluated under two indices of goodness of fit. The applications of the proposed approach are studied in modeling some real data sets.
M. Akram; S. Jamil
Volume 22, Issue 3 , May and June 2025, Pages 103-124
Abstract
Evaluating third-party reverse logistics providers (3PRLPs) is a complex task, often challenged by cognitive biases andincomplete, uncertain data in group decision-making contexts. To overcome these challenges, this study proposes anovel decision-support framework that integrates Fermatean fuzzy rough ...
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Evaluating third-party reverse logistics providers (3PRLPs) is a complex task, often challenged by cognitive biases andincomplete, uncertain data in group decision-making contexts. To overcome these challenges, this study proposes anovel decision-support framework that integrates Fermatean fuzzy rough numbers with an extended entropy weightmethod and a new ranking technique. Fermatean fuzzy rough numbers effectively capture uncertainty and subjectivitywithout relying on predefined parameters, addressing key limitations in provider evaluation. The extended entropyweight method objectively determines the importance of decision criteria across economic, environmental, social, andrisk dimensions. The framework enhances decision accuracy by integrating three ranking techniques into an aggregatedindex, minimizing information loss while accommodating expert preferences. A case study on sustainable 3PRLPevaluation in the Malaysian food industry demonstrates the model’s practicality, while sensitivity and comparativeanalyses validate its robustness and superiority over existing approaches.
M. Hadinejad; M. M. Zahedi; A. Borumand Saeid
Volume 22, Issue 3 , May and June 2025, Pages 125-138
Abstract
The present paper aims to study the notion of Stonean filters on equality algebras and discusses the connection betweenthese filters and other types of filters on equality algebras. We show that any implicative filter, positive implicative filterand Boolean filter is a Stonean filter on equality algebras ...
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The present paper aims to study the notion of Stonean filters on equality algebras and discusses the connection betweenthese filters and other types of filters on equality algebras. We show that any implicative filter, positive implicative filterand Boolean filter is a Stonean filter on equality algebras and by some counterexample, we show that the vice versa donot generally hold. In addition, it is checked that the relations of Stonean filter with implicative filter, fantastic filter,Boolean filter, prime filter, maximal filter, ultra filter and positive implicative filter on equality algebras, while theimplicative, positive implicative, Boolean and Stonean filters are equivalent together under the condition involutive onan equality algebra. The concept of primary filter is introduced, and its relationship with the prime filter is investigated.Finally, Stonean radical filter (Rads(F)) is introduced according to the concept of Stonean filter on equality algebras,and we prove that under a suitable condition if F is a prime filter, then Rads(F) = F. Also, in this article, we provideseveral examples to make the definitions clearer.
Optimization
Ayyub sheikhi; RAdko Mesiar
Volume 22, Issue 3 , May and June 2025, Pages 139-149
Abstract
In the realm of classification studies, existing literature indicates that, when the relationships among exploratory variables extend beyond linear functions, nonlinear classifiers tend to outperform their linear counterparts. This study employs concordance measures to attain optimal outcomes in a classification ...
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In the realm of classification studies, existing literature indicates that, when the relationships among exploratory variables extend beyond linear functions, nonlinear classifiers tend to outperform their linear counterparts. This study employs concordance measures to attain optimal outcomes in a classification task.In this regard, we examine the connection copula among the exploratory variables, as well as the copula linking the exploratory attributes to the target attribute are taken into consideration. As a major novelty, our classification approach utilizes a convex combination of the pairwise Spearman’s rank correlation coefficient $\rho$ and the pairwise Kendall’s association $\tau$. Through a simulation analysis, we assess the performance of our algorithm, which demonstrates its superiority over alternatives, including copula-based classification methods as well as machine learning classification models. We also, provide an application of our method to the classification of COVID-19 dataset for more illustration.
A. Ghodousian; M. Mollakazemiha; M. Mashinchi; R. Mesiar
Volume 22, Issue 3 , May and June 2025, Pages 151-179
Abstract
We investigate the linear objective function optimization problem constrained by a new system of fuzzy relationequations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region ischaracterized as a finite union of closed convex cells. We provide necessary and ...
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We investigate the linear objective function optimization problem constrained by a new system of fuzzy relationequations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region ischaracterized as a finite union of closed convex cells. We provide necessary and sufficient conditions to determinethe problem’s feasibility. To streamline optimization, seven novel rules are proposed, on which an algorithm is basedto achieve a global optimum. Notably, a specific instance of our problem is shown to be equivalent to the well-knownminimal vertex cover problem. The efficacy of our algorithm is demonstrated through a concrete example.
Decision Making
Mojtaba Elahi; Ramin Enayati; Mehdi Keramatpour
Volume 22, Issue 3 , May and June 2025, Pages 181-217
Abstract
Multi-attribute decision-making (MADM) methods are essential tools for solving complex decision problems by offering systematic approaches for evaluating and ranking multiple criteria and alternatives. Despite considerable progress in MADM techniques, challenges persist in ensuring the reliability and ...
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Multi-attribute decision-making (MADM) methods are essential tools for solving complex decision problems by offering systematic approaches for evaluating and ranking multiple criteria and alternatives. Despite considerable progress in MADM techniques, challenges persist in ensuring the reliability and consistency of outcomes, particularly under fuzzy environments. A recent advancement the hybrid best-worst method with fuzzy preference programming approach (the BWM-FPP model) has demonstrated promise, notably in hospital performance evaluations. However, the weight vector derived from the BWM-FPP model is a locally weakly efficient, and but not necessarily a locally efficient weight vector, which limits its robustness in practical applications. To address this shortcoming, we propose an enhanced two-phase model that guarantees the derivation of a locally efficient weight vector. In Phase 1, the model maximizes the minimum membership degree, ensuring a strong baseline of reliability, while Phase 2 improves overall robustness by maximizing the mean membership degree. The proposed model's effectiveness is demonstrated through theoretical validation, four numerical examples, and a real-world case study in the automotive after-sales service sector. Results show significant improvements in membership degrees and reliability, validating the model’s practical applicability. In the case study, key service quality criteria such as Reliability, Tangibles, and Assurance emerged as most influential, underscoring their critical role in after-sales service evaluation.
