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Search Results (631)

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Keywords = Type-1 fuzzy sets

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29 pages, 1017 KB  
Article
Intelligent Automobile Bionic Cockpit Selection Considering Personalization Requirements: Multiple-Criterion Model and Decision-Making Method
by Liangliang Shi, Shaolin Zhang, Tao Han, Niansong Liu, Guoquan Xie and Guangdong Tian
Biomimetics 2025, 10(10), 706; https://doi.org/10.3390/biomimetics10100706 - 17 Oct 2025
Viewed by 163
Abstract
The extensive integration of intelligent and bionic technologies in the automotive industry has significantly heightened interest in the advancement of smart vehicle cockpits. The growing demand for automobile cockpit functions makes the personalization of intelligent automobile bionic cockpits more challenging. In addition, the [...] Read more.
The extensive integration of intelligent and bionic technologies in the automotive industry has significantly heightened interest in the advancement of smart vehicle cockpits. The growing demand for automobile cockpit functions makes the personalization of intelligent automobile bionic cockpits more challenging. In addition, the evaluation and selection for cockpits considering multiple attributes remains incomplete, which hinders the development of intelligent automobile bionic cockpits. Thus, this paper constructed a multiple criterion model considering the personalization needs of drivers and passengers, which include comfort, security, and spiritual entertainment needs. A novel decision-making approach that merges the entropy measure and the Elimination and Choice Expressing Reality (ELECTRE) method is introduced to address the selection challenges of smart vehicle cockpits. This methodology incorporates the Spherical Fuzzy Set (SFS) to accurately gather and interpret the data within the decision matrix. This study employs a practical application by examining three types of intelligent automobile cockpits to validate the effectiveness of the proposed decision-making method. Through sensitivity analysis and comprehensive validation, the findings substantiate that the research offers a potent instrument for addressing the selection challenges associated with intelligent automobile cockpits, providing valuable insights for designers. Full article
(This article belongs to the Special Issue Computer-Aided Biomimetics: 3rd Edition)
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21 pages, 3492 KB  
Article
A Fuzzy Model for Predicting the Group and Phase Velocities of Circumferential Waves Based on Subtractive Clustering
by Youssef Nahraoui, El Houcein Aassif, Samir Elouaham and Boujemaa Nassiri
Signals 2025, 6(4), 56; https://doi.org/10.3390/signals6040056 - 16 Oct 2025
Viewed by 144
Abstract
Acoustic scattering is a highly effective tool for non-destructive control and structural analysis. In many real-world applications, understanding acoustic scattering is essential for accurately detecting and characterizing defects, assessing material properties, and evaluating structural integrity without causing damage. One of the most critical [...] Read more.
Acoustic scattering is a highly effective tool for non-destructive control and structural analysis. In many real-world applications, understanding acoustic scattering is essential for accurately detecting and characterizing defects, assessing material properties, and evaluating structural integrity without causing damage. One of the most critical aspects of characterizing targets—such as plates, cylinders, and tubes immersed in water—is the analysis of the phase and group velocities of antisymmetric circumferential waves (A1). Phase velocity helps identify and characterize wave modes, while group velocity allows for tracking energy, detecting, and locating anomalies. Together, they are essential for monitoring and diagnosing cylindrical shells. This research employs a Sugeno fuzzy inference system (SFIS) combined with a Fuzzy Subtractive Clustering (FSC) identification technique to predict the velocities of antisymmetric (A1) circumferential signals propagating around an infinitely long cylindrical shell of different b/a radius ratios, where a is the outer radius, and b is the inner radius. These circumferential waves are generated when the shell is excited perpendicularly to its axis by a plane wave. Phase and group velocities are determined by using resonance eigenmode theory, and these results are used as training and testing data for the fuzzy model. The proposed approach demonstrates high accuracy in modeling and predicting the behavior of these circumferential waves. The fuzzy model’s predictions show excellent agreement with the theoretical results, as confirmed by multiple error metrics, including the Mean Absolute Error (MAE), Standard Error (SE), and Mean Relative Error (MRE). Full article
(This article belongs to the Special Issue Recent Development of Signal Detection and Processing)
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25 pages, 370 KB  
Article
Lukasiewicz Fuzzy Set Theory Applied to SBE-Algebras
by Tahsin Oner, Hashem Bordbar, Neelamegarajan Rajesh and Akbar Rezaei
Mathematics 2025, 13(19), 3203; https://doi.org/10.3390/math13193203 - 6 Oct 2025
Viewed by 210
Abstract
In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed ζ-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-algebras). We introduce [...] Read more.
In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed ζ-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-algebras). We introduce and examine the concepts of ζ-Lukasiewicz fuzzy SBE-subalgebras and ζ-Lukasiewicz fuzzy SBE-ideals, with a focus on their algebraic properties. Furthermore, we define three specific types of subsets, referred to as ∈-sets, q-sets, and O-sets, and investigate the necessary conditions for these subsets to constitute subalgebras or ideals within the SBE-algebraic context. Full article
(This article belongs to the Special Issue Advances in Hypercompositional Algebra and Its Fuzzifications)
21 pages, 1482 KB  
Article
Models and Methods for Assessing Intruder’s Awareness of Attacked Objects
by Vladimir V. Baranov and Alexander A. Shelupanov
Symmetry 2025, 17(10), 1604; https://doi.org/10.3390/sym17101604 - 27 Sep 2025
Viewed by 235
Abstract
The formation of strategies and tactics of destructive impact (DI) at the stages of complex computer attacks (CCAs) largely depends on the content of intelligence data obtained by the intruder about the attacked elements of distributed information systems (DISs). This study analyzes scientific [...] Read more.
The formation of strategies and tactics of destructive impact (DI) at the stages of complex computer attacks (CCAs) largely depends on the content of intelligence data obtained by the intruder about the attacked elements of distributed information systems (DISs). This study analyzes scientific papers, methodologies and standards in the field of assessing the indicators of awareness of the intruder about the objects of DI and symmetrical indicators of intelligence security of the elements of the DIS. It was revealed that the aspects of changing the quantitative and qualitative characteristics of intelligence data (ID) at the stages of CCA, as well as their impact on the possibilities of using certain types of simple computer attacks (SKAs), are poorly studied and insufficiently systematized. This paper uses technologies for modeling the process of an intruder obtaining ID based on the application of the methodology of black, grey and white boxes and the theory of fuzzy sets. This allowed us to identify the relationship between certain arrays of ID and the possibilities of applying certain types of SCA end-structure arrays of ID according to the levels of identifying objects of DI, and to create a scale of intruder awareness symmetrical to the scale of intelligence protection of the elements of the DIS. Experiments were conducted to verify the practical applicability of the developed models and techniques, showing positive results that make it possible to identify vulnerable objects, tactics and techniques of the intruder in advance. The result of this study is the development of an intruder awareness scale, which includes five levels of his knowledge about the attacked system, estimated by numerical intervals and characterized by linguistic terms. Each awareness level corresponds to one CCA stage: primary ID collection, penetration and legalization, privilege escalation, distribution and DI. Awareness levels have corresponding typical ID lists that can be potentially available after conducting the corresponding type of SCA. Typical ID lists are classified according to the following DI levels: network, hardware, system, application and user level. For each awareness level, the method of obtaining the ID by the intruder is specified. These research results represent a scientific contribution. The practical contribution is the application of the developed scale for information security (IS) incident management. It allows for a proactive assessment of DIS security against CCAs—modeling the real DIS structure and various CCA scenarios. During an incident, upon detection of a certain CCA stage, it allows for identifying data on DIS elements potentially known by the intruder and eliminating further development of the incident. The results of this study can also be used for training IS specialists in network security, risk assessment and IS incident management. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2025)
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25 pages, 2019 KB  
Article
Statistical Convergence for Grünwald–Letnikov Fractional Differences: Stability, Approximation, and Diagnostics in Fuzzy Normed Spaces
by Hasan Öğünmez and Muhammed Recai Türkmen
Axioms 2025, 14(10), 725; https://doi.org/10.3390/axioms14100725 - 25 Sep 2025
Cited by 1 | Viewed by 227
Abstract
We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove [...] Read more.
We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove a Cauchy characterization: fuzzy statistical convergence implies fuzzy statistical Cauchyness, while the converse holds in fuzzy-complete spaces (and in the completion, otherwise). We further develop an inclusion theory linking fuzzy strong Cesàro summability—including weighted means—to fuzzy statistical convergence. Via the discrete Q-operator, all statements transfer verbatim between nabla-left and delta-right GL forms, clarifying the binomial GL↔discrete Riemann–Liouville correspondence. Beyond structure, we propose density-based residual diagnostics for GL discretizations of fractional initial-value problems: when GL residuals are fuzzy statistically negligible, trajectories exhibit Ulam–Hyers-type robustness in the fuzzy topology. We also formulate a fuzzy Korovkin-type approximation principle under GL smoothing: Cesàro control on the test set {1,x,x2} propagates to arbitrary targets, yielding fuzzy statistical convergence for positive-operator sequences. Worked examples and an engineering-style case study (thermal balance with memory and bursty disturbances) illustrate how the diagnostics certify robustness of GL numerical schemes under sparse spikes and imprecise data. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Difference and Differential Equations)
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19 pages, 408 KB  
Article
Exploring Symmetry Structures in Integrity-Based Vulnerability Analysis Using Bipolar Fuzzy Graph Theory
by Muflih Alhazmi, Gangatharan Venkat Narayanan, Perumal Chellamani and Shreefa O. Hilali
Symmetry 2025, 17(9), 1552; https://doi.org/10.3390/sym17091552 - 16 Sep 2025
Viewed by 303
Abstract
The integrity parameter in vulnerability refers to a set of removed vertices and the maximum number of connected components that remain functional. A bipolar fuzzy graph (BFG) assigns membership values to both positive and negative attributes. A new parameter, integrity, is defined and [...] Read more.
The integrity parameter in vulnerability refers to a set of removed vertices and the maximum number of connected components that remain functional. A bipolar fuzzy graph (BFG) assigns membership values to both positive and negative attributes. A new parameter, integrity, is defined and discussed using an example of a BFG. The integrity value of a special type of graph is determined, and the node strength sequence (NSS) for BFG is introduced. Specific NSS values are used to discuss the integrity values of paths and cycles. The integrity of the union, join, and Cartesian product of two BFGs is presented. This parameter is then applied to a road network with both positive and negative attributes, and the findings are discussed with a conclusion. Full article
(This article belongs to the Section Mathematics)
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19 pages, 21550 KB  
Article
The Float-Over Installation with a Dynamic Positioning Vessel Using Improved Fuzzy Control: An Experimental Study
by Yiting Wang, Ruiyan Gong, Lei Wang and Xuefeng Wang
J. Mar. Sci. Eng. 2025, 13(9), 1782; https://doi.org/10.3390/jmse13091782 - 16 Sep 2025
Viewed by 399
Abstract
To improve the maneuverability of the installation vessel and shorten the operational timeframe, a dynamic positioning (DP) semi-submersible vessel with a sophisticated control strategy is utilized to replace the conventional traction systems and towing tugs. In this paper, an improved fuzzy control law [...] Read more.
To improve the maneuverability of the installation vessel and shorten the operational timeframe, a dynamic positioning (DP) semi-submersible vessel with a sophisticated control strategy is utilized to replace the conventional traction systems and towing tugs. In this paper, an improved fuzzy control law is developed for the standby and docking stage of the float-over installation. The control thrust is divided into a dynamic part and a static part. Both parts are computed based on a set of logical if–then-type statements based on the human sense of realism and expert experience. The dynamic part acts as the proportional–derivative control, while the static part contributes the integral action. The implementation of accumulation time enhances the static thrust’s effectiveness in positioning the vessel compared to traditional integral control methods. A model test is further conducted to validate the effectiveness of the proposed improved fuzzy control based on a DP barge. Wind, wave, and current are considered from different directions in the experiment to simulate the practical operation condition. Experimental results illustrate that the proposed improved fuzzy control law can accurately keep position and guide the vessel into the slot of the jacket. Finally, some conclusions are summarized for the characteristic of fender forces in different environmental load directions. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 866 KB  
Article
Hybrid Interval Type-2 Fuzzy Set Methodology with Symmetric Membership Function for Application Selection in Precision Agriculture
by Radovan Dragić, Adis Puška, Branislav Dudić, Anđelka Štilić, Lazar Stošić, Miloš Josimović and Miroslav Nedeljković
Symmetry 2025, 17(9), 1504; https://doi.org/10.3390/sym17091504 - 10 Sep 2025
Viewed by 454
Abstract
The development of technology has influenced changes in agricultural production. Farmers are increasingly using modern devices and machinery that provide valuable information, and to manage this information effectively, it is necessary to use specialized applications. This research aims to evaluate various applications and [...] Read more.
The development of technology has influenced changes in agricultural production. Farmers are increasingly using modern devices and machinery that provide valuable information, and to manage this information effectively, it is necessary to use specialized applications. This research aims to evaluate various applications and determine which one is most suitable for small- and medium-sized farmers to adopt in precision agriculture. This research employed expert decision-making to determine the importance of criteria and evaluate applications using linguistic values. Due to the presence of uncertainty in decision-making, an interval type-2 fuzzy (IT2F) set was used, which addresses this problem through the support of a membership function. This approach allows for the display of uncertainty and imprecision using an interval rather than a single exact value. This enables a more flexible and realistic representation of ratings, leading to more confident decision-making. These membership functions are formed in such a way that there is symmetry around the central linguistic value. To use this approach, the SiWeC (simple weight calculation) and CORASO (compromise ranking from alternative solutions) methods were adapted. The results of the IT2F SiWeC method revealed that the most important criteria for experts are data accuracy, efficiency, and simplicity. The results of the IT2F CORASO method displayed that the A3 application delivers the best results, confirmed by additional analyses. This research has indicated that digital tools, in the form of applications, can be effectively used in small- and medium-scale precision agriculture production. Full article
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14 pages, 292 KB  
Article
Oettli-Théra Theorem and Ekeland Variational Principle in Fuzzy b-Metric Spaces
by Xuan Liu, Fei He and Ning Lu
Axioms 2025, 14(9), 679; https://doi.org/10.3390/axioms14090679 - 3 Sep 2025
Viewed by 370
Abstract
The purpose of this paper is to establish the Oettli–The´ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the [...] Read more.
The purpose of this paper is to establish the Oettli–The´ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the proof process. Based on the Oettli–The´ra theorem, we further demonstrate the equivalence of Ekeland variational principle, Caristi’s fixed point theorem, and Takahashi’s nonconvex minimization theorem in fuzzy b-metric spaces. Notably, the results obtained in this paper are consistent with the conditions of the corresponding theorems in classical fuzzy metric spaces, thereby extending the existing theories to the broader framework of fuzzy b-metric spaces. Full article
(This article belongs to the Section Mathematical Analysis)
14 pages, 1297 KB  
Article
Analyzing Safety Management Failure Paths in Coal Mines via the 24Model Accident Causation Framework and fsQCA
by Li Wang, Wanxin Xu and Jiang Li
Safety 2025, 11(3), 84; https://doi.org/10.3390/safety11030084 - 1 Sep 2025
Viewed by 591
Abstract
This study investigated safety management performance in small- and medium-sized private coal mining enterprises (SMPCMEs) through an integrated application of the 24Model accident causation theory and fuzzy-set qualitative comparative analysis (fsQCA). Analyzing 40 sudden incidents (2013–2023), we examined six key factors—organizational, individual, and [...] Read more.
This study investigated safety management performance in small- and medium-sized private coal mining enterprises (SMPCMEs) through an integrated application of the 24Model accident causation theory and fuzzy-set qualitative comparative analysis (fsQCA). Analyzing 40 sudden incidents (2013–2023), we examined six key factors—organizational, individual, and external dimensions—to identify nonlinear risk pathways. Results revealed four critical failure types—Internally Balanced (cultural–behavioral–environmental collapse), Safety Culture–Deficient (institutional hollowing), Cultural–External Environment (policy-implementation paradox), and External Environment–Integrated (technological-regulatory failure)—that collectively explained 83% of performance variance. Tailored strategies, including IoT-based real-time monitoring and AI-driven inspections, are proposed to transition from fragmented interventions to systemic governance. These findings provide actionable insights for enhancing safety resilience in high-risk mining sectors. Full article
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25 pages, 7693 KB  
Article
Spatio-Temporal Differentiation and Enhancement Path of Tourism Eco-Efficiency in the Yellow River Basin Under the “Dual Carbon” Goals
by Dandan Zhao, Yuxin Liang, Luyun Li, Yumei Ma and Guangkun Xiao
Sustainability 2025, 17(17), 7827; https://doi.org/10.3390/su17177827 - 30 Aug 2025
Viewed by 602
Abstract
Enhancing tourism eco-efficiency (TEE) is crucial for achieving China’s “dual carbon” objectives. This study examines nine provinces in the Yellow River Basin from 2010 to 2022, employing a super-efficiency SBM model, kernel density estimation, gravity center migration, standard deviation ellipse, Tobit regression, and [...] Read more.
Enhancing tourism eco-efficiency (TEE) is crucial for achieving China’s “dual carbon” objectives. This study examines nine provinces in the Yellow River Basin from 2010 to 2022, employing a super-efficiency SBM model, kernel density estimation, gravity center migration, standard deviation ellipse, Tobit regression, and fuzzy-set Qualitative Comparative Analysis (fsQCA) to investigate spatial-temporal variations and influencing factors. The results show that TEE increased steadily before 2019, declined during the COVID-19 pandemic, and recovered after 2021. Spatially, widening disparities and a polarization trend were observed, with the efficiency center remaining relatively stable in Shaanxi Province. Factors such as advancements in tourism economic development, regional economic growth, technological innovation, and infrastructure improvements significantly promote TEE, whereas stringent environmental regulations and greater openness exert constraints, and the impact of human capital remains uncertain. Four types of condition combinations were identified—economic-driven, market-innovation-driven, scale-innovation-driven, and balanced development. Managerial implications highlight the need for region-specific pathways and regional cooperation, with a dual focus on technological and institutional drivers as well as ecological value orientation, to sustainably enhance TEE in the Yellow River Basin. Full article
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21 pages, 2681 KB  
Article
A Novel q-Type Semi-Dependent Neutrosophic Decision-Making Approach and Its Applications in Supplier Selection
by Jinbo Zhang and Minghua Shi
Information 2025, 16(9), 742; https://doi.org/10.3390/info16090742 - 28 Aug 2025
Viewed by 459
Abstract
The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets [...] Read more.
The principles of least effort and the illusion of control may influence the decision-making process. It is challenging for a decision-maker to maintain complete independence when assessing the membership and non-membership degrees of indicators. However, existing neutrosophic sets and q-rung orthopair fuzzy sets assume full independence of such information. In view of this, this paper proposes a new neutrosophic set, namely the q-type semi-dependent neutrosophic set (QTSDNS), based on the classical neutrosophic set, whose membership and non-membership degrees are interrelated. QTSDNS is a generalized form of classical semi-dependent fuzzy sets, such as the intuitionistic neutrosophic set. It contains a regulatory parameter, which allows for decision-makers to flexibly adjust the model. Furthermore, a multi-attribute group decision-making (MAGDM) algorithm is proposed by integrating QTSDNS with evidence theory to solve the supplier selection problem. The algorithm first utilizes QTSDNS to represent the preference information of experts, then employs the q-TSDNWAA (or q-TSDNWGA) operator to aggregate the evaluation information of individual experts. Following the analysis of the mathematical relationship between QTSDNS and evidence theory, evidence theory is used to aggregate the evidence from each expert to obtain the group trust interval. Then, the best supplier is determined using interval number ranking methods. Finally, a numerical example is provided to demonstrate the feasibility of the proposed method. Full article
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16 pages, 530 KB  
Article
The Synergistic Empowerment of Digital Transformation and ESG on Enterprise Green Innovation
by Zixin Dou and Shuaishuai Jia
Systems 2025, 13(9), 740; https://doi.org/10.3390/systems13090740 - 26 Aug 2025
Viewed by 698
Abstract
Digital transformation enhances the processes and efficiency of enterprise green innovation through technological empowerment, while the ESG framework guides the direction and value of such innovation via institutional norms. However, existing studies often examine digital transformation and ESG in isolation, resulting in insufficient [...] Read more.
Digital transformation enhances the processes and efficiency of enterprise green innovation through technological empowerment, while the ESG framework guides the direction and value of such innovation via institutional norms. However, existing studies often examine digital transformation and ESG in isolation, resulting in insufficient exploration of their synergistic effects. Based on data from manufacturing high-tech enterprises, this study employs necessary condition analysis (NCA) and fuzzy-set qualitative comparative analysis (FsQCA) to systematically examine the synergistic effects of digital transformation and ESG on enterprise green innovation. The key findings are as follows: (1) While no single factor constitutes a necessary condition for high green innovation, the elements of social governance and digital management demonstrate universal applicability in enabling enterprises to achieve high levels of green innovation. (2) The dual-core-driven configuration achieves green innovation through the synergy between social governance and digital management, with its specific pathways varying according to the coordinated combinations of auxiliary factors. This delineates three distinct types, including compliance-oriented, environmentally empowered, and comprehensively balanced pathways. (3) The digitally driven configuration establishes an endogenous linkage between technological innovation and green development through the deep coupling of digital technology R&D and application. (4) The low green innovation configuration exhibits insufficient efficacy due to either isolated single elements or the absence of digital management, resulting in suboptimal green innovation performance. This study empirically demonstrates that the effective advancement of green innovation fundamentally relies on the endogenous dynamics of social governance, the technological underpinnings of digital management, and the systemic synergy among key elements, offering significant strategic implications for enterprises to develop differentiated green innovation approaches. Full article
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14 pages, 452 KB  
Article
An Integrated Intuitionistic Fuzzy-Clustering Approach for Missing Data Imputation
by Charlène Béatrice Bridge-Nduwimana, Aziza El Ouaazizi and Majid Benyakhlef
Computers 2025, 14(8), 325; https://doi.org/10.3390/computers14080325 - 12 Aug 2025
Viewed by 597
Abstract
Missing data imputation is a critical preprocessing task that directly impacts the quality and reliability of data-driven analyses, yet many existing methods treat numerical and categorical data separately and lack the integration of advanced techniques. We suggest a novel imputation technique to overcome [...] Read more.
Missing data imputation is a critical preprocessing task that directly impacts the quality and reliability of data-driven analyses, yet many existing methods treat numerical and categorical data separately and lack the integration of advanced techniques. We suggest a novel imputation technique to overcome these restrictions that synergistically combines regression imputation using HistGradientBoostingRegressor and fuzzy rule-based systems and is enhanced by a tailored clustering process. This integrated approach effectively handles mixed data types and complex data structures using regression models to predict missing numerical values, fuzzy logic to incorporate expert knowledge and interpretability, and clustering to capture latent data patterns. Categorical variables are managed by mode imputation and label encoding. We evaluated the method on twelve tabular datasets with artificially introduced missingness, employing a comprehensive set of metrics focused on originally missing entries. The results demonstrate that our iterative imputer performs competitively with other established imputation techniques, achieving better and comparable error rates and accuracy. By combining statistical learning with fuzzy and clustering frameworks, the method achieves 15% lower Root Mean Square Error (RMSE), 10% lower Mean Absolute Error (MAE), and 80% higher precision in UCI datasets, thus offering a promising advance in data preprocessing in practical applications. Full article
(This article belongs to the Special Issue Emerging Trends in Machine Learning and Artificial Intelligence)
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25 pages, 15183 KB  
Article
Permittivity Measurement in Multi-Phase Heterogeneous Concrete Using Evidential Regression Deep Network and High-Frequency Electromagnetic Waves
by Zhaojun Hou, Hui Liu, Jianchuan Cheng, Qifeng Zhang and Zheng Tong
Materials 2025, 18(16), 3766; https://doi.org/10.3390/ma18163766 - 11 Aug 2025
Viewed by 455
Abstract
Permittivity measurements of concrete materials benefit from the application of high-frequency electromagnetic waves (HF-EMWs), but they still face the problem of being aleatory and exhibit epistemic uncertainty, originating from multi-phase heterogeneous materials and the limited knowledge of HF-EMW propagation. This limitation restricts the [...] Read more.
Permittivity measurements of concrete materials benefit from the application of high-frequency electromagnetic waves (HF-EMWs), but they still face the problem of being aleatory and exhibit epistemic uncertainty, originating from multi-phase heterogeneous materials and the limited knowledge of HF-EMW propagation. This limitation restricts the precision of non-destructive testing. This study proposes an evidential regression deep network for conducting permittivity measurements with uncertainty quantification. This method first proposes a finite-difference time-domain (FDTD) model with multi-phase heterogeneous concrete materials to simulate HF-EMW propagation in a concrete sample or structure, obtaining the HF-EMW echo that contains aleatory uncertainties owing to the limited knowledge of wave propagation. A U-net-based model is then proposed to denoise an HF-EMW, where the difference between a couple of observed and denoised HF-EMWs characterizes aleatory uncertainty owing to measurement noise. Finally, a Dempster–Shafer theory-based (DST-based) evidential regression network is proposed to compute permittivity, incorporating the quantification of two types of uncertainty using a Gaussian random fuzzy number (GRFN): a type of fuzzy set that has the characteristics of a Gaussian fuzzy number and a Gaussian random variable. An experiment with 1500 samples indicates that the proposed method measures permittivity with a mean square error of 7.50% and a permittivity uncertainty value of 74.70% in four types of concrete materials. Additionally, the proposed method can quantify the uncertainty in permittivity measurements using a GRFN-based belief measurement interval. Full article
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