Search Results (123)

In this study, a generalized and advanced form of the near soft set theory (NST) framework is proposed for information aggregation (IA) processes. The primary motivation of the study is to address the lack of similarity-based uncertainty modeling in the literature by integrating the parametric structure of soft sets with the similarity-oriented structure of nearness approximation spaces. Within this framework, the AND-product and OR-product operations are introduced as the main methodological tools, and their algebraic structures are analyzed in detail. It is mathematically demonstrated that these operations satisfy fundamental properties such as idempotency, absorption, distributivity, and De Morgan identities. The principal original contribution of the study is the development of a novel Uni–Int-based decision-making mechanism that enables the systematic distinction between strong and acceptable alternatives. In addition, the boundary frequency indicator ($b_r$), which quantitatively evaluates the reliability of objects under perceptual uncertainty and is introduced for the first time in the literature, is proposed. The applicability of the proposed model is demonstrated through a real-estate selection problem, and a sensitivity analysis is conducted to reveal the determining effect of the nearness parameter r on decision granularity. The obtained findings indicate that the proposed NST framework provides a more flexible, more discriminative, and structurally robust decision-support model than classical approaches, particularly for similarity-based IA problems. Full article

Entropic soft-min relaxations are widely used to obtain smooth approximations of minimum operators in optimization, machine learning, and control. The accuracy of this approximation is governed by an inverse temperature (or sharpness) parameter that controls the trade-off between smoothness and fidelity, yet its principled selection is typically heuristic. This work studies the data-driven calibration of the inverse temperature parameter governing the entropic soft-min relaxation, with explicit guarantees on the relaxation error between the soft-min operator and the infimum of the cost function. After establishing monotonicity properties and approximation bounds for the relaxation error, we introduce a conformal calibration rule that selects the smallest inverse temperature ensuring that the approximation error satisfies a prescribed tolerance with distribution-free finite-sample validity. The resulting selector adapts to the distribution of candidate cost-vector geometries represented in the calibration sample, enabling regime-specific inverse temperature selection in heterogeneous settings. Numerical experiments, including an adaptive cruise control application with safety filtering, show that the proposed method accurately tracks oracle calibration inverse temperatures and achieves near-target coverage in the exchangeable setting covered by the theory, while an additional shifted evaluation illustrates the role of this assumption. Full article

In this paper, a new type of soft group called the soft symmetric difference group (SSD-group) is introduced and systematically developed. This structure is constructed by integrating soft set theory with group theory through the symmetric difference operation and set inclusion. Fundamental concepts such as characteristic soft symmetric difference groups, soft symmetric difference subgroups, normal soft symmetric difference subgroups, soft normalizers, and soft cosets are defined, and their essential algebraic properties are investigated. Several characterizations of soft normality are also established through these concepts. Various axiomatic results are obtained, providing necessary and sufficient conditions for a soft set to form an SSD-group. Furthermore, soft quotient (factor) groups of SSD-groups are introduced and their structural properties are examined in detail. The relationship between SSD-group theory and classical group theory is also established through several corresponding concepts. Illustrative examples are provided to demonstrate the applicability and internal consistency of the proposed framework. Overall, the results obtained in this study extend existing soft group structures and contribute to the development of algebraic theory within the context of soft sets, while also providing a foundation for further generalizations to other algebraic frameworks such as semigroups, rings, and fields. Full article

This paper introduces a novel hybrid framework called Interval-Valued Picture Fuzzy Soft Rough Sets (IVPFSRS) designed to address complex uncertainty in multi-criteria group decision-making (MCGDM) problems. The model achieves a synergistic integration of three powerful mathematical theories: interval-valued picture fuzzy sets (IVPFS) for representing nuanced, interval-valued degrees of membership, neutrality, and non-membership; soft sets for parameterized problem formulation; and rough sets for handling data granularity and approximation under incompleteness. We formally define the IVPFSRS framework, investigate its fundamental properties and algebraic operations, and develop a comprehensive MCGDM algorithm with explicit weight incorporation to address the critical role of criterion importance. The effectiveness and robustness of the proposed approach are demonstrated through a detailed illustrative example of administrative position selection and a systematic comparative analysis with existing models. Results show that the IVPFSRS framework provides a more powerful, flexible, and logically coherent tool for robust decision making in highly uncertain and information-deficient environments. The proposed framework complements recent advancements in cloud-rough integration for large group decision making while offering unique advantages in parameterized three-way uncertainty representation and structured multi-criteria evaluation. Full article

Subsurface deposition determines whether soils, aquifers, or ocean sediment represent a sink or temporary reservoir for microplastics. Deposition is generally studied by applying the Smoluchowski–Levich equation to determine a particle’s sticking efficiency, which relates the number of particles filtered by sediment to the probability of attachment occurring from an interaction between particles and sediment. Sticking efficiency is typically measured using column experiments or estimated from theory using the Interaction Force Boundary Layer (IFBL) model. However, there is generally a large discrepancy (orders of magnitude) between the values predicted from IFBL theory and the experimental column measurements. One way to bridge this gap is to directly measure a microparticle’s interaction forces using Atomic Force Microscopy (AFM). Herein, an AFM method is presented to measure sticking efficiency for a model polystyrene microparticle (2 μm) on a model geomaterial surface (glass or quartz) in environmentally relevant, synthetic freshwaters of varying ionic strength (de-ionized water, soft water, hard water). These data, collected over nanometer length scales, are compared to sticking efficiencies determined through traditional approaches. Force measurement results show that AFM can detect extremely low sticking efficiencies, surpassing the sensitivity of column studies. These data also demonstrate that the 75th to 95th percentile, rather than the mean or median force values, provides a better approximation to values measured in model column experiments or field settings. This variability of the methods provides insight into the fundamental mechanics of microplastic deposition and suggests AFM is isolating the physicochemical interactions, while column experiments also include physical interactions like straining. Advantages of AFM over traditional column/field experiments include high throughput, small volumes, and speed of data collection. For example, at a ramp rate of 1 Hz, 60 sticking efficiency measurements could be made in only a minute. Compared to column or field experiments, the AFM requires much less liquid (μL volume) making it effortless to examine the impact of solution chemistry (temperature, pH, ionic strength, valency of dissolved ions, presence of organics, etc.). Potential limitations of this AFM approach are presented alongside possible solutions (e.g., baseline correction, numerical integration). If these challenges are successfully addressed, then AFM would provide a completely new approach to help elucidate which subsurface minerals represent a sink or temporary storage site for microparticles on their journey from terrestrial to oceanic environments. Full article

Studying the thermodynamic properties of soft rocks is critical for geothermal energy extraction, as it elucidates their temperature-dependent mechanical behaviors and heat transfer mechanisms, thereby optimizing reservoir stimulation, enhancing extraction efficiency, and ensuring long-term operational stability. Owing to the intricate geothermal settings and interconnected physicochemical processes, the thermodynamic properties exhibit pronounced spatial heterogeneity and interdependencies. Concurrently, constraints imposed by technical and economic limitations result in scarce practical field survey and experimental data on these properties, severely hampering comprehensive assessments of geothermal energy potential and exploitation feasibility. To evaluate the spatial variability of thermodynamic properties for heterogeneous soft rock using limited data, the thermal conductivity (TC), heat capacity (HC), and thermal diffusivity (TD) were measured. A new Copula statistical method is used to analyze thermodynamic properties under limited measurement data. Spatial variability in heterogeneous soft rocks is quantified using random field theory. The methodology’s reliability is confirmed through cross-validation against theoretical predictions, empirical measurements, and simulation outputs. The analysis framework of thermodynamic variability characteristics has been presented by stability point analysis and linear regression analysis processes. The variance reduction function, scale of fluctuation, autocorrelation distances, and autocorrelation structure of thermodynamic properties for heterogeneous soft rock are analyzed and discussed. This study can provide scientific data for thermal energy analysis and geothermal reservoir modification specifically applicable to soft rock formations with diagenetic and tectonic histories similar to those investigated in the Weishan Lake area. Full article

This work constructs a new mathematical model for the vibrations of a Bernoulli beam that can come in contact with a reactive obstacle situated below its right end. The obstacle reaction is described by the Damped Normal Compliance (DNC) contact condition. This condition, unlike the usual Normal Compliance (NC) contact condition, takes into account the energy dissipation during the contact process. The steady states of the model are described and the model is studied computationally for different values of obstacle stiffness and damping. The computational scheme is shown numerically to converge with a rate higher than 1. The numerical simulations illustrate how the beam’s end penetration and vibrations differ in soft vs. stiff obstacle environments, and how damping modifies the dynamic behavior. The results may be useful for vibration control and material interaction in settings when collisions or repetitive contacts occur. By providing computational and analytical insights, the study is an addition to the currently maturing Mathematical Theory of Contact Mechanics (MTCM). Full article

In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle ${\mathbb{S}}^1$, we extend the approach to compact and non-compact group manifolds, coset spaces, and soft deformations thereof. After recalling the necessary geometric background on Riemannian manifolds, Hilbert bases, and Killing vectors, we present the construction of generalized current algebras $\mathfrak{g}\left(\mathcal{M}\right)$, their semidirect extensions with isometry algebras, and their central extensions. We show how the resulting algebras are controlled by the structure of the underlying manifold, and we illustrate the framework through explicit realizations on $SU\left(2\right)$, $SU\left(2\right)/U\left(1\right)$, and higher-dimensional spheres, highlighting their relation to Virasoro-like algebras. We also discuss the compatibility conditions for cocycles, the role of harmonic analysis, and some applications in higher-dimensional field theory and supergravity compactifications. This provides a unifying perspective on KM algebras beyond one-dimensional settings, paving the way for further exploration of their mathematical and physical implications. Full article

This paper provides a theoretical investigation of the OR-product (∨-product) in soft set theory, an operation of central importance for handling uncertainty in decision-making. A comprehensive algebraic analysis is carried out with respect to various types of subsets and equalities, with particular emphasis on M-subset and M-equality, which represent the strictest forms of subsethood and equality. This framework reveals intrinsic algebraic symmetries, particularly in commutativity, associativity, and idempotency, which enrich the structural understanding of soft set theory. In addition, certain missing results on OR-products in the literature are completed, and our findings are systematically compared with existing ones, ensuring a more rigorous theoretical framework. A central contribution of this study is the demonstration that the collection of all soft sets over a universe, equipped with a restricted/extended intersection and the OR-product, forms a commutative hemiring with identity under soft L-equality. This structural result situates the OR-product within one of the most fundamental algebraic frameworks, connecting soft set theory with broader areas of algebra. To illustrate its practical relevance, the int-uni decision-making method on the OR-product is applied to a pilot recruitment case, showing how theoretical insights can support fair and transparent multi-criteria decision-making under uncertainty. From an applied perspective, these findings embody a form of symmetry in decision-making, ensuring fairness and balanced evaluation among multiple decision-makers. By bridging abstract algebraic development with concrete decision-making applications, the results affirm the dual significance of the OR-product—strengthening the theoretical framework of soft set theory while also providing a viable methodology for applied decision-making contexts. Full article

Radio frequency (RF) fingerprinting, as an emerging physical layer security technology, demonstrates significant potential in the field of Internet of Things (IoT) security. However, most existing methods operate under a ‘closed-set’ assumption, failing to effectively address the continuous emergence of unknown devices in real-world scenarios. To tackle this challenge, this paper proposes an open-set radio frequency fingerprint identification (RFFI) method based on Multi-Task Prototype Learning (MTPL). The core of this method is a multi-task learning framework that simultaneously performs discriminative classification, generative reconstruction, and prototype clustering tasks through a deep network that integrates an encoder, a decoder, and a classifier. Specifically, the classification task aims to learn discriminative features with class separability, the generative reconstruction task aims to preserve intrinsic signal characteristics and enhance detection capability for out-of-distribution samples, and the prototype clustering task aims to promote compact intra-class distributions for known classes by minimizing the distance between samples and their class prototypes. This synergistic multi-task optimization mechanism effectively shapes a feature space highly conducive to open-set recognition. After training, instead of relying on direct classifier outputs, we propose to adopt extreme value theory (EVT) to statistically model the tail distribution of the minimum distances between known class samples and their prototypes, thereby adaptively determining a robust open-set discrimination threshold. Comprehensive experiments on a real-world dataset with 16 Wi-Fi devices show that the proposed method outperforms five mainstream open-set recognition methods, including SoftMax thresholding, OpenMax, and MLOSR, achieving a mean AUROC of 0.9918. This result is approximately 1.7 percentage points higher than the second-best method, demonstrating the effectiveness and superiority of the proposed approach for building secure and robust wireless authentication systems. This validates the effectiveness and superiority of our approach in building secure and robust wireless authentication systems. Full article

The reliability of decision-making algorithms within soft set theory is fundamentally constrained by their underlying membership functions. Traditional binary approaches overlook the implicit connections between the attributes a candidate possesses and those it lacks—connections that can be inferred from the wider candidate pool. To address this core challenge, this paper puts forward the Relational Membership Value Calculation (RMVC), an algorithmic framework whose core is a fine-grained relational membership function. Our approach moves beyond binary logic to capture these nuanced interrelationships. We provide a rigorous theoretical analysis of the proposed algorithm, including its computational complexity and robustness, which is validated through a comprehensive sensitivity analysis. Crucially, a comparative analysis using the Gini Index quantitatively demonstrates that our method provides significantly higher granularity and discriminatory power on a representative case study. The RMVC is implemented as an open-source Python program, providing a foundational tool to enhance the reasoning capabilities of AI-driven decision support and expert systems. Full article

Graph theory models relationships by representing entities as vertices and their interactionsas edges. To handle directionality and multiple head–tail assignments, various extensions—directed, bidirected, and multidirected graphs—have been introduced, with the multidirected graph unifying the first two. In this work, we further enrich this landscape by proposing the Multidirected hypergraph, which merges the flexibility of hypergraphs and superhypergraphs to describe higher-order and hierarchical connections. Building on this, we introduce five uncertainty-aware Multidirected frameworks—fuzzy, neutrosophic, plithogenic, rough, and soft multidirected graphs—by embedding classical uncertainty models into the Multidirected setting. We outline their formal definitions, examine key structural properties, and illustrate each with examples, thereby laying groundwork for future advances in uncertain graph analysis and decision-making. Full article

This study investigates how persuasion, trust, and empathy from Human Resources (HR) managers affect the acceptance of nudging practices in workplace, especially when these interventions are meant to be ethical and supportive. Based on the theory of advisory nudge, the research connects ideas from Human Resource Management and ethical marketing. A quantitative method was applied using a structured questionnaire answered by 733 HR professionals in European companies. The model was tested with PLS-SEM, and results confirmed strong influence of supervisor’s persuasion and empathy on HR professionals’ perception of nudges as ethical and autonomy-enhancing. The findings also showed that empathy plays important role in how HR professionals experience the intention behind soft interventions, with gender-based differences being significant. Additional analyses with IPMA and MGA confirmed the strategic importance of trust and emotional intelligence in organizational settings. The results help to understand when a persuasive act is seen as ethical guidance and when it is not, offering theoretical and practical insights both for HR leadership and marketing communication. The study suggests future research to explore different types of nudging and include variables such as organizational culture or HR professionals’ values, to better understand the ethical acceptance of influence at work. Full article

This review explores recent advances in data processing for atomic force microscopy (AFM) nanoindentation on soft samples, with a focus on “apparent” or “average” Young’s modulus distributions used for cancer diagnosis and treatment monitoring. Young’s modulus serves as a potential key biomarker, distinguishing normal from cancerous cells or tissue by assessing stiffness variations at the nanoscale. However, user-independent, reproducible classification remains challenging due to assumptions in traditional mechanics models, particularly Hertzian theory. To enhance accuracy, depth-dependent mechanical properties and polynomial corrections have been introduced to address sample heterogeneity and finite thickness. Additionally, AFM measurements are affected by tip imperfections and the viscoelastic nature of biological samples, requiring careful data processing and consideration of loading conditions. Furthermore, a quantitative approach using distributions of mechanical properties is suitable for tissue classification and for evaluating treatment-induced changes in nanomechanical properties. As part of this review, the use of AFM-based mechanical properties as a tool for monitoring treatment outcomes—including treatments with antifibrotic drugs and photodynamic therapy—is also presented. By analyzing nanomechanical property distributions before and after treatment, AFM provides insights for optimizing therapeutic strategies, reinforcing its role in personalized cancer care and expanding its applications in research and clinical settings. Full article

This study introduces a novel framework leveraging Rough Set Theory (RST)-based feature selection—MLReduct, MLSpecialReduct, and MLFuzzyRoughSet—to enhance machine learning performance on uncertain data. Applied to a private cardiovascular dataset, our MLSpecialReduct algorithm achieves a peak Random Forest accuracy of 0.99 (versus 0.85 without feature selection), while MLFuzzyRoughSet improves accuracy to 0.83, surpassing our MLVarianceThreshold (0.72–0.77), an adaptation of the traditional VarianceThreshold method. We integrate these RST techniques with preprocessing (discretization, normalization, encoding) and compare them against traditional approaches across classifiers like Random Forest and Naive Bayes. The results underscore RST’s edge in accuracy, efficiency, and interpretability, with MLSpecialReduct leading in minimal attribute reduction. Against baseline classifiers without feature selection and MLVarianceThreshold, our framework delivers significant improvements, establishing RST as a vital tool for explainable AI (XAI) in healthcare diagnostics and IoT systems. These findings open avenues for future hybrid RST-ML models, providing a robust, interpretable solution for complex data challenges. Full article