Search Results (454)

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 $\{1,x,x^2\}$ 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

Survival analysis is a fundamental tool for modeling time-to-event data in healthcare, engineering, and finance, where censored observations pose significant challenges. While traditional methods like the Beran estimator offer nonparametric solutions, they often struggle with the complex data structures and heavy censoring. This paper introduces three novel survival models, iSurvM (imprecise Survival model based on Mean likelihood functions), iSurvQ (imprecise Survival model based on Quantiles of likelihood functions), and iSurvJ (imprecise Survival model based on Joint learning), that combine imprecise probability theory with attention mechanisms to handle censored data without parametric assumptions. The first idea behind the models is to represent censored observations by interval-valued probability distributions for each instance over time intervals between event moments. The second idea is to employ the kernel-based Nadaraya–Watson regression with trainable attention weights for computing the imprecise probability distribution over time intervals for the entire dataset. The third idea is to consider three decision strategies for training, which correspond to the proposed three models. Experiments on synthetic and real datasets demonstrate that the proposed models, especially iSurvJ, consistently outperform the Beran estimator from accuracy and computational complexity points of view. Codes implementing the proposed models are publicly available. Full article

Background/Objectives: A mandatory monitoring of the use of antibiotics in horses in the European Union will come into force from 2029 on. The aim of the study was to explore the potential implementation of a monitoring system and to provide an overview of antibiotic use in horses in Germany. Methods: Data on all consultations from 57 German practices between 2018 and 2023 were obtained. The dataset included basic data about the horse, free-text diagnoses (allocated to one of 20 categories), and treatments. Information on the administered or dispensed pharmaceutical product was recorded for antibiotic treatment consultations. Results: This study analyzed 225,622 consultations with more than 50,000 horses. Antibiotics were administered in around 7% of consultations, but practice-specific rates varied considerably. Treatment was most frequent in ophthalmology cases. The most commonly used drug classes were sulfonamides combined with trimethoprim and aminopenicillins. Horses receiving antibiotics required follow-up visits more often than untreated animals, and changes in antibiotic substance occurred occasionally. Conclusions: Routine practice data provide valuable insights into antibiotic use in equine medicine. While incomplete entries and imprecise details (e.g., missing concentrations or diagnoses) remain a limitation, the approach offers clear advantages: it is cost-effective, allows large-scale data collection, and supports continuous monitoring over time. Such systems can be used to evaluate the effects of upcoming EU regulations and to identify priorities for antibiotic stewardship in equine practice. Full article

Boat collisions pose severe threats to maritime safety, economic activity, and environmental sustainability. Conventional risk assessment methods—such as Failure Mode and Effects Analysis, and Fault Tree Analysis—are widely applied but remain inadequate for addressing the uncertainty, subjectivity, and interdependency of risk factors in complex maritime environments. This study proposes a fuzzy Multi-Criteria Decision-Making framework for the risk assessment of boat collisions. The model integrates fuzzy logic with Analytic Hierarchy Process for criterion weighting and the Technique for Order Preference by Similarity to the Ideal Solution for risk ranking. Fuzzy logic is employed to capture linguistic expert judgments and to manage vague or incomplete data, which are common challenges in marine operations. Key collision risk factors—human error, boat engine system failure, environmental conditions, and intentional threats—are identified through literature review, incident data analysis, and expert consultation. A comparative analysis with a baseline non-fuzzy model demonstrates the added value of the fuzzy-integrated framework, showing improved capacity to handle imprecision and uncertainty. The model outputs not only prioritise risk rankings but also support the identification of critical control actions and effective safety measures. A case study of Nigerian waters illustrates the practicality of the framework in guiding risk mitigation strategies and informing policy decisions under uncertainty. Full article

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

In this article, a novel procedure is developed to properly handle the 3-D mispositioning of the scanning probe in the near-field to far-field (NFtFF) transformations with spherical scanning for quasi-planar antennas under test, which make use of a non-redundant (NR) number of samples. It proceeds through two stages. In the former, a phase correction technique, named spherical wave correction, is applied to compensate for the phase shifts of the collected NF samples, which do not belong to the measurement sphere, due to mechanical defects of the arc, or inaccuracy of the robotic arm employed in the considered NF facility driving the probe. Once the phase shifts have been compensated, the recovered NF samples belong to the set spherical surface, but their positions differ from those prescribed by the adopted NR representation, because of an imprecise control and/or inaccuracy of the positioning system. Thus, the resulting sampling arrangement is affected by 2-D mispositioning errors. Accordingly, an iterative procedure is used in the latter step to restore the NF samples at their exact locations from those determined at the first step. Once the correct sampling arrangement has been retrieved from the 3-D mispositioned one, an optimal sampling interpolation formula is employed to obtain the massive input NF data necessary for the classical spherical NFtFF transformation technique. Numerical results, showing the precision of the NF and FF reconstructions, assessed the efficacy of the developed procedure. Full article

Mount Falakro in Northern Greece historically hosted populations of the Balkan-endemic butterfly Polyommatus orphicus and its larval host plant Onobrychis alba. In this study, we surveyed six historically confirmed localities during the peak flight period of P. orphicus in 2024, but neither the butterfly nor the host plant were detected. While the historical data on both species are scarce and often imprecise, our field observations indicate severe habitat degradation, dominated by overgrazing and suspected climate-driven shifts. Habitat conditions were assessed qualitatively, with special attention to limestone substrates previously known to support O. alba. Although definitive absence cannot be statistically confirmed, the lack of detection in previously occupied sites raises urgent concerns about possible local extinction. Our findings suggest that both species may already be extirpated from parts of their former range. This case study underscores the conservation relevance of absence data and highlights the importance of site-based monitoring in mountainous ecosystems undergoing rapid environmental change. Long-term surveys, regulated grazing, and post-disturbance habitat restoration are urgently needed to clarify the conservation status of these species and guide future management strategies. Full article

A fundamental aspect in the evaluation of mining projects is the classification of mineral resources, as it directly influences the definition of mineral reserves and affects both the planning and operational phases of the mine. Traditional methods employed in the industry are based on geometric or geostatistical criteria which, while constituting the fundamental basis of the process, may prove insufficient when applied in isolation to reflect the uncertainty inherent in the databases used for the evaluation of mineral deposits. As discussed throughout the article, this limitation can lead to an incorrect or imprecise assignment of resource categories. This work presents a methodology to integrate variables related to sample quality as an additional criterion in resource classification. This allows for the identification of areas with greater uncertainty and the adjustment of their categories more consistently with data reliability. The effectiveness of the proposed method is demonstrated through its application to a real case study, complemented by a comprehensive analysis of its implications and results. Full article

Hydroponic systems can drain nutrient-rich waste into the environment. Increasing irrigation efficiency would decrease effluent and improve cost efficiency for growers. However, current methods accessible to small- and mid-sized growers to determine moisture content in growth media are often imprecise. Simplified transpiration models could inform irrigation needs. This study aimed to improve transpiration estimates using vapor pressure deficit (VPD) and solar radiation. We compared our model to an existing transpiration model. Three years of transpiration and environmental data from tomato production were used to calibrate (year 2) and validate (years 1 and 3) the model. Randomly chosen subsets from all years of data were also used. The new model (TVPD) predicted the observed values more closely than the previous model (PG) in year 1 (TVPD: RMSE = 0.1570 mm, r² = 0.95; PG: RMSE = 0.5594 to 0.6875 mm, r² = 0.27 to 0.78) but not in year 3 (TVPD: RMSE = 0.5430 mm, r² = 0.44; PG: RMSE = 0.1873 to 0.2065 mm, r² = 0.95). TVPD calibrated using random subsets of the combined data improved consistency and predictive capacity (RMSE = 0.2387 to 0.2419 mm, r² = 0.87 to 0.91). TVPD is a simpler alternative to complex models and to those focusing on solar radiation alone. TVPD is less reliable under low solar radiation (year 3); however, reliability could be improved by calibration across a broader environmental range. TVPD also allows for exploration of the relative influences of low VPD and high solar radiation on evapotranspiration found in greenhouse settings. Full article

While Evidence Theory (also known as Dempster–Shafer Theory, or Belief Functions Theory) is being increasingly used in data fusion, its potentialities in the Social and Life Sciences are often obscured by lack of awareness of its distinctive features. In particular, with this paper I stress that an extended version of Evidence Theory can express the uncertainty deriving from the fear that events may materialize, that one is not even able to figure out. By contrast, Probability Theory must limit itself to the possibilities that a decision-maker is currently envisaging. I compare this extended version of Evidence Theory to cutting-edge extensions of Probability Theory, such as imprecise and sub-additive probabilities, as well as unconventional versions of Information Theory that are employed in data fusion and transmission of cultural information. A possible application to creative usage of Large Language Models is outlined, and further extensions to multi-agent interactions are outlined. Full article

In real-world decision-making situations, experts often rely on subjective and imprecise judgments, frequently expressed using linguistic terms. While fuzzy logic offers a valuable tool to capture and process such uncertainty, traditional methods often convert fuzzy inputs into crisp values too early in the process. This premature defuzzification can result in significant loss of information and reduced interpretability. To address this issue, the present study introduces an enhanced fuzzy TOPSIS model that utilizes expected interval representations instead of early crisp transformation. This approach allows the original fuzzy data to be preserved throughout the analysis, leading to more transparent, realistic, and informative decision outcomes. The practical application of the proposed method is demonstrated through a supplier selection case study, which illustrates the model’s capability to handle real-world, complex, and qualitative decision environments. By explicitly linking the method to this domain, the study provides a concrete anchor for practitioners and decision-makers seeking transparent and robust evaluation tools. Full article

Objective: This umbrella review aims to analyze the effectiveness of exercise therapy for low back pain through an analysis of systematic reviews that evaluate pain reduction, quality of life improvement, and functional outcomes. Methods: This review adhered to PRISMA guidelines and systematic review of review recommendations by searching across PubMed, Scopus, and the Cochrane Library. This study searched for systematic reviews alongside meta-analyses that evaluated exercise interventions in treating low back pain (LBP). This study included reviews that examined exercise therapy for LBP patients and presented data regarding their pain intensity, disability, and quality-of-life outcomes. Data extraction and quality assessment were performed independently by several reviewers. The methodological quality of the included systematic reviews was assessed using the AMSTAR 2 tool. Results: This research yielded 88 systematic reviews from 997 evaluated records. Reduction of pain emerged as the primary measured outcome in systematic reviews (81.8%, n = 72), and these studies showed significant improvement rates of 83.0%. The proportion of studies that concluded no change was 9.1%. The most frequently studied exercises were strengthening, aerobic, and mind–body exercises. The reviews reported quality of life improvements in 27.3% (n = 24), but most reviews (68.2%) did not assess this outcome. No studies indicated worsening outcomes. Exercise interventions demonstrated various forms that effectively contribute to LBP management, according to the study results. Conclusions: This umbrella review of 88 systematic reviews highlights that exercise therapy is a safe, effective, and commonly used strategy for managing low back pain. However, key limitations include the low methodological quality of several included reviews, risk of bias, imprecision, limited reporting of adverse effects, and confounding from multicomponent interventions. While there is limited certainty that any one type of exercise is more effective than others, individualized approaches and patient adherence appear to be critical factors in optimizing outcomes. Full article

Trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are the real generalizations of intuitionistic fuzzy numbers, interval-valued intuitionistic fuzzy numbers, and triangular intuitionistic fuzzy numbers, which effectively model real-life problems that consist of imprecise and incomplete data. This study incorporates the Aczel-Alsina aggregation operators (which consist of parameter-based flexibility) for solving any group of decision-making problems modeled in a trapezoidal-valued intuitionistic fuzzy (TrVIF) environment. In this study, we first define new operations on TrVIFNs based on the Aczel-Alsina operations. Secondly, we introduce new trapezoidal-valued intuitionistic fuzzy aggregation operators, such as the TrVIF Aczel-Alsina weighted averaging operator, the TrVIF Aczel-Alsina ordered weighted averaging operator, and the TrVIF Aczel-Alsina hybrid averaging operator, and we discuss their fundamental mathematical properties by examining various theorems. This study also includes a new algorithm named ‘three-stage multi-criteria group decision-making’, where we obtain the criteria weights using the newly proposed TrVIF-MEREC method. Additionally, we introduce a new modified algorithm called TrVIF-WASPAS to solve the multi-criteria decision-making (MCDM) problem in the trapezoidal-valued intuitionistic fuzzy environment. Then, we apply this proposed method to solve a model case study problem involving location selection for a wind power plant project. Then, we discuss the proposed algorithm’s sensitivity analysis by changing the criteria weights concerning different parameter values. Finally, we compare our proposed methods with various existing methods, like some subclasses of TrVIFNs such as IVIFWA, IVIFWG, IVIFEWA, and IVIFEWG, and also with some MCGDM methods of TrVIFNs, such as the Dombi aggregation operator-based method in TrVIFNs and the TrVIF-Topsis method-based MCGDM, to show the efficacy of our proposed algorithm. This study has many advantages, as it consists of a total ordering principle in ranking alternatives in the newly proposed TrVIF-MCGDM techniques and TrVIF-WASPAS MCDM techniques for the first time in the literature. Full article

The concept of fuzzy modeling and fuzzy system design has opened new horizons of research in functional analysis, having a significant impact on major fields such as data science, machine learning, and so on. In this research, we use fuzzy set theory to analyze the global dynamics and oscillatory behavior of nonlinear fuzzy difference equations with exponential decay. We discuss the stability, oscillatory patterns, and convergence of solutions under different initial conditions. The exponential structure simplifies the analysis while providing a clear understanding of the system’s behavior over time. The study reveals how fuzzy parameters influence growth or decay trends, emphasizing the method’s effectiveness in handling uncertainty. Our findings advance the understanding of higher-order fuzzy difference equations and their potential applications in modeling systems with imprecise data. Using the characterization theorem, we convert a fuzzy difference equation into two crisp difference equations. The g-division technique was used to investigate local and global stability and boundedness in dynamics. We validate our theoretical results using numerical simulations. Full article

Chronological age is an imprecise proxy for reproductive capacity, necessitating biomarkers that reflect the underlying pathophysiology of the ovary. Fibrotic remodeling of the ovarian stroma is a key hallmark of biological ovarian aging, yet it cannot be assessed by current clinical tools. This study aimed to identify and validate a novel serum biomarker for fibrotic ovarian aging by applying supervised machine learning (ML) to human ovarian transcriptomic data. Transcriptomic data from the Genotype-Tissue Expression (GTEx) database were analyzed using ML algorithms to identify candidate genes predictive of ovarian aging, and finally, fibroblast activation protein (FAP) and collectin-11 (COLEC11) were selected for clinical validation. In a cross-sectional study, serum levels of FAP and COLEC11, along with key hormonal indices, were measured in two nested patient cohorts, and their associations with ovarian reserve and clinical parameters were analyzed. Serum FAP levels did not correlate with age but showed a strong inverse correlation with anti-Müllerian hormone (AMH) (r = −0.61, p = 0.001), a finding accentuated in women with decreased ovarian reserve (DOR). While COLEC11 correlated with age, it failed to differentiate DOR status. FAP levels were independent of central hormonal regulation, consistent with preclinical fibrotic models. Circulating FAP reflects age-independent, fibrotic ovarian aging, offering stromal-specific information not captured by conventional hormonal markers. This study provides the first clinical validation of FAP as a biomarker for ovarian stromal aging, holding potential for improved reproductive risk assessment. Full article