Search Results (35)

This paper proposes a fuzzy copula-based optimization framework for modeling dependence structures and financial risk under parameter uncertainty. The parameters of selected copula families are represented as trapezoidal fuzzy numbers, and their α-cut intervals capture both the support and core ranges of plausible dependence values. This fuzzification transforms the estimation of copula parameters into a fuzzy optimization problem, enhancing robustness against sampling variability. The methodology is empirically applied to gold and oil futures (1 January 2015–1 January 2025), comparing symmetric copulas, i.e., Gaussian and Frank and asymmetric copulas, i.e., Clayton, Gumbel and Student-t. The results prove that the fuzzy copula framework provides richer insights than classical point estimation by explicitly expressing uncertainty in dependence measures (Kendall’s τ, Spearman’s ρ) and risk indicators (Value-at-Risk, Conditional Value-at-Risk). Rolling-window analyses reveal that fuzzy VaR and fuzzy CVaR effectively capture temporal dependence shifts and tail severity, with fuzzy CVaR consistently producing more conservative risk estimates. This study highlights the potential of fuzzy optimization and fuzzy dependence modeling as powerful tools for quantifying uncertainty and managing extreme co-movements in financial markets. Full article

Transformer reliability is crucial to grid security, with core loosening a common fault. This paper proposes a transformer core loosening fault diagnosis method based on a fusion feature extraction approach and Categorical Boosting (CatBoost) optimized by the Crested Porcupine Optimizer (CPO) algorithm. Firstly, the audio signal is decomposed into six Intrinsic Mode Functions (IMF) components through Variational Mode Decomposition (VMD). This paper utilizes Gaussian membership functions to quantify the energy proportion, central frequency, and kurtosis of IMF and constructs a fuzzy entropy discrimination function. Then, the IMF noise components are removed through an adaptive threshold. Subsequently, the denoised signal undergoes a wavelet packet transform instead of a short-time Fourier transform to optimize Mel-frequency cepstral coefficients (WPT-MFCC), combining time-domain statistical features and frequency-band energy distribution to form a 24-dimensional fusion feature. Finally, the CatBoost algorithm is employed to validate the effects of different feature schemes. The CPO is introduced to optimize its iteration number, learning rate, tree depth, and random strength parameters, thereby enhancing overall performance. The CPO-optimized CatBoost model had 99.0196% fault recognition accuracy in experimental testing, 15% better than the standard CatBoost. Accuracy exceeded 90% even under extreme 0 dB noise. This method makes fault diagnosis more accurate and reliable. Full article

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

This study addresses the dual challenges of complex road environments and diverse task-safety requirements in mobile-robot path planning by proposing an innovative method that integrates a dual-layer fuzzy control system with an improved genetic algorithm. Initially, an expert system-based dual-layer fuzzy control system is developed. The first layer translates complex road conditions and obstacles into road-safety levels, while the second layer combines these with task-safety levels to generate fitness weights for the genetic algorithm. Furthermore, road-safety factors are incorporated into the genetic algorithm’s fitness function to enhance safety considerations in path planning. The algorithm implementation incorporates Bernoulli chaotic mapping, Gaussian operators, and Symmetrical Sigmoid operators to optimize the selection, crossover, and mutation processes, significantly boosting the algorithm’s global search capability and efficiency. Experimental results indicate that the proposed method reduces path distance by up to 5.9% and decreases the number of turns by up to 85.7%, demonstrating superior universality and robustness across various comparative experiments. This research contributes to resolving the issues posed by complex road environments and varying task-safety requirements in mobile-robot path planning. Full article

Efficient energy management relies on uncovering meaningful consumption patterns from large-scale electricity load demand profiles. With the widespread adoption of sensor technologies such as smart meters and IoT-based monitoring systems, granular and real-time electricity usage data have become available, enabling deeper insights into consumption behaviors. Clustering is a widely used technique for this purpose, but previous studies have primarily focused on a limited set of algorithms, often treating clustering as a black-box approach without addressing interpretability. This study explores a wide number of clustering algorithms by comparing hard clustering algorithms (K-Means, K-Medoids) versus soft clustering techniques (Fuzzy C-Means, Gaussian Mixture Models) in segmenting electricity consumption profiles. The clustering performance is evaluated using five different clustering validation indices (CVIs), assessing intra-cluster cohesion and inter-cluster separation. The results show that soft clustering methods effectively capture inter-cluster characteristics, leading to better cluster separation, whereas intra-cluster characteristics exhibit similar behavior across all clustering approaches. This study assesses which CVIs provide reliable evaluations independent of clustering algorithm sensitivity. It provides a comprehensive analysis of the different CVIs’ responses to changes in data characteristics, highlighting which indices remain robust and which are more susceptible to variations in cluster structures. Beyond evaluating clustering effectiveness, this study enhances interpretability by introducing two decision tree models, axis-aligned and sparse oblique decision trees, to generate human-readable rules for cluster assignments. While the axis-aligned tree provides a complete explanation of all clusters, the sparse oblique tree offers simpler, more interpretable rules, emphasizing a trade-off between full interpretability and rule complexity. This structured evaluation provides a framework for balancing transparency and complexity in clustering explanations, offering valuable insights for utility providers, policymakers, and researchers aiming to optimize both clustering performance and explainability in sensor-driven energy demand analysis. Full article

The maize tassel represents one of the most pivotal organs dictating maize yield and quality. Investigating its phenotypic information constitutes an exceedingly crucial task within the realm of breeding work, given that an optimal tassel structure is fundamental for attaining high maize yields. High-throughput phenotyping technologies furnish significant tools to augment the efficiency of analyzing maize tassel phenotypic information. Towards this end, we engineered a fully automated multi-angle digital imaging apparatus dedicated to maize tassels. This device was employed to capture images of tassels from 1227 inbred maize lines falling under three genotype classifications (NSS, TST, and SS). By leveraging the 3D reconstruction algorithm SFM (Structure from Motion), we promptly obtained point clouds of the maize tassels. Subsequently, we harnessed the TreeQSM algorithm, which is custom-designed for extracting tree topological structures, to extract 11 archetypal structural phenotypic parameters of the maize tassels. These encompassed main spike diameter, crown height, main spike length, stem length, stem diameter, the number of branches, total branch length, average crown diameter, maximum crown diameter, convex hull volume, and crown area. Finally, we compared the GFC (Gaussian Fuzzy Clustering algorithm) used in this study with commonly used algorithms, such as RF (Random Forest), SVM (Support Vector Machine), and BPNN (BP Neural Network), as well as k-Means, HCM (Hierarchical), and FCM (Fuzzy C-Means). We then conducted a correlation analysis between the extracted phenotypic parameters of the maize tassel structure and the genotypes of the maize materials. The research results showed that the Gaussian Fuzzy Clustering algorithm was the optimal choice for clustering maize genotypes. Specifically, its classification accuracies for the Non-Stiff Stalk (NSS) genotype and the Tropical and Subtropical (TST) genotype reached 67.7% and 78.5%, respectively. Moreover, among the materials with different maize genotypes, the number of branches, the total branch length, and the main spike length were the three indicators with the highest variability, while the crown volume, the average crown diameter, and the crown area were the three indicators with the lowest variability. This not only provided an important reference for the in-depth exploration of the variability of the phenotypic parameters of maize tassels but also opened up a new approach for screening breeding materials. Full article

This paper presents a comprehensive study of the signed distance metric for fuzzy numbers. Due to the property of directionality, this measure has been widely used. However, it has a main drawback in handling asymmetry and irregular shapes in fuzzy numbers. To overcome this rather bad feature, we introduce two new distances, the balanced signed distance (BSGD) and the generalised signed distance (GSGD), seen as generalisations of the classical signed distance. The developed distances successfully and effectively take into account the shape, the asymmetry and the overlap of fuzzy numbers. The GSGD is additionally directional, while the BSGD satisfies the requirements for being a metric of fuzzy quantities. Analytical simplifications of both distances in the case of often-used particular types of fuzzy numbers are provided to simplify the computation process, making them as simple as the classical signed distance but more realistic and precise. We empirically analyse the sensitivity of these distances. Considering several scenarios of fuzzy numbers, we also numerically compare these distances against established metrics, highlighting the advantages of the BSGD and the GSGD in capturing the shape properties of fuzzy numbers. One main finding of this research is that the defended distances capture with great precision the distance between fuzzy numbers; additionally, they are theoretically appealing and are computationally easy for traditional fuzzy numbers such as triangular, trapezoidal, Gaussian, etc., making these metrics promising. Full article

Smart meter data provide an in-depth perspective on household energy usage. This research leverages on such data to enhance demand response (DR) programs through a novel application of ensemble clustering. Despite its promising capabilities, our literature review identified a notable under-utilization of ensemble clustering in this domain. To address this shortcoming, we applied an advanced ensemble clustering method and compared its performance with traditional algorithms, namely, K-Means++, fuzzy K-Means, Hierarchical Agglomerative Clustering, Spectral Clustering, Gaussian Mixture Models (GMMs), BIRCH, and Self-Organizing Maps (SOMs), across a dataset of 5567 households for a range of cluster counts from three to nine. The performance of these algorithms was assessed using an extensive set of evaluation metrics, including the Silhouette Score, the Davies–Bouldin Score, the Calinski–Harabasz Score, and the Dunn Index. Notably, while ensemble clustering often ranked among the top performers, it did not consistently surpass all individual algorithms, indicating its potential for further optimization. Unlike approaches that seek the algorithmically optimal number of clusters, our method proposes a practical six-cluster solution designed to meet the operational needs of utility providers. For this case, the best performing algorithm according to the evaluation metrics was ensemble clustering. This study is further enhanced by integrating Explainable AI (xAI) techniques, which improve the interpretability and transparency of our clustering results. Full article

This work proposes a new unsupervised method to evaluate the behavior of urban green areas in the presence of heatwave scenarios by analyzing three indices extracted from satellite data: the Normalized Difference Vegetation Index (NDVI), the Normalized Difference Moisture Index (NDMI), and Land Surface Temperature (LST). The aim of this research is to analyze the behavior of urban vegetation types during heatwaves through the analysis of these three indices. To evaluate how these indices characterize urban green areas during heatwaves, an unsupervised classification method of the three indices is proposed that uses the Elbow method to determine the optimal number of classes and the Jenks classification algorithm. Each class is assigned a Gaussian fuzzy set and the green urban areas are classified using zonal statistics operators. The membership degree of the corresponding fuzzy set is calculated to assess the reliability of the classification. Finally, for each type of greenery, the frequencies of types of green areas belonging to NDVI, NDMI, and LST classes are analyzed to evaluate their behavior during heatwaves. The framework was tested in an urban area consisting of the city of Naples (Italy). The results show that some types of greenery, such as deciduous forests and olive groves, are more efficient, in terms of health status and cooling effect, than other types of urban green areas during heatwaves; they are classified with NDVI and NDMI values of mainly High and Medium High, and maximum LST values of Medium Low. Conversely, uncultivated areas show critical behaviors during heatwaves; they are classified with maximum NDVI and NDMI values of Medium Low and maximum LST values of Medium High. The research results represent a support to urban planners and local municipalities in designing effective strategies and nature-based solutions to deal with heat waves in urban settlements. Full article

Ammonia nitrogen (NH₃-N) is a key water quality variable that is difficult to measure in the water treatment process. Data-driven soft computing is one of the effective approaches to address this issue. Since the detection cost of NH₃-N is very expensive, a large number of NH₃-N values are missing in the collected water quality dataset, that is, a large number of unlabeled data are obtained. To enhance the prediction accuracy of NH₃-N, a semi-supervised soft computing method using a self-constructing fuzzy neural network with an active learning mechanism (SS-SCFNN-ALM) is proposed in this study. In the SS-SCFNN-ALM, firstly, to reduce the computational complexity of active learning, the kernel k-means clustering algorithm is utilized to cluster the labeled and unlabeled data, respectively. Then, the clusters with larger information values are selected from the unlabeled data using a distance metric criterion. Furthermore, to improve the quality of the selected samples, a Gaussian regression model is adopted to eliminate the redundant samples with large similarity from the selected clusters. Finally, the selected unlabeled samples are manually labeled, that is, the NH₃-N values are added into the dataset. To realize the semi-supervised soft computing of the NH₃-N concentration, the labeled dataset and the manually labeled samples are combined and sent to the developed SCFNN. The experimental results demonstrate that the test root mean square error (RMSE) and test accuracy of the proposed SS-SCFNN-ALM are 0.0638 and 86.31%, respectively, which are better than the SCFNN (without the active learning mechanism), MM, DFNN, SOFNN-HPS, and other comparison algorithms. Full article

Fuzzy Inference System behavior can be described qualitatively using a natural language, which is known as the expert-driven approach to handling non-statistical uncertainty. Generally, practical applications involve conceptualizing the problem by integrating linguistic uncertainty and using data by integrating stochastic uncertainty. The proposed probabilistic fuzzy system uses the Gaussian Density Function (GDF) to assign a probability to input variables integrating stochastic uncertainty. In addition, a linguistic interpretation is used to project various categories of the GDF integrating linguistic uncertainty. Likewise, one of the relevant aspects of the proposal is to weigh each input variable according to the heuristic interpretation that determines the probability assigned to each of them a priori. Therefore, the main contribution of the research focuses on using the Bayesian Linguistic Conditional System (BLCS) as a mechanism of attention to relate the categories of the different input variables and find their posterior-weighted probability at a normalization stage. Finally, the knowledge base is established through linguistic rules, and the system’s output is a Bayesian classifier multiplying its normalized posterior conditional probabilities. The highest probability value of the knowledge base is identified, and the Risk Priority Number Weighted (RPNW) is determined using their respective posterior-normalized probabilities for each input variable. The results are expressed on a simple and precise scale from 1 to 10. They are compared with the Risk Priority Number (RPN), which results in a Failure Mode and Effect Analysis (FMEA). They show similar behaviors for multiple combinations in the evaluations while highlighting different scales. Full article

This paper presents (a) a novel hybrid learning method to train interval type-1 non-singleton type-3 fuzzy logic systems (IT3 NSFLS-1), (b) a novel method, named enhanced Wagner–Hagras (EWH) applied to IT3 NSFLS-1 fuzzy systems, which includes the level alpha 0 output to calculate the output $y$ alpha using the average of the outputs $y$ alpha $k$ instead of their weighted average, and (c) the novel application of the proposed methodology to solve the problem of transfer bar surface temperature prediction in a hot strip mill. The development of the proposed methodology uses the orthogonal least square (OLS) method to train the consequent parameters and the backpropagation (BP) method to train the antecedent parameters. This methodology dynamically changes the parameters of only the level alpha 0, minimizing some criterion functions as new information becomes available to each level alpha $k$. The precursor sets are type-2 fuzzy sets, the consequent sets are fuzzy centroids, the inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations, and the secondary membership functions are modeled as two Gaussians with uncertain standard deviation and the same mean. Based on the firing set of the level alpha 0, the proposed methodology calculates each firing set of each level alpha $k$ to dynamically construct and update the proposed EWH IT3 NSFLS-1 (OLS–BP) system. The proposed enhanced fuzzy system and the proposed hybrid learning algorithm were applied in a hot strip mill facility to predict the transfer bar surface temperature at the finishing mill entry zone using, as inputs, (1) the surface temperature measured by the pyrometer located at the roughing mill exit and (2) the time taken to translate the transfer bar from the exit of the roughing mill to the entry of the descale breaker of the finishing mill. Several fuzzy tools were used to make the benchmarking compositions: type-1 singleton fuzzy logic systems (T1 SFLS), type-1 adaptive network fuzzy inference systems (T1 ANFIS), type-1 radial basis function neural networks (T1 RBFNN), interval singleton type-2 fuzzy logic systems (IT2 SFLS), interval type-1 non-singleton type-2 fuzzy logic systems (IT2 NSFLS-1), type-2 ANFIS (IT2 ANFIS), IT2 RBFNN, general singleton type-2 fuzzy logic systems (GT2 SFLS), general type-1 non-singleton type-2 fuzzy logic systems (GT2 NSFLS-1), interval singleton type-3 fuzzy logic systems (IT3 SFLS), and interval type-1 non-singleton type-3 fuzzy systems (IT3 NSFLS-1). The experiments show that the proposed EWH IT3 NSFLS-1 (OLS–BP) system presented superior capability to learn the knowledge and to predict the surface temperature with the lower prediction error. Full article

Image de-noising is an important scheme that makes an image visually prominent and obtains enough useful information to produce a clear image. Many applications have been developed for effective noise suppression that produce good image quality. This study assumed that a residual image consisted of noise with edges produced by subtracting the original image with a low-pass-filter-smoothed image. The Moran statistics were then used to measure the variation in spatial information in residual images and we then used this information as feature data input into the Fuzzy C-means (FCM) algorithm. Three clusters were pre-assumed for FCM in this work: they were heavy, medium, and less noisy areas. The rates for each position partially belonged to each cluster determined using an FCM membership function. Each pixel in a noisy image was assumed in de-noising processing as a linear combination of the product of three de-noised images with membership functions in the same position. Average filters with different windows and a Gaussian filter were a priori applied to this noisy image to create three de-noised versions. The results showed that this scheme worked better than the non-adaptive smoothing. This scheme‘s performance was evaluated and compared to the bilateral filter and non-local means (NLM) using the peak signal to noise ratio (PSNR) and structure similarity index measure (SSIM). The developed scheme is a pilot study. Further future studies are needed on the optimized number of clusters and smoother versions used in linear combination. Full article

Accurately determining rock elastic modulus (EM) and uniaxial compressive strength (UCS) using laboratory methods requires considerable time and cost. Hence, the development of models for estimating the mechanical properties of rock is a very attractive alternative. The current research was conducted to predict the UCS and EM of sandstone rocks using quartz%, feldspar%, fragments%, compressional wave velocity (PW), the Schmidt hardness number (SN), porosity, density, and water absorption via simple regression, multivariate regression (MVR), K-nearest neighbor (KNN), support vector regression (SVR) with a radial basis function, the adaptive neuro-fuzzy inference system (ANFIS) using the Gaussian membership (GM) function, and the back-propagation neural network (BPNN) based on various training algorithms. The samples were categorized as litharenite and feldspathic litharenite. By increasing the feldspar% and quartz% and decreasing the fragments%, the static properties increased. The results of the statistical analysis showed that the SN and porosity have the greatest effect on the UCS and EM, respectively. Among the Levenberg–Marquardt (LM), Bayesian regularization, and Scaled Conjugate Gradient training algorithms using the BPNN method, the LM achieved the best results in forecasting the UCS and EM. The ideal obtained BPNN, using a trial-and-error process, contains four neurons in a hidden layer with eight inputs. All five models attained acceptable accuracy (correlation coefficient greater than 70%) for estimating the static properties. By comparing the methods, the ANFIS showed higher precision than the other methods. The UCS and EM of the samples can be determined with very high accuracy (R² > 99%). Full article

Many factors contribute to soil compaction. One of these factors is the pressure applied by tires and tillage tools. The aim of this study was to study soil compaction under two sizes of tractor tire, considering the effect of tire pressure and traffic on different depths of soil. Additionally, to predict soil density under the tire, an adaptive neuro-fuzzy inference system (ANFIS) was used. An ITM70 tractor equipped with a lister was used. Standard cylindrical cores were used and soil samples were taken at four depths of the soil inside the tire tracks. Tests were conducted based on a randomized complete-block design with three replications. We tested two types of narrow and normal tire using three inflation pressures, at traffic levels of 1, 3 and 5 passes and four depths of 10, 20, 30 and 40 cm. A grid partition structure and four types of membership function, namely triangular, trapezoid, Gaussian and General bell were used to model soil compaction. Analysis of variance showed that tire size was significant on soil density change, and also, the binary effect of tire size on depth and traffic were significant at 1%. The main effects of tire pressure, traffic and depth were significant on soil compaction at 1% level of significance for both tire types. The inputs of the ANFIS model included tire type, depth of soil, number of tire passes and tire inflation pressure. To evaluate the performance of the model, the relative error (ε) and the coefficient of explanation (R²) were used, which were 1.05 and 0.9949, respectively. It was found that the narrow tire was more effective on soil compaction such that the narrow tire significantly increased soil density in the surface and subsurface layers. Full article