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A thermal aging experiment was conducted for oil-paper insulation to evaluate the insulation's response under thermal stress. Oil-papers at different aging stages were used to create oil-paper bound gas cavity specimens, which were used to collect data on degrees of polymerization (DP) and partial discharge (PD). Evaluation of oil-paper aging was based on statistical operators of PD and factor analysis was used to extract the principle parameters of PD. Three types of fuzzy clustering approaches were used to classify PD of aged oil-paper: the fuzzy c-means, the kernel fuzzy c-means, and the possibilistic fuzzy c-means. The clustering results showed that the possibilistic fuzzy c-means clustering was capable of classifying PD of oil-paper bound gas cavity specimens. The factor analysis method was also verified to be helpful in fuzzy clustering of PD data samples by reducing number of parameters.

It is shown that when two images are registered by cross-correlating one image with a functional of the other image the minimum registration error variance results when the operation performed cofresponds to that of matched filtering.

IEEEWhile the zeitgeist of today prescribes localization as a key to eliminate the excessive transportation for manufacturing firms, firm-level practical and workable guidelines that go beyond maxims are scant. Laden with analytical methods, this paper offers a phronetic, customizable framework based on Lean Six Sigma (LSS). The framework mimics Define-Measure-Analyze-Improve-Control (DMAIC) process. The early phases of the framework, ex-ante, prescribe the use of a variety tools and techniques from Lean Six sigma (LSS) and employ fuzzy analytic hierarchy process (FAHP) to extract the vital few root-causes that may impede localization. The latter phases suggest the use of design of experiments (DOE) to evaluate the root-causes, ex-post. The paper outlines a clear and established procedure and demonstrates each analytical phase using evidence from a two-year real-world application in steel industry.

The sampled-data stabilization problem of nonlinear stochastic singular systems on the basis of the Takagi-Sugeno (T-S) fuzzy models under variable samplings is discussed in this paper. A new piecewise Lyapunov-Krasovskii (L-K) functional is constructed, which can capture the actual sampling mode's available features more fully, and an enhanced input delay method is presented. By using the proper augmented scheme based on the auxiliary vector function, the new mean square admissibility criteria are derived by making good use of the convex combination techniques and the free weighting matrix approach. It is shown that the obtained results in this paper contain less conservatism when compared with the existing ones. The superiority and correctness of our results are verified by an application example of a truck-trailer model.

Best-worst method (BWM) has attracted increasing attention. It has been generalized to different fuzzy environments and applied to various real-life decision problems. This paper develops a new intuitionistic fuzzy (IF) best-worst method (IFBWM) for multi-criteria decision-making (MCDM). When a decision maker (DM) makes comparisons, there may be some hesitancies. Thus, the reference comparisons are represented as intuitionistic fuzzy values (IFVs), the Best-to-Others vector and the Others-to-Worst vector are IF vectors. According to the multiplicative consistency of intuitionistic fuzzy preference relation, this paper gives the consistency equations and views them as IF equations. The derivation of optimal IF weights of criteria is formulated as an IF decision-making problem. Thereby, a mathematical programming model is constructed to assure that the derived optimal IF weights of criteria is a normalized IF weight vector. Depending on the risk preference of DM, four linear programming models are presented to obtain the optimal IF weights based on the constructed mathematical programming model for the optimistic DM, the pessimistic DM and the neutral DM, respectively. Furthermore, this paper investigates the process of improving the consistency. Several examples are demonstrated to show the application and effectiveness of the proposed IF BWM.

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via state-dependent switching rules. Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid. These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type. In some cases, the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function. In this paper, we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently. The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size. Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size, i.e., a purely numerical method and a numerical-analytical one. In the former, both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities. The latter is established on a principle that the attractiveness of a set implies its invariance. Thus, the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension. Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

This paper presents a complete, accurate, and efficient solution for the Perspective-n-Line (PnL) problem. Generally, the camera pose can be determined from $N \geq 3$ 2D-3D line correspondences. The minimal problem ( $N= 3$ ) and the least-squares problem ( $N > 3$ ) are generally solved in different ways. This paper shows that a least-squares PnL problem can be transformed into a quadratic equation system that has the same form as the minimal problem. This leads to a unified solution for the minimal and least-squares PnL problems. We adopt the Gram-Schmidt process and a novel hidden variable polynomial solver to increase the numerical stability of our algorithm. Experimental results show that our algorithm is more accurate and robust than the state-of-the-art least-squares algorithms [1] – [4] and is significantly faster. Moreover, our algorithm is more stable than previous minimal solutions [3] , [5] , [6] with comparable runtime.

Accurate diagnosis of corn crop diseases is a complex challenge faced by farmers during the growth and production stages of corn. In order to address this problem, this paper proposes a method based on K-means clustering and an improved deep learning model for accurately diagnosing three common diseases of corn leaves: gray spot, leaf spot, and rust. First, to diagnose three diseases, use the K-means algorithm to cluster sample images and then feed them into the improved deep learning model. This paper investigates the impact of various k values (2, 4, 8, 16, 32, and 64) and models (VGG-16, ResNet18, Inception v3, VGG-19, and the improved deep learning model) on corn disease diagnosis. The experiment results indicate that the method has the most significant identification effect on 32-means samples, and the diagnostic recall of leaf spot, rust, and gray spot disease is 89.24 %, 100 %, and 90.95 %, respectively. Similarly, VGG-16 and ResNet18 also achieve the best diagnostic results on 32-means samples, and their average diagnostic accuracy is 84.42% and 83.75%. In addition, Inception v3 (83.05%) and VGG-19 (82.63%) perform best on the 64-means samples. For the three corn diseases, the approach cited in this paper has an average diagnostic accuracy of 93%. It has a more significant diagnostic effect than the other four approaches and can be applied to the agricultural field to protect crops.

Objective: This paper aims at proposing a new machine-learning based model to improve the calculation of mealtime insulin boluses (MIB) in type 1 diabetes (T1D) therapy using continuous glucose monitoring (CGM) data. Indeed, MIB is still often computed through the standard formula (SF), which does not account for glucose rate-of-change ( $\Delta$ G), causing critical hypo/hyperglycemic episodes. Methods: Four candidate models for MIB calculation, based on multiple linear regression (MLR) and least absolute shrinkage and selection operator (LASSO) are developed. The proposed models are assessed in silico , using the UVa/Padova T1D simulator, in different mealtime scenarios and compared to the SF and three $\Delta$ G-accounting variants proposed in the literature. An assessment on real data, by retrospectively analyzing 218 glycemic traces, is also performed. Results: All four tested models performed better than the existing techniques. LASSO regression with extended feature-set including quadratic terms (LASSO $_Q$ ) produced the best results. In silico, LASSO $_Q$ reduced the error in estimating the optimal bolus to only 0.86 U (1.45 U of SF and 1.36–1.44 U of literature methods), as well as hypoglycemia incidence (from 44.41% of SF and 44.60–45.01% of literature methods, to 35.93%). Results are confirmed by the retrospective application to real data. Conclusion: New models to improve MIB calculation accounting for CGM- $\Delta$ G and easy-to-measure features can be developed within a machine learning framework. Particularly, in this paper, a new LASSO $_Q$ model was developed, which ensures better glycemic control than SF and other literature methods. Significance: MIB dosage with the proposed LASSO $_Q$ model can potentially reduce the risk of adverse events in T1D therapy.

This paper aims to give a design strategy on the prescribed performance $ {H_{\infty }}$ tracking control problem for a class of strict-feedback stochastic nonlinear systems based on the backstepping technique. Generally, by using the backstepping design method, the stochastic nonlinear systems can only be made to be bounded in probability and it is difficult to achieve the $ {H_{\infty }}$ performance criterion due to the positive constant term appeared in the stability analysis. Thus, a novel concept with regard to the bounded- $ {H_{\infty }}$ performance is proposed in this paper to overcome the design difficulty. By using the new concept and the adaptive neural network technique as well as Gronwall inequality, an adaptive neural network prescribed performance bounded- $ {H_{\infty }}$ tracking controller is designed. Therein, neural networks are used to approximate the unknown packaged nonlinear functions. The assumption that the approximation errors of neural networks are square-integrable in some literature is eliminated. The designed controller guarantees that all the signals in the closed-loop stochastic nonlinear systems are bounded in probability, the tracking error is constrained into an adjustable neighborhood of the origin with the prescribed performance bounds, and the controlled system has a given $ {H_{\infty }}$ disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.

Computing the centroid of an interval type-2 fuzzy set (IT2 FS) is an important type-reduction method. The aim of this paper is to develop a new method to calculate the centroid of an IT2 FS when the problems of centroid computation of an IT2 FS are continuous. For the continuous centroid computation problems, the structures of optimal solutions are strictly proven from mathematics for the first time in this paper. Furthermore, we also prove that the structures of the optimal solutions are unique in the sense of almost everywhere equal, i.e., if there are two optimal solutions $f_1(x)$ and $f_2(x)$ , the Lebesgue measure of $\{x|f_1(x)\neq f_2(x)\}$ is equal to 0. Subsequently, a combinatorial iterative (CI) method is proposed to solve the roots of the sufficiently differentiable objective functions. It is proven that the convergence of the proposed iterative method is at least sixth order. Based on the proposed iterative method, two algorithms, called CI algorithms, are devised to compute the centroid of an IT2 FS. The efficiencies of CI algorithms are demonstrated by comparing the continuous Karnik–Mendel algorithms and the Hallye's methods with the CI algorithms through three numerical examples.

This paper is devoted to make a framework for studying a class of uncertain differential equations called Z -differential equations. In order to achieve the purpose, we first introduce four basic operations on $Z^{+}$ -numbers based on semigranular function. Then, the limit and continuity concepts of a Z -number-valued function are given, under a definition of a metric on the space of $Z^{+}$ -numbers. Moreover, the concepts of Z -differentiability, Z -integral, and Z -Laplace transform of a Z -number-valued function are introduced. In addition, by giving some theories proved in this paper, a basis for calculus— Z -calculus—is established. We further give theories based on which existence and uniqueness of Z -differential equations are investigated. A conceptual unity between Z -differential equations and $Z^{+}$ -numbers is also shown. The conceptual unity demonstrates that a Z -differential equation may be expressed as a bimodal differential equation combining a fuzzy differential equation (FDE) and a random differential equation. Moreover, the concept of a bimodal cut called $ (s, \mu)$ -cut is introduced and its relation to other new concepts such as acceptable time and acceptable information area is explained. Using an example, the application of Z -differential equations in medicine is clarified. It is demonstrated that Z -differential equations outperform FDEs in making a decision under uncertainty.

This paper is concerned with the design of $H_{\infty }$ observers for fuzzy system with immeasurable state variables via a new Lyapunov function. By decomposing the space of premise variables into crisp regions and fuzzy regions, piecewise fuzzy $H_{\infty }$ observers are established at different instants to cope with the challenges caused by the mismatch of the premise variables and exogenous disturbances. Based on the proposed new Lyapunov functions that depend on the different regions where the premise variables are located, sufficient conditions in terms of linear matrix inequalities are obtained to guarantee the stability and desired performance of the error systems. Finally, a simulation example is provided to show that the new design technology proposed in this paper achieves better $H_{\infty }$ performance than the existing design methods.

This paper is devoted to decomposing one given image into the cartoon and texture. The cartoon parts correspond to the main large objects in the image, and the textural parts contain fine scale details. Mathematically, these two components should belong to the different function spaces corresponding to different norms. In most variational models of image decomposition, the cartoon parts are described by the total variation norm and the texture parts are characterized by its dual norm. Using these methods, the cartoon and texture can be separated from the original image. Some structures, such as edges, are well preserved in the cartoon image. However, as far as we know, none of these methods considers the geometric characteristics information of the texture position in the separated cartoon images. That is, the geometrical information in those separated cartoon images may have been destroyed, which can be seen from the experiments in this paper. To maintain these geometrical characteristics, we introduce one smoothed vector field and let it approximate to the negative gradient direction of the cartoon image, and then for the smoothed vector field, we let it belong to the Lebesgue space, thus a new variational decomposition model is proposed. The corresponding alternating direction method is discussed in detail. Experimental results are reported to show the visual qualities compared with other methods.

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two stability criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

Background . The most common and successful technique for signal denoising with non-stationary signals, such as electroencephalogram (EEG) and electrocardiogram (ECG) is the wavelet transform (WT). The success of WT depends on the optimal configuration of its control parameters which are often experimentally set. Fortunately, the optimality of the combination of these parameters can be measured in advance by using the mean squared error (MSE) function. Method . In this paper, five powerful metaheuristic algorithms are proposed to find the optimal WT parameters for EEG signal denoising which are harmony search (HS), $\beta $ -hill climbing ( $\beta $ -hc), particle swarm optimization (PSO), genetic algorithm (GA), and flower pollination algorithm (FPA). It is worth mentioning that this is the initial investigation of using optimization methods for WT parameter configuration. This paper then examines which efficient algorithm has obtained the minimum MSE and the best WT parameter configurations. Result . The performance of the proposed algorithms is tested using two standard EEG datasets, namely, Kiern’s EEG dataset and EEG Motor Movement/Imagery dataset. The results of the proposed algorithms are evaluated using five common criteria: signal-to-noise-ratio (SNR), SNR improvement, mean square error (MSE), root mean square error (RMSE), and percentage root mean square difference (PRD). Interestingly, for almost all evaluating criteria, FPA achieves the best parameters configuration for WT and empowers this technique to efficiently denoise the EEG signals for almost all used datasets. To further validate the FPA results, a comparative study between the FPA results and the results of two previous studies is conducted, and the findings favor to FPA. Conclusion . In conclusion, the results show that the proposed methods for EEG signal denoising can produce better results than manual configurations based on ad hoc strategy. Therefore, using metaheuristic approaches to optimize the parameters for EEG signals positively affects the denoising process performance of the WT method.

Industrial data usually have nonlinear or multimodal characteristics which do not meet the data assumptions of statistics in principal component analysis (PCA). Therefore, PCA has a lower fault detection rate in industrial processes. Aiming at the above limitations of PCA, a fault detection method using principal component difference based on k-nearest neighbors (Diff-PCA) is proposed in this paper. First, find the k nearest neighbors set of each sample in the training data set and calculate its mean vector. Second, build an augmented vector using each sample and its corresponding mean vector. Third, calculate the loading matrix and score matrix using PCA. Next, calculate the estimated scores using the mean vector of each sample and missing data imputation technique for PCA. At last, build two new statistics using the difference between the real scores and estimated scores to detect faults. In addition, the fault diagnosis method based on contribution plots of monitored variables is also proposed in this paper. In Diff-PCA, the difference skill can eliminate the impact of the nonlinear and multimodal structure on fault detection. Meanwhile, the monitored subspaces by the two new statistics are different from that by T2 and SPE in PCA. The efficiency of the proposed strategy is implemented in two numerical cases (nonlinear and multimode) and the Tennessee Eastman (TE) processes. The fault detection results indicate that Diff-PCA outperforms the conventional PCA, Kernel PCA, dynamic PCA, principal component-based k nearest neighbor rule and k nearest neighbor rule.

This paper proposes a novel Lyapunov stabilization analysis of discrete-time polynomial-fuzzy-model-based control systems with time delay under positivity constraint. The polynomial fuzzy model is constructed to describe the dynamics of a nonlinear discrete-time system with time delay. A model-based polynomial fuzzy controller is designed using nonparallel distributed compensation technique to stabilize the system while driving the system states to positive using the positivity constraints. The Lyapunov stability and positivity conditions are formulated as sum-of squares. To relax the conservativeness of the obtained stability results, two main methods are proposed in this paper: first, the piecewise linear membership functions (PLMFs) are used to introduce the approximate error between piecewise and the original membership functions into the stability analysis; and second, introduce the boundary information of the premise variables into the stability analysis since the premise variables hold rich nonlinearity information. A numerical example is given to demonstrate the effectiveness of the proposed approach.

In this paper, sampled-data control is proposed to stabilize the nonlinear system, which is expressed as a Takagi–Sugeno (T–S) fuzzy submodels. Based on suitable Lyapunov– Krasovskii functional (LKF) along with new weighted integral inequalities, the sufficient conditions are derived in terms of linear matrix inequalities, which ensure the exponential stability of the proposed closed loop T–S fuzzy system. The peculiarity of this paper is: as novel integral inequalities and LKF are proposed, less conservative results are provided when compared to existing results. Besides that, wind energy conversion systems, chaotic systems, and an inverted pendulum are validated with derived sufficient conditions. The corresponding simulation results show the merit of the proposed results over the existing works.

This paper investigates the stability problem for time-varying delay systems. To obtain a larger delay bound, this paper uses the second-order canonical Bessel-Legendre &#x0028 BL &#x0029 inequality. Secondly, using four couples of integral terms in the augmented Lyapunov-Krasovskii function &#x0028 LKF &#x0029 to enhance the relationship between integral functionals and other vectors. Furthermore, unlike the construction of the traditional LKF, a novel augmented LKF is constructed with two new delay-product-type terms, which adds more state information and leads to less conservative results. Finally, two numerical examples are provided to demonstrate the effectiveness and the significant improvement of the proposed stability criteria.

This paper is concerned with the global nonfragile Mittag-Leffler synchronization and the global synchronization in finite time for fractional-order discontinuous neural networks, where activation functions are discontinuous at 0, or modeled as a local Hölder functions with the nonlinear growth property in a neighborhood of 0. First, two lemmas concerned with the convergence with respect to an absolutely continuous function are developed. Second, a new property, which introduces an inequality of the fractional derivative for the variable upper limit integral with respect to the nonsmooth integrable function, is presented and applied in the synchronization results' analysis. In addition, under the fractional Filippov differential inclusion framework, by utilizing the Lur'e Postnikov-type Lyapunov functional, nonsmooth analysis method, and the convergence properties developed in this paper, the synchronization conditions are derived in the form of linear matrix inequalities. Moreover, the upper bound of the setting time for the global nonfragile synchronization in finite time is calculated accurately. Finally, two illustrations are presented to verify the correctness of the theoretical results.

Type-2 fuzzy sets (T2FSs) were introduced by L. A. Zadeh in 1975 as an extension of type-1 fuzzy sets (T1FSs). In this extension, the degree to which an element belongs to a set is just a label of the linguistic variable “TRUTH,” which allows to represent reality in a more appropriate way. On the other hand, negations play an essential role within fuzzy sets theory. In fact, they are necessary in order to obtain, for example, complements of fuzzy sets, dual of a t-norm or a t-conorm, entropies, implications, as well as to study the possible contradictions appearing in a fuzzy system. However, meanwhile negations on [0, 1] (set of the membership degrees of a fuzzy set) have been deeply studied throughout the literature, the same has not happened with the negations on ${\bf M}$ = $\text{Map} \;([\text{0}, \text{1}],[\text{0}, \text{1}])$ , set of functions from [0, 1] to [0, 1] (and also set of the membership degrees of a T2FS), and so many aspects of the negations on ${\bf M}$ have not yet been investigated. In a previous paper, the axioms that an operation must satisfy to be considered a negation or a strong negation on a bounded partially ordered set were established. A family of strong negations on L and set of normal and convex functions of ${\bf M}$ were also presented. Moreover, let us note that the main characteristic of fuzzy systems is just the flexibility in order to be able to represent knowledge according to each situation, offering different models among which the expert can choose the one that best suits his/her criteria. Thus, it seems useful to find broad sets of negations in ${\bf M}$ and in L , which, as far as we know, have not been done by other researchers. According to these ideas, in this paper, the authors first present new negations and strong negations on L , and then show, for the first time, some negations on ${\bf M}$ with respect to each of the two partial orders defined in this set.

This paper provides the stability analysis for a model-free action-dependent heuristic dynamic programing (HDP) approach with an eligibility trace long-term prediction parameter ( $\lambda $ ). HDP( $\lambda $ ) learns from more than one future reward. Eligibility traces have long been popular in Q-learning. This paper proves and demonstrates that they are worthwhile to use with HDP. In this paper, we prove its uniformly ultimately bounded (UUB) property under certain conditions. Previous works present a UUB proof for traditional HDP [HDP( $\lambda =0$ )], but we extend the proof with the $\lambda $ parameter. By using Lyapunov stability, we demonstrate the boundedness of the estimated error for the critic and actor neural networks as well as learning rate parameters. Three case studies demonstrate the effectiveness of HDP( $\lambda $ ). The trajectories of the internal reinforcement signal nonlinear system are considered as the first case. We compare the results with the performance of HDP and traditional temporal difference [TD( $\lambda $ )] with different $\lambda $ values. The second case study is a single-link inverted pendulum. We investigate the performance of the inverted pendulum by comparing HDP( $\lambda $ ) with regular HDP, with different levels of noise. The third case study is a 3-D maze navigation benchmark, which is compared with state action reward state action, Q( $\lambda $ ), HDP, and HDP( $\lambda $ ). All these simulation results illustrate that HDP( $\lambda $ ) has a competitive performance; thus this contribution is not only UUB but also useful in comparison with traditional HDP.

This paper presents an improved method for reducing high-order dynamical system models via clustering. Agglomerative hierarchical clustering based on performance evaluation (HC-PE) is introduced for model order reduction. This method computes the reduced order denominator of the transfer function model by clustering system poles in a hierarchical dendrogram. The base layer represents an $n{\textrm {th}}$ order system, which is used to calculate each successive layer to reduce the model order until finally reaching a second-order system. HC-PE uses a mean-squared error (MSE) in every reduced order, which modifies the pole placement process. The coefficients for the numerator of the reduced model are calculated by using the Pade approximation (PA) or alternatively a genetic algorithm (GA). Several numerical examples of reducing techniques are taken from the literature to compare with HC-PE. Two classes of results are shown in this paper. The first sets are single-input single-output models that range from simple models to 48th order systems. The second sets of experiments are with a multi-input multioutput model. We demonstrate the best performance for HC-PE through minimum MSEs compared with other methods. Furthermore, the robustness of HC-PE combined with PA or GA is confirmed by evaluating the third-order reduced model for the triple-link inverted pendulum model by adding a disturbance impulse signal and by changing model parameters. The relevant stability proofs are provided in Appendixes A and B in the supplementary material. HC-PE with PA slightly outperforms its performance with GA, but both approaches are attractive alternatives to other published methods.

This paper deals with the concept and application of general three-dimensional (3-D) type-2 fuzzy logic systems in the polar frame (G3DT2FLS). 1 1 Because many acronyms are used in this paper, they are summarized in Table I for the convenience of the reader. We focused on the automatic membership function (MF) Generator, general type-2 polar fuzzy membership, new geometric operators in polar frame, inference consisting of fuzzy 3-D polar rules and antecedents/consequents $\theta$ -slice and $\alpha$ -planes. The cubic smoothing spline is introduced to generate the upper and lower MFs according to the information theory. Three indices of compactness, smoothness, and entropy are employed for tuning of MFs. A measure of ultrafuzziness, min, max, equal, and reduced ultrafuzziness are suggested for the polar method. Additionally, the set theoretic operations of 3-D type-2 fuzzy sets in the polar frame are discussed. We also prove the join, meet, centroid, and type-reduction operations in the polar frame. Several rule sets are given to show the usefulness and complexity of the proposed method. The performance of the partial general 3D polar type-2 fuzzy logic system showed linear growth as the number of rules was increased. Computation time tests showed that the algorithm reduces the computation time by a maximum of 67% compared with discrete MF and is shown by an extreme 98% for the geometric procedure. These results indicate significant improvements in computation time for the spline interpolation over the existing methods.

Ordered weighted averaging (OWA) operators, a family of aggregation functions, are widely used in human decision-making schemes to aggregate data inputs of a decision maker's choosing through a process known as OWA aggregation. The weight allocation mechanism of OWA aggregation employs the principle of linear ordering to order data inputs after the input variables have been rearranged. Thus, OWA operators generally cannot be used to aggregate a collection of $n$ inputs obtained from any given convex partially ordered set (poset). This poses a problem since data inputs are often obtained from various convex posets in the real world. To address this problem, this paper proposes methods that practitioners can use in real-world applications to aggregate a collection of $n$ inputs from any given convex poset. The paper also analyzes properties related to the proposed methods, such as monotonicity and weighted OWA aggregation on convex posets.

Mental workload assessment is essential for maintaining human health and preventing accidents. Most research on this issue is limited to a single task. However, cross-task assessment is indispensable for extending a pre-trained model to new workload conditions. Because brain dynamics are complex across different tasks, it is difficult to propose efficient human-designed features based on prior knowledge. Therefore, this paper proposes a concatenated structure of deep recurrent and 3D convolutional neural networks (R3DCNNs) to learn EEG features across different tasks without prior knowledge. First, this paper adds frequency and time dimensions to EEG topographic maps based on a Morlet wavelet transformation. Then, R3DCNN is proposed to simultaneously learn EEG features from the spatial, spectral, and temporal dimensions. The proposed model is validated based on the EEG signals collected from 20 subjects. This paper employs a binary classification of low and high mental workload across spatial n-back and arithmetic tasks. The results show that the R3DCNN achieves an average accuracy of 88.9%, which is a significant increase compared with that of the state-of-the-art methods. In addition, the visualization of the convolutional layers demonstrates that the deep neural network can extract detailed features. These results indicate that R3DCNN is capable of identifying the mental workload levels for cross-task conditions.

China's soybean supply and demand are seriously imbalanced. It is crucial to improve the level of soybean breeding. Hundred-grain weight is one of the most essential phenotypic parameters for crop breeding. Accurate soybean seed counting is a key step for 100-grain weight. There are several seed counting methods, which have their own limitations one way or the other. Among these, manual counting is time-consuming, electronic automatic seed counter devices are expensive and their counting speed is very slow, and the traditional digital image processing techniques are not suitable for seed counting based on individual pod images. This paper attempted to develop a method that would combine the density estimation-based methods and the convolution neural network (CNN)-based methods to accurately estimate the seed count from an individual soybean pod image with a single perspective. In this paper, we first introduced a new large-scale seed counting dataset, named Soybean-pod. The dataset contains 500 annotated pod images with a total of 32 126 seeds and is the largest annotated dataset for soybean seed counting so far. Simultaneously, we used annotation information to generate a ground-truth density map by convolving a Gaussian kernel and, then, devised a simple but effective method that would elucidate pod images to a seed density map using a two-column CNN (TCNN) and thus accomplish seed counting ultimately. We conducted relevant experiments from three aspects on the new dataset to verify the effectiveness of our model and method, which provided 13.21 mean absolute error (MAE) and 17.62 mean squared error (mse). In addition, our research results showed that deep learning techniques can be easily adapted to precision tasks for plant phenotyping and breeding purposes.

Machine learning (ML) is a fast-growing topic that enables the extraction of patterns from varying types of datasets, ranging from medical data to financial data. However, the application of the ML methodology to understand the key characteristics of highly cited research articles has not been thoroughly investigated, despite the potential practical guidance that ML can provide for researchers during the publication process. To address this research gap, an ML algorithm known as principal component (PC) analysis is used to detect patterns in highly and lowly cited papers. In this paper, eight features (number of citations, number of views, number of characters with no spaces, number of figures, number of tables, number of equations, number of authors, and title length) are extracted from highly and lowly cited papers, leading to eight PCs (PC1-PC8). PC1 shows that the numbers of citations are positively correlated with the character count and negatively correlated with the title length. PC2 shows that the number of tables is positively correlated with the title length. PC3 shows that the number of figures is positively correlated with the number of tables. PC4-PC8 rank the importance of individual features in the descending order: number of equations, number of characters with no spaces, number of figures, number of views, and then the number of authors. The results of the ML analysis provide interesting and valuable tips for researchers, students, and all academic and non-academic writers who are seeking to improve their citation rates.

This paper proposes a novel adaptive sliding mode control &#x0028 SMC &#x0029 method for synchronization of non-identical fractional-order &#x0028 FO &#x0029 chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller &#x0028 ASMC &#x0029. Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization &#x0028 PSO &#x0029 is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

In the Ziegler-Nichols &#x02BC s method of reaction curve, the proportional gain should be calculated as an inverse relation of the plant steady-state gain. One of the reasons behind this is to avoid an excessively high loop gain, which can jeopardize many required characteristics of the closed loop. However, many reports, scientific papers and books have been neglecting such gain compensation in the tuning formulae. This brief presents a comprehensive discussion about such uncompensated tuning rules. The main paper finding is that either the stability margin or the disturbance rejection is reduced in this case. A theoretical analysis is performed to obtain the main result. Moreover, a consistent simulation study is also performed to show the impact of the lack of compensation on performance.

This paper is concerned with the stability and robust stability of switched positive linear systems &#x0028 SPLSs &#x0029 whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.

In the multiple-attribute group decision-making (MAGDM), the decision objective is to obtain a complete ranking of the alternatives from best to worst. In the real world, however, obtaining such a complete ranking of alternatives is very time-consuming, and it is sometimes not necessary. There are many MAGDM problems that we need to assign two rank levels only, so as to create a ranking of one subset of alternatives above another subset. This type of MAGDM problem is called a 2-rank MAGDM problem. This paper investigates the 2-rank MAGDM problem under the multigranular linguistic context, and proposes a 2-rank consensus reaching framework with the minimum adjustments. In the consensus reaching framework, a 2-rank selection process is proposed to find the individual and collective 2-rank preference vectors, and a 2-rank consensus reaching process with the minimum adjustments is put forwarded to help decision makers achieve a consensus. To demonstrate the consensus efficiency of the 2-rank consensus reaching model, a comparison analysis between our proposal and the classical MAGDM models is presented. The main improvement of this paper is to provide a flexible framework to constitute a better approximate decision model to real-world MAGDM problems.

The uncertain variable is used to model a quantity under human uncertainty, and the weighted $k$ -out-of- $n$ system is used to model a system of $n$ components, which functions if and only if the total weights of functioning components is greater than $k$ . Considering the human uncertainty in operating the system, this paper introduces the uncertain variable to the weighted $k$ -out-of- $n$ system, and proposes a concept of uncertain weighted $k$ -out-of- $n$ system. Some formulas are derived to calculate the reliability index of such a system. As a generalization, this paper also studies an uncertain weighted $k$ -out-of- $n$ system whose weights are estimated by experts and modeled by uncertain variables instead of crisp numbers. In addition, this paper analyzes the importance measure of the components in the uncertain weighted $k$ -out-of- $n$ systems.

In this paper, a novel electroencephalographic (EEG)-based method is introduced for the quantification of brain-electrical connectivity changes over a longitudinal evaluation of mild cognitive impaired (MCI) subjects. In the proposed method, a dissimilarity matrix is constructed by estimating the coupling strength between every pair of EEG signals, Hierarchical clustering is then applied to group the related electrodes according to the dissimilarity estimated on pairs of EEG recordings. Subsequently, the connectivity density of the electrodes network is calculated. The technique was tested over two different coupling strength descriptors: wavelet coherence (WC) and permutation Jaccard distance (PJD), a novel metric of coupling strength between time series introduced in this paper. Twenty-five MCI patients were enrolled within a follow-up program that consisted of two successive evaluations, at time T0 and at time T1, three months later. At T1, four subjects were diagnosed to have converted to Alzheimer's Disease (AD). When applying the PJD-based method, the converted patients exhibited a significantly increased PJD (p < 0.05), i.e., a reduced overall coupling strength, specifically in delta and theta bands and in the overall range (0.5-32 Hz). In addition, in contrast to stable MCI patients, converted patients exhibited a network density reduction in every subband (delta, theta, alpha, and beta). When WC was used as coupling strength descriptor, the method resulted in a less sensitive and specific outcome. The proposed method, mixing nonlinear analysis to a machine learning approach, appears to provide an objective evaluation of the connectivity density modifications associated to the MCI-AD conversion, just processing noninvasive EEG signals.

This paper investigates the finite-time event-triggered $\mathcal{H}_{\infty }$ control problem for Takagi–Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this paper is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closed-loop system is finite-time bounded and satisfies a prescribed $\mathcal{H}_{\infty }$ performance level, but also the communication burden is reduced. First, a sufficient condition is established for the finite-time bounded $\mathcal{H} _{\infty }$ performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the method of the desired controller design is presented. Two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method.

In this paper, intuitionistic fuzzy spiking neural P (IFSNP) systems as a variant are proposed by integrating intuitionistic fuzzy logic into original spiking neural P systems. Compared with a common fuzzy set, intuitionistic fuzzy set can more finely describe the uncertainty due to its membership and non-membership degrees. Therefore, IFSNP systems are very suitable to deal with fault diagnosis of power systems, specially with incomplete and uncertain alarm messages. The fault modeling method and fuzzy reasoning algorithm based on IFSNP systems are discussed. Two examples are used to demonstrate the availability and effectiveness of IFSNP systems for fault diagnosis of power systems. Case studies involve single fault, complex fault, and multiple faults with protection device failures and incorrect tripping signals. National Natural Science Foundation of China No. 61472328 Chunhui Project Foundation of the Education Department of China Z2016143 Chunhui Project Foundation of the Education Department of China Z2016148 Research Foundation of the Education Department of Sichuan Province, China 17TD0034. Paper no. TSG-01301-2016

Tear film instability is one of the major characteristics of dry eye syndrome. However, traditional diagnostic methods, such as the fluorescein tear film break-up time (FTBUT) test, are limited by the subjective interpretation of results. The test needs to manually identify break-up areas in the fluorescent image, thus producing variable diagnosis results. This paper proposes an automatic method to detect the fluorescent tear film break-up area using a deep convolutional neural network (CNN) model and to define its appearance as CNN-BUT. A digital slit-lamp recorded the standard FTBUT measurement for each of 80 study participants. Fifty participants were used to train the CNN model to identify the tear film break-up area, while the remaining 30 were used to validate the proposed CNN-BUT test. Among six normal controls and 24 dry eye patients enrolled in this paper, CNN-BUT was significantly lower in dry eye patients ( ${p} ). The correlation between CNN-BUT and FTBUT was also significant ( ${r} =0.9$ ; ${p} ). Using 5 s as the cutoff value, the CNN-BUT offered acceptable sensitivity and specificity to screen dry eye patients (0.83 and 0.95, respectively). These results indicate that CNN-BUT may be used to evaluate tear film stability and to assess the status of dry eye syndrome automatically.

© 2012 IEEE. Random forests (RFs) are recognized as one type of ensemble learning method and are effective for the most classification and regression tasks. Despite their impressive empirical performance, the theory of RFs has yet been fully proved. Several theoretically guaranteed RF variants have been presented, but their poor practical performance has been criticized. In this paper, a novel RF framework is proposed, named Bernoulli RFs (BRFs), with the aim of solving the RF dilemma between theoretical consistency and empirical performance. BRF uses two independent Bernoulli distributions to simplify the tree construction, in contrast to the RFs proposed by Breiman. The two Bernoulli distributions are separately used to control the splitting feature and splitting point selection processes of tree construction. Consequently, theoretical consistency is ensured in BRF, i.e., the convergence of learning performance to optimum will be guaranteed when infinite data are given. Importantly, our proposed BRF is consistent for both classification and regression. The best empirical performance is achieved by BRF when it is compared with state-of-the-art theoretical/consistent RFs. This advance in RF research toward closing the gap between theory and practice is verified by the theoretical and experimental studies in this paper.

This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

In this paper, a class of uncertain linear dynamical systems called fuzzy fractional linear dynamical systems is investigated. The aim is to find control inputs to keep the states of the fuzzy fractional dynamical systems near the zero in an optimal manner. The optimality criterion is in a form of a granular fuzzy integral whose integrand is a quadratic function of the state variables and control inputs. The fuzzy fractional dynamical system is described using fuzzy fractional differential equations (FFDEs). In order to achieve the aim, an effective approach for solving FFDEs should be at disposal. Due to some restrictions imposed by the previous approaches dealing with FFDEs, a new approach is proposed. The proposed approach is based on the granular derivative and the so-called relative-distance-measure fuzzy interval arithmetic. New definitions of fuzzy fractional derivatives and integral called left and right granular Riemann–Liouville fuzzy fractional derivatives, left and right granular Caputo fuzzy fractional derivatives, and the left and right granular fuzzy fractional integral are also presented. In addition, the concepts of granular fuzzy partial derivative and granular fuzzy chain rule are introduced. By the approximations of the granular fuzzy fractional integral and the granular Caputo fuzzy fractional derivative, the approximation solution to the FFDEs is obtained. Consequently, based on the new concepts and theorems, the solution to the fuzzy fractional quadratic regulator problem is given by a theorem. This paper closes with an example of regulating the motion of Boeing 747 in longitudinal direction with the presence of uncertainty in the initial conditions and the coefficients.

Till now, there are lots of stability and stabilization results about Takagi–Sugeno (T–S) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov–Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T–S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov–Krasovskii functional in this paper depends not only on the integral variable, but also on the membership functions, and thus, the information of the time derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time derivative of membership, a number of controllers are designed according to their sign, and then, a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.

The law of importation is an important property of fuzzy implication functions with interesting applications in approximate reasoning and image processing. This property has been extensively studied and some open problems have been proposed in the literature. In particular, in this paper, we partially solve an open problem related to this property posed some years ago. Specifically, given a fixed uninorm, all fuzzy implication functions that satisfy the law of importation with respect to this uninorm, and having an $\alpha$ -section that is a continuous negation, are characterized. This characterization is specially detailed for the case of uninorms lying in each one of the most usual classes of uninorms. This is done in two different papers, this paper and the forthcoming paper (S. Massanet, D. Ruiz-Aguilera, and J. Torrens, “Characterization of a class of fuzzy implication functions satisfying the law of importation with a fixed uninorm—Part II,” IEEE Trans. Fuzzy Syst., to be published). In particular, in this paper the case of uninorms in $\mathcal {U}_{\min }$ is solved, whereas the cases where the uninorm is in the other usual classes (that is, idempotent, representable, and continuous in the open unit square) are left for the above-mentioned paper.

High-order uncertain differential equations are used to model differentiable uncertain systems with high-order differentials, and how to solve the high-order uncertain differential equations is a core issue in practice. This paper aims at proposing a numerical method to solve the high-order uncertain differential equations based on the Runge–Kutta recursion formula, which is of high precision degree. A procedure is designed and some numerical experiments are performed to illustrate the effectiveness and efficiency of the Runge–Kutta method. In addition, this paper also presents a numerical method to calculate the expected value of a function of the solution.

As a generalized fuzzy number, the hesitant fuzzy element (HFE) has received increasing attention. However, it is noted that the occurring probabilities of the elements in the HFE are equal, which is obviously problematic; thus, the preference relations on the HFEs can be inaccurate. To address this issue, this paper proposes the probabilistic hesitant fuzzy preference relations (PHFPRs) based on the probabilistic HFE (PHFE). It seems difficult to provide accurate probabilities that describe the occurring possibilities of the elements in the PHFPRs. This paper further demonstrates the probability calculation method for the PHFPEs based on a proposed variable, which is called the expected consistency. Moreover, the expected consistency index and the judgment principle are designed to evaluate the degree to which the PHFPRs are consistent. For the inconsistent PHFPRs, this paper presents an iterative optimization algorithm to improve their expected consistency by optimizing some elements in the PHFPRs. When the iteration terminates, the consistent PHFPRs and the priorities of the alternatives are identified. Finally, an example that selects a Ph.D. candidate is presented, and the results demonstrate the feasibility and effectiveness of using the PHFPRs and the consistency methods.

This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

This paper is concerned with dissipativity-based fuzzy integral sliding mode control (FISMC) of continuous-time Takagi-Sugeno (T-S) fuzzy systems with matched/unmatched uncertainties and external disturbance. To better accommodate the characteristics of T-S fuzzy models, an appropriate integral-type fuzzy switching surface is put forward by taking the state-dependent input matrix into account, which is the key contribution of the paper. Based on the utilization of Lyapunov function and property of the transition matrix for unmatched uncertainties, sufficient conditions are presented to guarantee the asymptotic stability of corresponding sliding mode dynamics with a strictly dissipative performance. A FISMC law is synthesized to drive system trajectories onto the fuzzy switching surface despite matched/unmatched uncertainties and external disturbance. A modified adaptive FISMC law is further designed for adapting the unknown upper bound of matched uncertainty. Two practical examples are provided to illustrate the effectiveness and advantages of developed FISMC scheme.

This paper presents a divide-and-conquer (DC) approach based on feature-space decomposition for classification. When large-scale data sets are present, typical approaches usually employed truncated kernel methods on the feature space or DC approaches on the sample space. However, this did not guarantee separability between classes, owing to overfitting. To overcome such problems, this paper proposes a novel DC approach on feature spaces consisting of three steps. First, we divide the feature space into several subspaces using the decomposition method proposed in this paper. Subsequently, these feature subspaces are sent into individual local classifiers for training. Finally, the outcome of local classifiers are fused together to generate the final classification results. We also propose a Cascade-TRBFKRR classifier to reweight training samples for data refinement. Experiments on large-scale data sets are carried out for performance evaluation. The results show that the error rates of the proposed DC method decreased compared with the state-of-the-art fast support vector machine solvers, e.g., reducing error rates by 10.53% and 7.53% on RCV1 and covtype data sets, respectively.

In this paper, a correntropy-based evolving fuzzy neural system (correntropy-EFNS) is proposed for approximation of nonlinear systems. Different from the commonly used meansquare error criterion, correntropy has a strong outliers rejection ability through capturing the higher moments of the error distribution. Considering the merits of correntropy, this paper brings contributions to build EFNS based on the correntropy concept to achieve a more stable evolution of the rule base and update of the rule parameters instead of the commonly used meansquare error criterion. The correntropy-EFNS (CEFNS) begins with an empty rule base and all rules are evolved online based on the correntropy criterion. The consequent part parameters are tuned based on the maximum correntropy criterion where the correntropy is used as the cost function so as to improve the non-Gaussian noise rejection ability. The steady-state convergence performance of the CEFNS is studied through the calculation of the steady-state excess mean square error (EMSE) in two cases: i) Gaussian noise; and ii) non-Gaussian noise. Finally, the CEFNS is validated through a benchmark system identification problem, a Mackey-Glass time series prediction problem as well as five other real-world benchmark regression problems under both noise-free and noisy conditions. Compared with other evolving fuzzy neural systems, the simulation results show that the proposed CEFNS produces better approximation accuracy using the least number of rules and training time and also owns superior non-Gaussian noise handling capability.

The dynamic uncertain causality graph (DUCG) is a newly presented framework for uncertain causality representation and probabilistic reasoning. It has been successfully applied to online fault diagnoses of large, complex industrial systems, and decease diagnoses. This paper extends the DUCG to model more complex cases than what could be previously modeled, e.g., the case in which statistical data are in different groups with or without overlap, and some domain knowledge and actions (new variables with uncertain causalities) are introduced. In other words, this paper proposes to use $i$ -mode, $e$ -mode, and $h$ -mode of the DUCG to model such complex cases and then transform them into either the standard $i$ -mode or the standard $e$ -mode. In the former situation, if no directed cyclic graph is involved, the transformed result is simply a Bayesian network (BN), and existing inference methods for BNs can be applied. In the latter situation, an inference method based on the DUCG is proposed. Examples are provided to illustrate the methodology.