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Object detection is one of the core tasks of computer vision, and bounding box (bbox) regression is one of the basic tasks of object detection. In recent years of related research, bbox regression is often used in the Intersection over Union (IoU) loss and its improved version. In this paper, for the first time, we introduce the Dice coefficient into the regression loss calculation and propose a new measure which is superior to and can replace the IoU. We define three properties of the new measure and prove the theory by mathematical reasoning and analysis of the existing work. This paper also proposes the N-IoU regression loss family. And the superiority of the N-IoU regression loss family is proved by designing simulation experiments and comparative experiments. The main results of this paper are: (1) The proposed new measure is better than IoU which can be used to evaluate bounding box regression, and the three properties of the new measure can be used as a broad criterion for the design of regression loss functions; and (2) we propose N-IoU loss. The parameter n of N-IOU can be debugged, which can be widely adapted to different application scenarios with higher flexibility, and the regression performance is better. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

A lot of research has validated that zeroing neural network (ZNN) model is a reliable tool for solving time-varying problems. Generally, convergent performance is often one of the most important measures for the practicability of the ZNN model. Besides, its practicability is also up to its anti-noise ability in the process of solving time-varying problems. It is worth noting that numerous existing ZNN models perform well in terms of the above two issues. In order to further enhance the robustness and convergence of the ZNN model, two novel activation functions (novel activation function-1 (NAF-1) and novel activation function-2 (NAF-2)) are designed. Based on the above two NAFs, two robust ZNN models (zeroing neural network-1 (ZNN-1) and zeroing neural network-2 (ZNN-2)) with fixed time convergence and strong robustness to noise for solving time-varying Sylvester equation (TVSE) are proposed in this paper. The robustness and convergence of the two proposed ZNN models are verified by rigorous mathematical analysis, and their practicability are validated by three simulation experiments (second-order and third-order TVSE solving and manipulator trajectory tracking). All the studies indicate that the two ZNN models can quickly find the accurate solution of TVSE in noiseless and noisy environment. [ABSTRACT FROM AUTHOR]

Mathematical model-based analysis and control of human immunodeficiency virus (HIV) infection have recently provided important advantages in medicine. In this paper, firstly the literature on mathematical models and applied control methods will be surveyed to evaluate the HIV models and therapy. Secondly, a cubature Kalman filter-based nonlinear model predictive control is proposed for the multi-input multi-output control of HIV infection for decreasing the cost of sensory devices and increasing the efficiency of therapy. By doing so both unmeasurable states and personalized parameters of the HIV infection are jointly estimated in a control process to generate suitable drug dosages. In the literature, the applied drug dosages are in continuous or on/off levels. For a practical application of continuous drug dosage-level, it has been discretized into 10 levels of full dosage level. Therefore, the applied drug dosages are in piecewise-continuous levels instead of continuous values or on/off levels. The proposed observer–controller configuration has been applied to the strong and moderate therapy levels of long-term non-progressive as well as fast-progressive patients with personalized parameters, where the application results are discussed for 1-, 5-, 10- and 20-year periods. The computational results show that satisfactory performances are obtained for future applications in terms of the root-mean-squared error of the estimation and control, and in terms of the integral sum of the control input. [ABSTRACT FROM AUTHOR]

This paper focuses on the lag synchronization issue for a kind of general complex networks with multiple time-varying delays via the pinning control strategy. By applying the Lyaponov functional theory and mathematical analysis techniques, sufficient verifiable criteria that depend on both intrinsic time-varying delay and coupled time-varying delay are obtained to achieve lag synchronization of the networks. Moreover, the coupling configuration matrices are not required to be symmetric or irreducible, and the minimum number of pinned nodes is determined by node dynamics, coupling matrices, and the designed parameter matrices. Finally, a numerical example is given to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Effective dimension, an indicator for the difficulty of high-dimensional integration, describes whether a function can be well approximated by low-dimensional terms or sums of low-order terms. Some problems in option pricing are believed to have low effective dimensions, which help explain the success of quasi-Monte Carlo (QMC) methods recently observed in financial engineering. This paper provides a way of studying the structure of effective dimensions by finding a proper space the function of interest belongs to and then determining the effective dimension of that space. To this end, we extend the definitions of effective dimensions to weighted function spaces with product-order-dependent weights and give bounds on norms and variances. Furthermore, we show that the proposed method is applicable to functions arising in option pricing and consequently offers some hints on the performance of QMC methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the lag quasi-synchronization for memristive neural networks (MNNs) with switching jumps mismatch. The inherent characteristic of MNNs is fully taken into account. Based on Lyapunov-Krasovskii functional and differential inclusions theory, intermittent control approach is utilized to realize the exponential lag quasi-synchronization of the considered model. The error level is closely related to the switching jumps. In addition, a simple design procedure of controller is presented to ensure that the synchronization error between the master system and the slave system converges to a predetermined level. Two numerical examples are offered to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Early-warning models provide means for ex ante identification of elevated risks that may lead to a financial crisis. This paper taps into the early-warning literature by introducing biologically inspired models for predicting systemic financial crises. We create three models: a conventional statistical model, a back-propagation neural network (NN) and a neuro-genetic (NG) model that uses a genetic algorithm for choosing the optimal NN configuration. The models are calibrated and evaluated in terms of usefulness for policymakers that incorporates preferences between type I and type II errors. Generally, model evaluations show that biologically inspired models outperform the statistical model. NG models are, however, shown not only to provide largest usefulness for policymakers as an early-warning model, but also in form of decreased expertise and labor needed for, and uncertainty caused by, manual calibration of an NN. For better generalization of data-driven models, we also advocate adopting to the early-warning literature a training scheme that includes validation data. [ABSTRACT FROM AUTHOR]

This paper presents two algebraic criteria for the input-to-state stability of recurrent neural networks with time-varying delays. The criteria which also ensure global exponential stability when the input u( t) is equal to 0 and is easy to be verified only with the connection weights of the recurrent neural networks. Two numerical examples are given to demonstrate the effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

Machining operations involving complex multivariate parameters are defined by many machining parameters. Correct selection of these parameters is crucial for an efficient and economical cutting operation. The grooving operation required in many cases is one of the most problematic methods in all metal cutting operations, especially in terms of chip control. This paper covers theoretical analysis and mathematical modeling of deformation and stresses of the grooving tool. Cutting forces affecting the service life of the grooving tool were measured by various cutting experiments. Deformation and stresses of grooving tool caused by cutting forces were analyzed by finite element method using Ansys software. In modeling with artificial neural networks (ANN), grooving insert width, cutting speed, feed rate, radial force and primary cutting force are inputs in the model and deformation and stresses of the grooving tool are outputs. An algorithm, which is a Matlab script file, was developed to determine the optimal combination of neural network parameters such as the normalization method, number of hidden neurons, transfer function and training algorithm. The best-fitting set determined by the algorithm developed for the model was achieved with the Levenberg–Marquardt backpropagation algorithm, logistic sigmoid transfer function, nine hidden neurons and normalization method with a scaling factor. The MSE, R2, MAPE values of the ANN model are 2.0327 × 10−6, 0.999992 and 0.379227, respectively. Performance results have shown that the proposed approach can also be used for ANN modeling of machining parameters in other cutting operations other than grooving. [ABSTRACT FROM AUTHOR]

A Bloom filter is a special case of an artificial neural network with two layers. Traditionally, it is seen as a simple data structure supporting membership queries on a set. The standard Bloom filter does not support the delete operation, and therefore, many applications use a counting Bloom filter to enable deletion. This paper proposes a generalization of the counting Bloom filter approach, called "autoscaling Bloom filters", which allows adjustment of its capacity with probabilistic bounds on false positives and true positives. Thus, by relaxing the requirement on perfect true positive rate, the proposed autoscaling Bloom filter addresses the major difficulty of Bloom filters with respect to their scalability. In essence, the autoscaling Bloom filter is a binarized counting Bloom filter with an adjustable binarization threshold. We present the mathematical analysis of its performance and provide a procedure for minimizing its false positive rate. [ABSTRACT FROM AUTHOR]

Though sparse representation (Wagner et al. in IEEE Trans Pattern Anal Mach Intell 34(2):372-386, , CVPR 597-604, ) can perform very well in face recognition (FR), it still can be improved. To improve the performance of FR, a novel sparse representation method based on virtual samples is proposed in this paper. The proposed method first extends the training samples to form a new training set by adding random noise to them and then performs FR. As the testing samples can be represented better with the new training set, the ultimate classification obtained using the proposed method is more accurate than the classification based on the original training samples. A number of FR experiments show that the classification accuracy obtained using our method is usually 2-5 % greater than that obtained using the method mentioned in Xu and Zhu (Neural Comput Appl, ). [ABSTRACT FROM AUTHOR]

This paper studies the problem of backstepping generalized synchronization problem of neural network with delays. Based on tracing control method, the controller of backstepping generalized synchronization is designed, and the controller can realize backstepping generalized synchronization for neural network with delays. The experiment of numerical simulation is provided to further demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Let n existing facilities be given in the plane. The classical version of the median line location problem asks to find a line L in the plane, so that the sum of the weighted distances from L to all existing facilities is minimized. We consider the semi-obnoxious case, where every point has either a positive or a negative weight. In this paper, we discuss some properties of semi-obnoxious median line location problem with Euclidean norm and propose a particle swarm optimization algorithm for this problem. [ABSTRACT FROM AUTHOR]

Quality function deployment is a planning and problem-solving tool for translating customer requirements into the technical attributes of a product. To obtain the rating order of technical attributes is a crucial step in applying quality function deployment. Based on the fuzzy soft theory proposed by Maji et al., which is a new mathematical tool to deal with uncertainties, a novel approach is proposed in this paper in order to prioritize technical attributes. We utilize the relative deviation between scores of customer requirements and their average to construct membership function in order to construct fuzzy soft sets. The weights of customer requirements and the final importance of technical attributes are obtained from fuzzy soft sets derived from raw data without other information. An illustrated example is cited to demonstrate the application of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework for transfer learning, referred to as transfer sparse subspace learning (TSSL). This framework is suitable for different assumptions on the divergence measures of the data distributions, such as maximum mean discrepancy, Bregman divergence, and K-L divergence. We introduce an effective sparse regularization to the proposed transfer subspace learning framework, which can reduce time and space cost obviously, and more importantly, which can avoid or at least reduce over-fitting problem. We give different solutions to the problems based on different distribution distance estimation criteria, and convergence analysis is also given. Comprehensive experiments on the text data sets and the face image data sets demonstrate that TSSL-based methods outperform existing transfer learning methods. [ABSTRACT FROM AUTHOR]

In this paper, we first define soft intersection near-ring (soft int near-ring) by using intersection operation of sets. This new notion can be regarded as a bridge among soft set theory, set theory and near-ring theory, since it shows how a soft set effects on a near-ring structure by means of intersection and inclusion of sets. We then derive its basic properties with illustrative examples. Moreover, we obtain some analog of classical near-ring theoretic concepts for soft int near-ring and give the applications of soft int near-ring to near-ring theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider the $$(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$$-fuzzy and $$(\overline{\in}_{\gamma},\overline{\in}_{\gamma} \vee \; \overline{\hbox{q}}_{\delta})$$-fuzzy subnear-rings (ideals) of a near-ring. Some new characterizations are also given. In particular, we introduce the concepts of (strong) prime $$(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$$-fuzzy ideals of near-rings and discuss the relationship between strong prime $$(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$$-fuzzy ideals and prime $$(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$$-fuzzy ideals of near-rings. [ABSTRACT FROM AUTHOR]

The paper focuses on the study of solving the large-scale traveling salesman problem (TSP) based on neurodynamic programming. From this perspective, two methods, temporal difference learning and approximate Sarsa, are presented in detail. In essence, both of them try to learn an appropriate evaluation function on the basis of a finite amount of experience. To evaluate their performances, some computational experiments on both the Euclidean and asymmetric TSP instances are conducted. In contrast with the large size of the state space, only a few training sets have been used to obtain the initial results. Hence, the results are acceptable and encouraging in comparisons with some classical algorithms, and further study of this kind of methods, as well as applications in combinatorial optimization problems, is worth investigating. [ABSTRACT FROM AUTHOR]

In this paper, we make an application of the harmonic balance (HB) analysis technique for studying oscillations in neural-network-based control systems where the closed-loop system can be transformed into a linear and a feedback nonlinear part (“Luré regulator problem”). The main goal of the present paper is to establish a test for the stability of limit cycles arising from a neural-network-control-based scheme operating over continuous nonlinear plants. The HB technique has been applied to the stability analysis of a quasilinearised nonlinear DC motor drive. The simple geometric interpretation of this technique contrasts other stability analysis techniques, such as Lyapunov, Input/Output, etc. [ABSTRACT FROM AUTHOR]

Bat algorithm (BA) is a new approach designed by imitating bat's behavior of searching and capturing preys. The existing results have demonstrated the effectiveness and efficiency in comparison with other heuristic algorithms such as genetic algorithms and particle swarm optimization. In this paper, we design a novel framework for bat algorithm named two-stage bat algorithm (TSBA) using a trade-off strategy which balances the relationship between exploration and exploitation at the most extent. Inspired by the multi-population methods (e.g., artificial bee colony), we not only concern some technologies to avoid premature inevitably encountered when using BA, but also use a trade-off strategy to improve the comprehensive search performance for optimization. Some typical test sets which consist of 27 benchmark functions are utilized in comparative experiment, and the simulation results in terms of convergence rate and accuracy illustrate that the TSBA has a competitive performance than other swarm intelligent optimization algorithms. In addition, the proposed algorithm will not lend to the tremendous increase in computing time and thus will be a powerful tool in practical applications. [ABSTRACT FROM AUTHOR]

Sparse Representation Method has been proved to outperform conventional face recognition (FR) methods and is widely applied in recent years. A novel Kernel-based Sparse Representation Method (KBSRM) is proposed in this paper. In order to cope with the possible complex variation of the face images caused by varying facial expression and pose, the KBSRM first uses a kernel-induced distance to determine N nearest neighbors of the testing sample from all the training samples. Then, in the second step, the KBSRM represents the testing sample as a linear combination of the determinate N nearest neighbors and performs the classification by the representation result. It can be inferred that the N nearest training samples selected are closer to the test sample than the rest, so using the N nearest neighbors to represent the testing sample can make the ultimate classification more accurate. A number of FR experiments show that the KBSRM can achieve a better classification result than the algorithm mentioned in Xu et al. (Neural Comput Appl doi:). [ABSTRACT FROM AUTHOR]

This paper proposes a novel nonparametric discriminant analysis criterion, named weighted marginal discriminant analysis (WMDA), whose purpose is to efficiently utilize the marginal information of sample distribution in the discriminant analysis. The local mean is calculated by using the data points near the margin with different weights. The more contributions to the margin information, the larger weights the data points have. By making use of the weighting strategy and local mean, WMDA simultaneously utilizes the marginal information and local structure which are important for discriminative feature extraction. Experiments on the artificial and real database show that the proposed WMDA is superior to other related methods. [ABSTRACT FROM AUTHOR]

Two-dimensional locality preserving projections (2DLPP) was recently proposed to extract features directly from image matrices based on locality preserving criterion. A significant drawback of 2DLPP is that it only works on one direction (left or right) to reduce the dimensionality of the image matrices and thus too many coefficients are needed for image representation in low-dimensional subspace. In this paper, we propose a novel method called two-dimensional bilinear preserving projections (2DBPP) for image feature extraction. We generalized the image-based (2D-based) feature extraction techniques into bilinear cases, in which 2DLPP is a special case of our proposed method. In order to obtain the bilinear projections, we proposed an iteration method by solving the corresponding generalized eigen-equations. Moreover, analyses show that 2DBPP has stronger locality preserving abilities than 2DLPP. By using the label information and defining different local neighborhood graphs, the proposed framework is further extended to supervised case. Experiments on three databases show that 2DBPP and its supervised extension are superior to some other image-based state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

This paper proposes an ontology learning method which is used to generate a graphical ontology structure called ontology graph. The ontology graph defines the ontology and knowledge conceptualization model, and the ontology learning process defines the method of semiautomatic learning and generates ontology graphs from Chinese texts of different domains, the so-called domain ontology graph (DOG). Meanwhile, we also define two other ontological operations-document ontology graph generation and ontology graph-based text classification, which can be carried out with the generated DOG. This research focuses on Chinese text data, and furthermore, we conduct two experiments: the DOG generation and ontology graph-based text classification, with Chinese texts as the experimental data. The first experiment generates ten DOGs as the ontology graph instances to represent ten different domains of knowledge. The generated DOGs are then further used for the second experiment to provide performance evaluation. The ontology graph-based approach is able to achieve high text classification accuracy (with 92.3 % in f-measure) over other text classification approaches (such as 86.8 % in f-measure for tf-idf approach). The better performance in the comparative experiments reveals that the proposed ontology graph knowledge model, the ontology learning and generation process, and the ontological operations are feasible and effective. [ABSTRACT FROM AUTHOR]

In this paper, the fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix have been found. To do this, the spreads are allocated to the obtained core from the corresponding crisp matrix which it makes a fuzzy number surely. [ABSTRACT FROM AUTHOR]

In this paper, the relationship between complete L-lattices and L-closure systems is investigated first. That is, each L-closure system is a complete L-lattice under the fuzzy inclusion order, and each complete L-lattice is isomorphic to an L-closure system. Next, we focus on information systems in fuzzy setting and propose the concept of L-information systems from the viewpoint of fuzzy logic. The cheerful result that L-information systems are a representation of complete L-lattices is presented. Furthermore, we define appropriate morphisms on L-information systems and complete L-lattices, respectively, and prove that they are categorically equivalent. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of sum and direct sum of soft submodules, small soft submodules and radical of a soft module. Moreover, we obtain basic properties of such soft submodules. [ABSTRACT FROM AUTHOR]

This paper proposes a modified ELM algorithm that properly selects the input weights and biases before training the output weights of single-hidden layer feedforward neural networks with sigmoidal activation function and proves mathematically the hidden layer output matrix maintains full column rank. The modified ELM avoids the randomness compared with the ELM. The experimental results of both regression and classification problems show good performance of the modified ELM algorithm. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to introduce and study the fuzzy soft ring and $$\left( \in,\in\vee q\right) $$-fuzzy soft subring that is generalization of fuzzy soft ring. We also study some of their basic properties and give several examples. [ABSTRACT FROM AUTHOR]

In this paper, we give the concept of L-fuzzy semi-preopen operator in L-fuzzy topological spaces and use it to score L-fuzzy SP-compactness in L-fuzzy topological spaces. We also study the relationship between L-fuzzy SP-compactness and fuzzy SP-compactness in L-topological spaces. [ABSTRACT FROM AUTHOR]

Maji et al. introduced the concept of a fuzzy soft set, which is an extension to the concept of a soft set. In this paper, we apply the concept of a fuzzy soft set to hemiring theory. The concepts of $$(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$$-fuzzy soft left h-ideals (right h-ideals, h-bi-ideals, and h-quasi-ideals) are introduced, and some related properties are obtained. The notion of left (right) h-hemiregular hemirings is provided. Some characterization theorems of (left) h-hemiregular and (left) duo hemirings are derived in terms of $$(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$$-fuzzy soft left (right) h-ideals, $$(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$$-fuzzy soft h-bi-ideals, and $$(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$$-fuzzy soft h-quasi-ideals. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $$(\in,\in\vee\,q_k)$$-fuzzy n-ary subpolygroup and $$(\overline\in,\overline \in\vee \overline q_k)$$-fuzzy n-ary subpolygroup, which are generalization of $$(\in,\in\vee\,q)$$-fuzzy n-ary subpolygroup and $$(\overline \in ,\overline \in\vee \overline q)$$-fuzzy n-ary subpolygroup of an n-ary polygroup. In particular, the notions of $$(\in,\in\vee\,q_k)$$-fuzzy cosets determined by $$(\in,\in\vee\,q_k)$$-fuzzy n-ary subplygroups are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we define a soft intersection group (soft int-group) on a soft set. This new concept functions as a bridge among soft set theory, set theory and group theory and shows the effect of soft sets on a group structure in the sense of intersection and inclusion of sets. We then derive the basic properties of soft int-groups and give its applications to group theory. [ABSTRACT FROM AUTHOR]

In this paper, as a special case of fuzzy domains, algebraic fuzzy directed-complete posets (shortly, algebraic fuzzy dcpos) are discussed. Throughout the algebraic fuzzy dcpos, some equivalent characterizations of fuzzy domains are given. Then, the construction of new algebraic fuzzy dcpos (resp., fuzzy domains) from known ones by means of forming products, taking some special subsets, and taking images under maps with appropriate operations is investigated. Finally, a new kind of fuzzy continuous section retraction pairs is proposed. Moreover, it is proved that every fuzzy domain is a fuzzy continuous retraction of an algebraic fuzzy dcpo, and the fuzzy continuous retraction of a fuzzy domain is also a fuzzy domain. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the notion of rough M-hypersystem, rough N-hypersystem, fuzzy M-hypersystem and fuzzy N-hypersystem in a $$\Upgamma$$-semihypergroup and some related properties are investigated. Moreover, we have introduced the notion of fuzzy $$\Upgamma$$-hyperideal in $$\Upgamma$$-semihypergroup. We have also introduced rough M-hypersystem and rough N-hypersystem in a quotient $$\Upgamma$$-semihypergroup. [ABSTRACT FROM AUTHOR]

In this paper, we consider a relationship between rough sets and lattice theory. The related properties of rough subsets of lattices are investigated. We introduce the notion of rough ideals which is a generalized notion of ideals of a lattice, and some properties and homomorphism of such ideals are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we define interval-valued $$(\in_{\gamma },\in_{\gamma }\vee q_{\delta })$$-fuzzy k-subhemirings, interval-valued $$(\in_{\gamma },\in_{\gamma }\vee q_{\delta })$$-fuzzy k-ideals, interval-valued $$(\in_{\gamma },\in_{\gamma }\vee q_{\delta})$$-fuzzy k-interior ideals, interval-valued $$(\in_{\gamma },\in_{\gamma }\vee q_{\delta })$$-fuzzy k-bi-ideals, interval-valued $$(\in_{\gamma },\in_{\gamma }\vee q_{\delta })$$-fuzzy k-quasi-ideals, and k-semisimple hemirings. We also characterize k-regular, k-intra-regular, and k-semisimple hemirings by the properties of these interval-valued $$(\in_{\gamma },\in_{\gamma}\vee q_{\delta })$$-fuzzy k-ideals. [ABSTRACT FROM AUTHOR]

In Jun et al. (Bull Malays Math Sci Soc (2) 32(3):391-408,), (α, β)-fuzzy bi-ideals are introduced and some characterizations are given. In this paper, we generalize the concept of (α, β)-fuzzy bi-ideals and define ( $$\in ,\in \vee q_{k}$$)-fuzzy bi-ideals in ordered semigroups, which is a generalization of the concept of an (α, β)-fuzzy bi-ideal in an ordered semigroup. Using this concept, some characterization theorems of regular, left (resp. right) regular and completely regular ordered semigroups are provided. In the last section, we give the concept of upper/lower parts of an ( $$\in ,\in \vee q_{k}$$)-fuzzy bi-ideal and investigate some interesting results of regular and intra-regular ordered semigroups. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of fuzzy filters(ideals) in CI-algebras. We study fuzzy congruence relation in detail and construct quotient of $$(X/\bar{\theta}; {\circ}, 1/\bar{\theta})$$ via a fuzzy congruence relation on CI-algebra X. [ABSTRACT FROM AUTHOR]

In this paper, by means of a kind of new idea, we consider the ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$-hyperrings. The notion of ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$-hyperrings is provided and some related properties are investigated. A kind of quotient $$\Upgamma$$-hyperring of a $$\Upgamma$$-hyperring by an ( ∈ , ∈ ∨ q)-fuzzy hyperideal is presented and the relationships among ( ∈ , ∈ ∨ q)-fuzzy hyperideals, quotient $$\Upgamma$$-hyperrings and homomorphisms are explored. Several homomorphism theorems in the framework of fuzzy setting are provided. [ABSTRACT FROM AUTHOR]

In this paper, generalization of the fuzzy BCK/ BCI-algebras of type (α, β) are introduced. Then we state and prove some theorems that determine the relationship between these notions and subalgebras of BCK/ BCI-algebras. Characterizations of (α, β)-fuzzy subalgebras in a BCK/ BCI-algebras are given. [ABSTRACT FROM AUTHOR]

In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨ q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨ q)-fuzzy interior ideals (resp. (∈, ∈ ∨ q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨ q)-fuzzy ideals and (∈, ∈ ∨ q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨ q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨ q)-fuzzy ideals (resp. (∈, ∈ ∨ q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a fast and new deterministic model selection methodology for incremental radial basis function neural network (RBFNN) construction in time series prediction problems. The development of such special designed methodology is motivated by the problems that arise when using a K-fold cross-validation-based model selection methodology for this paradigm: its random nature and the subjective decision for a proper value of K, resulting in large bias for low values and high variance and computational cost for high values. Taking into account these drawbacks, the proposed model selection approach is a combined algorithm that takes advantage of two balanced and representative training and validation sets for their use in RBFNN initialization, optimization and network model evaluation. This way, the model prediction accuracy is improved, getting small variance and bias, reducing the computation time spent in selecting the model and avoiding random and computationally expensive model selection methodologies based on K-fold cross-validation procedures. [ABSTRACT FROM AUTHOR]

This paper presents a method to creation of a servicing expert system including an artificial neural network. The theoretical basis was presented with the model of an operation process of objects in the form of the following models: mathematical (analytical), graphical and descriptional. For the tests, a model was developed of an organization of a servicing technical system of those technical objects which require short shutdown times (aircrafts, radiolocation systems, etc.). The mathematical basis was presented for the execution of the task of servicing of a technical object. The idea of the servicing of the object was described as a transformation of the properties of the operational function of the object from the space of the current servicing to the form of the space of the features of the nominal (model) operation of the object. The results were presented of the radar system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (weak) L-fuzzy polygroups and give a theorem to present the connection between the crisp polygroups and L-fuzzy polygroups. We also provide the notion of (normal) L-fuzzy subpolygroups of a (weak) L-fuzzy polygroup and investigate some of their properties. We show that the set of all the normal L-fuzzy subpolygroups is a modular lattice and obtain a kind of weak L-fuzzy quotient polygroup. Moreover, we define two kinds of operators on $${\fancyscript{L}(H)}$$, where $${\fancyscript{L}(H)}$$ is the set of all the L-fuzzy subsets in a weak L-fuzzy polygroup H, to characterize L-fuzzy subpolygroups and present some related theorems. Finally, we investigate the homomorphism properties of L-fuzzy polygroups. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Newton iterative method of solution for solving an ε-insensitive support vector regression formulated as an unconstrained optimization problem. The proposed method has the advantage that the solution is obtained by solving a system of linear equations at a finite number of times rather than solving a quadratic optimization problem. For the case of linear or kernel support vector regression, the finite termination of the Newton method has been proved. Experiments were performed on IBM, Google, Citigroup and Sunspot time series. The proposed method converges in at most six iterations. The results are compared with that of the standard, least squares and smooth support vector regression methods and of the exact solutions clearly demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present a thorough mathematical analysis of the use of neural networks to solve a specific classification problem consisting of a bilinear boundary. The network under consideration is a three-layered perceptron with two hidden neurons having the sigmoid serving as the activation function. The analysis of the hidden space created by the outputs of the hidden neurons will provide results on the network’s capacity to isolate two classes of data in a bilinear fashion, and the importance of the value of the sigmoid parameter is highlighted. We will obtain an explicit analytical function describing the boundary generated by the network, thus providing information on the effect each parameter has on the network’s behavior. Generalizations of the results are obtained with additional neurons, and a theorem concerned with analytical reproducibility of the boundary function is established. [ABSTRACT FROM AUTHOR]

Neural networks are widely deployed in many scenarios and have reached or exceeded human-level performance in some tasks. However, the researchers found that existing neural networks are vulnerable to attacks. One of the cases is that the network outputs the wrong result in the presence of small perturbations in the input. It indicates that the neural network does not meet the robustness. Neural networks, which do not meet robustness, will limit their application in safety-critical systems such as automatic driving and wise medical. Hence, the research on the robustness of neural networks is significant. Interval analysis is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation and can be used to calculate the exact output range of a real-valued function. Based on the theoretical framework of interval analysis, we define the interval extension of neural networks and prove that it includes the inclusion isotonicity and Lipschitzian property. It illustrates the feasibility of using interval extension to compute the output range of a neural network corresponding to a given input range. In order to evaluate the robustness of the neural network, we further analyze the characteristics of the neural network interval extension and design a neural network robustness evaluation method based on the greedy strategy. Experiment results on the MNIST and ACAS Xu datasets show that the method can effectively evaluate the robustness of the neural network with good time performance. [ABSTRACT FROM AUTHOR]

In this paper, we characterize different classes of hemirings by the properties of their $$(\overline{\in}, \overline{\in} \vee \overline{q})$$-fuzzy ideals, $$(\overline{\in}, \overline{\in} \vee \overline{q})$$-fuzzy quasi-ideals and $$(\overline{\in}, \overline{\in} \vee \overline{q}) $$-fuzzy bi-ideals. [ABSTRACT FROM AUTHOR]