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Social networking services allow users to adopt and spread information via diffusion actions, e.g., share, retweet, and reply. Real applications such as viral marketing and trending topic detection rely on information diffusion. Given past items with diffusion records on a social network, this paper aims at forecasting who will participate in the diffusion of a new item c (we use hashtags in the paper) with its k earliest adopters, without using content and profile information, i.e., finding which users will adopt c in the future. We define the Diffusion Participation Forecasting (DPF) problem, which is challenging since all users except for early adopters can be the candidates, comparing to existing studies that predict which one-layer followers will adopt a new hashtag given past diffusion observations with content and profile info. To solve the DFP problem, we propose an Adoption-based Participation Ranking (APR) model, which aims to rank the actual participants in reality at higher positions. The first is to estimate the adoption probability of a new hashtag for each user while the second is a random walk-based model that incorporates nodes with higher adoption probability values and early adopters to generate the forecasted participants. Experiments conducted on Twitter exhibit that our model can significantly outperform several competing methods in terms of Precision and Recall. Moreover, we demonstrate that an accurate DPF can be applied for effective targeted marketing using influence maximization and boosting the accuracy of popularity prediction in social media.

Keyword Spotting (KWS) systems can be divided into two main groups: Hidden Markov Model (HMM)-based and Discriminative KWS (DKWS) systems. In this paper, we propose an approach to improve a DKWS system using advantages of HMM-based systems. The proposed DKWS system contains feature extraction and classification (that includes a classifier and a search algorithm) parts. The focus of this paper is on the feature extraction part and the search algorithm. At first, we propose a method for using the advantages of a triphone-based HMM system and improving the monophone-based feature extraction, (proposed in our previous works), to triphone-based one. Then, we propose an N-best search algorithm instead of one-best algorithm. The results on TIMIT database indicate that the true detection rate of the triphone-based Evolutionary DKWS (EDKWS) system with N-best search (Tph-EDKWS-N-Best), in false alarm rate per keyword per hour greater than two, is 4.6% higher than that of the monophone-based EDKWS system with one-best search (Mph-EDKWS-1-Best). This improvement costs about 0.4 unit degradation in Real Time Factor (a common metric of measuring the speed of an automatic speech recognition system). Additionally, Figure of Merit (average true detection rate for different false alarm per keyword per hour from 1 to 10) of the Tph-EDKWS-N-Best system is noticeably higher than that of HMM-based KWS systems. However, the computational complexity of the Tph-EDKWS-N-Best system is considerably higher than that of the HMM-based KWS systems.

Identifying faulty program entities has been recognized as one of the most expensive, tedious and time-consuming processes in software debugging activity. Fault localization techniques are designed to assist developers in locating faults by giving a ranking of the probability that program entities incur failures. Mutation-based fault localization (MBFL) is a recently proposed fault localization approach via mutation analysis, which uses the location of mutants to identify the faulty statements. With improved effectiveness, the MBFL also brings huge execution cost. To reduce the execution cost of MBFL technique, this paper proposes a dynamic mutation execution strategy (DMES) to prioritize the execution on both mutants and test cases. As fewer mutants and test cases are executed with DMES, the whole process will become faster and the cost will be decreased. At the same time, it is proved that the fault localization accuracy of MBFL with DMES is the same as that of the original MBFL. Furthermore, this paper discusses the lowest mutation execution cost of MBFL in theory and gives a quick solution to compute the theoretical minimal mutation execution cost of MBFL in the case of keeping fault localization accuracy non-decreasing. The empirical studies show that MBFL with the dynamic strategy proposed in this paper can reduce mutant-test execution cost by 32.4–87% and is close to the theoretical optimal cost. Furthermore, the additional run time required by utilizing our strategy is minimum and can be ignored.

This paper focuses on recovering multi-dimensional signal called tensor which is corrupted by random missing areas. The performance of the conventional tensor completion techniques deteriorate when the tensor multi-rank is large and/or large missing areas. Moreover, these techniques are weak in preserving the edges in the signals like images/videos. This paper proposes an efficient method to overcome these problems by simultaneously combining novel twist tensor total variation norm to exploit spatio-temporal correlation and tensor-Singular Value Decomposition (t-SVD) based reweighted nuclear norm to improve low multi-rank tensor recovery. The twist tensor total variation norm takes care of edges in the recovered data and aids the recovery of missing areas by utilising the similarities in the adjacent samples. The reweighted nuclear norm handles corrupted large rank tensors by sparsity enhancement via reweighting its singular values. The effectiveness of the proposed method is established by applying to video completion problem, and experimental results reveal that the algorithm outperforms its counterparts.

The performance of differential evolution (DE) has been significantly influenced by trial vector generation strategies and control parameters. Various powerful trial vector generation strategies with adaptive parameter adjustment methods such that the population generation is guided by the elites have been proposed. This paper aims to strengthen the performance of DE by compositing these powerful trial vector generation strategies, making it possible to obtain the guidance of each individual from multiple elites concurrently and independently. In this manner, the deleterious behavior in which an individual is misguided by various local optimal solutions into unpromising areas could be restrained to a certain extent. An adaptive multiple-elites-guided composite differential evolution algorithm with a shift mechanism (abbreviated as AMECoDEs) has been proposed in this paper. This algorithm concurrently employs two elites-guided trial vector generation strategies for each individual to generate two candidate solutions accordingly, and the best one is adopted to participate in the selection. Moreover, a novel shift mechanism is established to handle stagnation and premature convergence issues. AMECoDEs has been tested on the CEC2014 benchmark functions. Experimental results show that AMECoDEs outperforms various classic state-of-the-art DE variants and is better than or at least comparable to various recently proposed DE methods.

In most cases, ELECTRE methods just apply to traditional multicriteria decision making (MCDM) problems with independent criteria. However, there exist more or less interdependences among criteria in actual situations. A special case is MCDM with prioritizations among criteria, called prioritized MCDM. In recent years, how to deal with MCDM problems in the environment of prioritized criteria becomes hot topic increasingly. Lots of existing methods, including PROMETHEE, are modified for the prioritized MCDM, but the advantages of ELECTRE have not been exploited to the prioritized MCDM. In my opinion, design specific ELECTRE methods for prioritized MCDM problems will benefit the developments of both ELECTRE and prioritized MCDM. In this paper, we firstly reformulate the expressions of concordance and discordance indices for use in the MCDM problems with dependent criteria, especially prioritized criteria, based on the concepts of fuzzy measures and digraphs respectively. After replacing the fuzzy measure by a prioritized measure, we successfully validate the concordance of an assertion under prioritized criteria. Furthermore, we design an approach to validate the discordance of the assertion based on a digraph constructed by the criteria and their prioritizations. Finally, we design three procedures to construct outranking relations in the prioritized MCDM environment according to the ideas of ELECTRE-I, ELECTRE-Iv, and ELECTRE-IS respectively. It is meaningful of this paper to provide a new idea to solve the prioritized MCDM problems and widen the application scope of ELECTRE methods by means of the reformulations of concordance and discordance.

In this paper, optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t-norm is considered as fuzzy composition, and fuzzy inequality replaces ordinary inequality in the constraints. Unlike most optimization algorithms, in fuzzy relational inequalities with fuzzy constraints (FRI-FC) we find a near-feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp (ordinary) inequality constraints. Such solutions are called super-optima in this paper. Subsequently, an algorithm is proposed to find a super-optimum with pre-specified desirable infeasibility. For this purpose, we firstly study some structural properties of the FRI-FC problem and present a new formulization that is independent of t-norms used in the constraints of the problem. This new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters. However, it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super-optimum under a certain sufficient condition. Finally, a modified PSO is presented in which the ability of PSO to solve unconstrained problems with continuous domain, the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized FRI-FC problems. The modified PSO algorithm has been applied to the generalized FRI-FC problem defined with ten well-known continuous t-norms. Additionally, an idea of the FRI-FC problems as outer approximators for FRI problems with ordinary inequalities is also investigated.

This paper addresses the control problem of MIMO stochastic nonlinear systems with unknown high-frequency gains. In the existing works, the prior knowledge of the high-frequency gain or its control direction is assumed known for the control design. This paper removes such assumptions, and proposes an adaptive neural network algorithm that allows the high-frequency gains to be time-varying and their control directions to be unknown. Nussbaum gain based approach and adaptive neural network mechanism are brought together such that all the signals in the closed-loop system are ensured bounded. A simulation study is carried out to confirm the validity of the proposed algorithm.

In the last decade, algebraic and fast algebraic attacks are regarded as the most successful attacks on LFSR-based stream ciphers . Since the notion of algebraic immunity was introduced, the properties and constructions of Boolean functions with maximum algebraic immunity have been researched in a large number of papers. However, there are few results with respect to Boolean functions with provably good immunity against fast algebraic attacks. In previous literatures, only Carlet–Feng function was proven to have good immunity to fast algebraic attacks. In this paper, we first study a large family of highly nonlinear Boolean functions in terms of the immunity to fast algebraic attacks, which includes the functions of Tu–Deng, the functions of Tang et al. and the functions of Jin et al. Based on a sufficient and necessary condition for measuring the immunity of Boolean functions against fast algebraic attacks using bivariate polynomial representation , we propose an efficient method for estimating the immunity of the functions of such family. Then we prove that a family of 2 k-variable Boolean functions, including the function recently constructed by Tang et al., are almost perfect algebraic immune for any integer k ≥ 3. More exactly, they achieve optimal algebraic immunity and almost perfect immunity to fast algebraic attacks. The functions of such family are balanced and have optimal algebraic degree. Besides, we prove a lower bound on their nonlinearity based on the work of Tang et al. which is better than that of Carlet–Feng function. It is also checked for 3 ≤ k ≤ 9 that the exact nonlinearity of such functions is very good, which is slightly smaller than that of Carlet–Feng function, and some functions of this family even have a slightly larger nonlinearity than Tang’s et al. function. To sum up, among the known functions with provably good immunity against fast algebraic attacks, the functions of this family make a trade-off between the exact value and the lower bound of nonlinearity.

Particle swarm optimizations (PSOs) are drawing extensive attention from both research and engineering fields due to their simplicity and powerful global search ability. However, there are two issues needing to be improved: one is that the classical PSO converges slowly; the other is that classical PSO tends to result in premature convergence, especially for multi-modal problems. This paper attempts to address these two issues. Firstly, to improve the convergent efficiency, this paper proposes an asymptotic predicting model of the globally-optimal solution, which is used to predict the global optimum based on extracting the features reflecting the evolutionary trend. The predicted global optimum is then taken as the third exemplar, in a way similar to the individual historical best solution and the swarm historical best solution in guiding the evolutionary process of other particles. To reduce the probability that the population is trapped into a local optimum due to the premature phenomenon, this paper proposes an adaptive mutation strategy, which is used to help the trapped particles to escape away from the local optimum by using the extended non-uniform mutation operator. Finally, we combine the two entities to develop a globally-optimal prediction-based adaptive mutation particle swarm optimization (GPAM-PSO). In numerical experimental parts, we compare the proposed GPAM-PSO with 11 existing PSO variants by using 22 benchmark problems of 30-dimensions and 100-dimensions, respectively. Numerical experiments demonstrate that the proposed GPAM-PSO could improve the accuracy and efficiency remarkably, which means that the combination of the globally-optimal prediction-based search and the adaptive mutation strategy could accelerate the convergence and reduce premature phenomenon effectively. Generally speaking, GPAM-PSO performs most efficiently and robustly. Moreover, the performance on an engineering problem demonstrates the practical application of the proposed GPAM-PSO algorithm.

This paper looks at the challenge of object recognition from the perspective of achieving the final goals of practical real-world autonomous robot-vision applications; that of identifying a target of interest in the robot’s field of view and properly localizing its position in preparation for the higher-level goal of tracking and navigation. A unified framework is introduced that combines a multidimensional feature histogram approach with a multiscale pyramid approach for training-less color object recognition and localization, with direct application to autonomous robotic agents. This framework addresses the high computational cost associated with multidimensional processing by deriving the Multidimensional “Laplacian Feature Histogram Pyramid”, a novel approach to a unified multidimensional-multiscale histogram representation. Furthermore, a Taylor series formulation is employed to combine the multiscale levels of the multidimensional Laplacian feature histogram pyramid into one efficient multidimensional-multiscale “Laplacian-Taylor Feature Histogram” for rapid object recognition and localization. The paper describes the criteria for target detection and localization by autonomous robots and how this newly developed framework fits these needs. Comparative results demonstrate the robustness of this recognition framework to noise and localization of target objects in cluttered scenes.

This study provides a comprehensive overview of the publications in Information Sciences (INS) from 1968 to 2016 inclusive, which encompasses the history of this journal from its inception. 7721 articles containing 153,606 references, which are the primary data source were downloaded from the Web of Science. It studies the most prolific authors, most cited authors, most representative articles, top influential institutions and the nationalities of the authors whose papers were published in the journal. The key contributors and INS articles that have made profound impact are highlighted on a basis of bibliometric and customized text mining techniques. CiteSpace, a data visualization software, was used to make the comprehensive analysis of the 153,606 citations and construct the co-citation network maps, which can illustrate salient patterns and emerging trends. This paper not only provides the important reference to future studies by exploring the structures and trends of INS publications, which have evolved over time, but also offers a demonstration of an effective analytical method for evaluating journal citation and co-citation data in the future.

This paper develops a particle swarm optimisation (PSO) based framework for multi-objective optimisation (MOO). As a part of development, a new PSO method, named self-adaptive PSO (SAPSO), is first proposed. Since the convergence of SAPSO determines the quality of the obtained Pareto front, this paper analytically investigates the convergence of SAPSO and provides a parameter selection principle that guarantees the convergence. Leveraging the proposed SAPSO, this paper then designs a SAPSO-based MOO framework, named SAMOPSO. To gain a well-distributed Pareto front, we also design an external repository that keeps the non-dominated solutions. Next, a circular sorting method, which is integrated with the elitist-preserving approach, is designed to update the external repository in the developed MOO framework. The performance of the SAMOPSO framework is validated through 12 benchmark test functions and a real-word MOO problem. For rigorous validation, the performance of the proposed framework is compared with those of four well-known MOO algorithms. The simulation results confirm that the proposed SAMOPSO outperforms its contenders with respect to the quality of the Pareto front over the majority of the studied cases. The non-parametric comparison results reveal that the proposed method is significantly better than the four algorithms compared at the confidence level of 90% over the 12 test functions.

The paper deals with two crucial steps in multi-criteria decision analysis, that are consistency of the judgments and priority vectors for alternatives/criteria. From a side, several consistency indices are proposed for measuring the consistency of a Pairwise Comparison Matrix. From another one, conditions weaker than consistency, such as transitivity and weak consistency, are proposed for representing further levels of coherence of a Decision Maker when he/she expresses his/her preferences by means of reciprocal Pairwise Comparison Matrix. Firstly, in this paper, a simulation is performed in order to establish a relation between random consistency index and coherence level. Then, since weak consistency ensures reliability to priority vectors proposed in literature, a second simulation is performed in order to measure, in case of no weak consistency, the reliability of these priority vectors.

Several recent papers have studied the problem of attribute reduction in concept lattices by using a discernibility matrix in various extensions of formal concept analysis. We recall the clarification and reduction method by Ganter & Wille and show that it is strictly superior to the methods based on discernibility matrix. Consequently, we show how to adapt the clarification and reduction method to the extensions of formal concept analysis considered in the recent papers.

This paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete-time systems with time-varying delay. The novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual Jensen inequality, the Abel-Lemma based inequality and the Seuret inequality. Based on the inequality, sufficient conditions are established to ensure the systems to be admissible. Moreover, the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed-loop system is admissible. The conditions can be solved by a modified cone complementarity linearization (CCL) algorithm. Examples are given to show the effectiveness of the proposed method.

This paper is concerned with the problem of designing decentralized quantized controller for networked control systems (NCSs) that are subject to time-varying transmission intervals, packet dropout, communication constraints and limited bandwidth. The convex overapproximation method proposed in Donkers and Heemels (2011) is used to handle with time-varying transmission intervals. Packet dropout process in this paper is modeled as both independent identically distributed process and homogeneous Markov jumping process. The uniform quantizer is adopted here to deal with limited bandwidth. In quantization strategy, which switches between zooming out and zooming in modes, a variable called proportionality coefficient of saturation value is used to handle with the complex coupling relationship between system states and quantized variables. Periodic protocol is used here to deal with communication constraints, under which only one node can access the network and send its information per transmission. Within this setup, we derive stability results in terms of linear matrix inequalities (LMIs). An illustrative example is given to show the usefulness of the proposed framework for the stability analysis of some classes of NCSs.

The traditional redundancy allocation problem (RAP) aims to determine a system structure that strikes an appropriate balance between series and parallel components and that maximizes reliability by using redundant components in parallel, thus satisfying resource consumption constraints. The RAP is a well-known NP-hard problem and has been an active area of research for the past four decades. By extending the seriesparallel structure to a more general network structure, this paper proposes a novel RAP called the generalized RAP (GRAP). To reduce the computational burden in solving this intractable GRAP, a new algorithm, called the hybrid swarm optimization (HSO), is proposed. The HSO combines concepts from simplified swarm optimization (SSO), particle swarm optimization (PSO), simulated annealing, and network reliability methods. The paper presents designed experiments and computational studies that demonstrate the potential of using the proposed HSO for the GRAP instead of using the genetic algorithm, PSO, or SSO.

Support vector machine (SVM) is one of the most successful classifiers for remote sensing image classification. However, the performance of SVM is mainly dependent on its parameters; in addition, for remote sensing images with high-dimensional features, feature redundancy will have a major influence on the classification efficiency and accuracy. Feature selection and parameter optimization are two important factors for improving the performance of SVM and are traditionally solved separately. In fact, these two issues are affected by each other, so to obtain the better classification performance, selection of the optimal feature subset and tuning of SVM parameters should be considered simultaneously, as they both belong to the combinatorial optimization problem and could be handled with evolutionary algorithms or swarm intelligence algorithms. In this paper, a remote sensing image classification technique based on the optimal SVM is proposed, in which the parameters of SVM and feature selection are handled integrally by a modified coded ant colony optimization algorithm combined with genetic algorithm. The results are compared with other evolutionary algorithms and swarm intelligence algorithms, such as genetic algorithm (GA), binary-coded particle swarm optimization (BPSO) algorithm, binary-coded ant colony optimization (BACO) algorithm, binary-coded differential evolution (BDE) algorithm, and binary-coded cuckoo search (BCS) algorithm. It is demonstrated that the proposed method is robust, adaptive and exhibits the better performance than the other methods involved in the paper in terms of fitness values, so could be suitable for some practical applications.

In the paper, we describe the new measure of matching fuzzy sets. The introduced measure of perturbation of one fuzzy set by another fuzzy set is considered instead of commonly used distance between two fuzzy sets. The operations known in the fuzzy set theory are used and the perturbation of one fuzzy set by another fuzzy set is understood as a measure describing changes of the first fuzzy set after adding the second one. Obviously, the opposite case can also be considered wherein the second fuzzy set is perturbed by the first one. In general, the new measure is asymmetric and can provide more information compare to a distance between fuzzy sets. The values of such measures of fuzzy sets perturbation are in range between 0 and 1. In this paper several mathematical properties of the measure of fuzzy sets perturbation are studied, and the measure of sets perturbation is compared to other selected measures.

This paper proposed a new algorithm based on kernel functions to predict activity of molecule.The proposed kernel functions used the paths of stars as vector of features.Reduction technique is proposed based on the relationship between features.The proposed algorithm was tested on two datasets and competitive results were obtained in accuracy and complexity. Information and computer science fields such as machine learning and graph theory are implemented in chemoinformatics to discover the properties of chemical compounds. This paper presents a new algorithm based on the two-class support vector machine (SVM) model, which has new kernel functions for paths of features, enabling the prediction of chemical compound activity. Initially, we extract all paths of features (star subgraphs) with certain lengths, and we encode them depending on their structure in the graphs. Then, we use these codes to construct two relationship matrices between those paths. These matrices contain common and different sub-paths between paths of stars. The number of sub-paths/paths for each compound is passed to the proposed kernel functions in the two-class SVM to predict the activity of chemical compounds. The relationship matrices created by the proposed algorithm help to reduce the number of features, which improves prediction accuracy. We apply the proposed algorithm with and without feature selection using two benchmark datasets, specifically, the monoamine oxidase (MAO) dataset and the AIDS antiviral screen database of active compound dataset, which have 68 and 2000 chemical compounds, respectively. We perform comparative experiments for the proposed kernel functions and many other two-class SVM prediction methods, and the results before feature selection show prediction accuracies of 94% and 99.5% for MAO and AIDS, respectively. After selection, the prediction accuracies are 96% and 99.5% for MAO and AIDS, respectively.

A novel concept extended salient region is proposed in this paper. It is defined as the combination of the salient region and its surrounding ones.A graph model with visual content nodes is proposed to represent the input image. We extract the visual content with the well-known Bag of Words model based on Gabor, SIFT and HSVH features.A novel matching algorithm between two images is designed. We define a new similarity measure by combining the similarities of the salient region and the surrounding regions with weights.An improved measure named as mean label average precision is proposed. It is used to evaluate the accuracy of image retrieval. The salient region is the most important part of an image. The salient portion in images also attracts the most attention when people search for images in large-scale datasets. However, to improve image retrieval accuracy, considering only the most salient object in an image is insufficient because the background also influences the accuracy of image retrieval. To address this issue, this paper proposes a novel concept called the extended salient region (ESR). First, the salient region of an input image is detected using a Region Contrast (RC) algorithm. Then, a polar coordinate system is constructed; the centroid of the salient region is set as the pole. Next, the regions surrounding the salient region are determined by the neighboring regions, moving in a counterclockwise direction. The resulting combination of the salient region and its surrounding regions is defined as the ESR. We extract the visual content from the ESR using the well-known Bag of Words (BoW) model based on Gabor, SIFT and HSVH features and propose a graph model of the visual content nodes to represent the input image. Then, we design a novel algorithm to perform matching between two images. We also define a new similarity measure by combining the similarities of the salient region and the surrounding regions using weights. Finally, to better evaluate the image retrieval accuracy, an improved measure called the mean label average precision (MLAP) is proposed. The results of experiments on three benchmark datasets (Corel, TU Darmstadt, and Caltech 101) demonstrate that our proposed ESR model and region-matching algorithm are highly effective at image retrieval, and can achieve more accurate query results than current state-of-the-art methods.

In this paper, we propose a new multiattribute decision making (MADM) method based on the interval-valued intuitionistic fuzzy weighted geometric average (IIFWGA) operator, the accuracy function of interval-valued intuitionistic fuzzy values (IVIFVs) and particle swarm optimization (PSO) techniques, where the weights of attributes and the evaluating values of alternatives with respect to attributes are represented by IVIFVs. First, the proposed method uses an accuracy function to transform the decision matrix given by the decision maker and represented by IVIFVs into a transformed decision matrix represented by real values in [1,1]. Then, it produces the optimal weights of the attributes based on the obtained transformed decision matrix and PSO techniques. It determines the weighted evaluating IVIFV of each alternative based on the IIFWGA operator, the obtained optimal weights of the attributes and the decision matrix given by the decision maker represented by IVIFVs. Finally, it calculates the transformed value of the weighted evaluating IVIFV of each alternative based on the accuracy function to get the preference order of the alternatives. The main contribution of this paper is that we propose a new MADM method based on the IIFWGA operator of IVIFVs, the accuracy function of IVIFVs and PSO techniques, which can overcome the drawbacks of the existing MADM methods for MADM in interval-valued intuitionistic fuzzy (IVIF) environments.

Stochastic processes with semicontious covariances are introduced in a flexible way.Useful optimal designs are computed.Groundbreaking financial applications for probabilities of ruin, Famas hypothesis on EMH and IS/LM model. We are encountering deep financial crisis. One of the basic problems we face is how to predict financial developments. Current modelling is clearly insufficient since continuity of autocorrelation oversmoothes the empirical financial data. We prove that geometric probability to chose positive definite continuous covariance by financial data is zero. We also have the empirical evidence for this fact from real stock data. In order to overcome this gap we introduce the novel abc class of semicontinuous covariance functions, which integrates both continuous and discontinuous covariances. The abc class of covariances is much more flexible, powerful, and realistic than its continuous counterpart. It gives answer to the question why financial markets face negative interest rates, cyclic downbreaks, and other difficulties nowadays. As it is clearly illustrated in this paper, the experimenter (e.g.the financial institution) can choose only up to some extent whether abc class member will be positive definite everywhere. To the best knowledge of the authors this fits well to the own Kolmogorovs opinions on axiomatic theory of probability. The Kolmogorovs axiomatic theory of probability was developed as one possible alternative in order to utilize the flexibility of Lebesgue integral in probability theory, but in many experiments e.g.in physics and finance, one should go beyond this axiomatics. That means one should accept negative probabilities (and consequently negative definite covariance functions). In this paper we clarify that the modelers choice of positive/negative definite functions should be considered within broader Information Theory setup. The introduced abc class is purely topologically defined, with soft regularity conditions on covariances, which are still applicable for increasing and infill domain asymptotics for regression problems, kriging, and finance. These conditions are related to semicontinuous maps of Ornstein Uhlenbeck (OU) processes. We provide several novel results for optimal design of random fields with abc covariances, random walks in finance, and probabilities of ruins related to shocks (e.g.by earthquakes). In particular, we construct a random walk model with semicontinuous covariance. The novel abc class provides a proper environment for unifying several contradictions on IS/ML model in the economic literature. All mentioned novel economical applications are hardly visible from currently used continuous covariance framework.

Rough set models on two universes are valuable generalizations of classic rough set model. These models can be applied into formal concept analysis and decision-making system. This paper focuses on catoptrical approach for rough set models over two universes using granule-based definition. In this paper, we propose a new catoptrical rough set model over dual universes. The properties of the proposed model are discussed. Consequently, a variable precision extension of the model is presented. Some properties of the extended model are obtained. Finally, we investigate a further extension of the proposed model, i.e. variable precision catoptrical rough set model with two parameters.

Pawlak’s rough membership functions not only give numerical characterizations of Pawlak’s rough set approximations, but also establishes the relationships between Pawlak’s rough sets and fuzzy sets or probabilistic rough sets. However, it is noteworthy that Pawlak’s rough membership functions have limitations when handling incomplete data that exist widely in the real world. As will be shown in this paper, one way to overcome this is to construct rough membership functions for covering-based rough sets. In this paper, we first use an example in evidence-based medicine to illustrate how to use Pawlak’s rough membership function on numerically characterizing decisions under the circumstances where data are complete. Then, we construct covering-based rough membership functions for four types of covering-based rough sets which were examined by Zhu and Wang (in IEEE Transactions on Knowledge and Data Engineering 19(8)(2007) 1131-1144 and Information Sciences 201(2012) 80-92), and use them to characterize these covering-based rough sets numerically. Finally, we present theoretical backgrounds for these covering-based rough membership functions, and illustrate how to apply them on numerically characterizing decisions under the circumstances where data are incomplete.

In this paper, we propose a new fuzzy forecasting method based on two-factors second-order fuzzy-trend logical relationship groups (TSFTLRGs), particle swarm optimization (PSO) techniques and similarity measures between the subscripts of fuzzy sets (FSs) for forecasting the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the New Taiwan Dollar/US Dollar (NTD/USD) exchange rates. First, we propose a PSO-based optimal-intervals partition algorithm to get the optimal partition of the intervals in the universe of discourse (UOD) of the main factor TAIEX and to get the optimal partition of the intervals in the UOD of the secondary factor SF, where SF ź {Dow Jones, NASDAQ, M1B}. Based on the proposed PSO-based optimal-intervals partition algorithm, the constructed TSFTLRGs, and similarity measures between the subscripts of FSs, we propose a new method for forecasting the TAIEX and the NTD/USD exchange rates. The main contribution of this paper is that we propose a new fuzzy forecasting method based on TSFTLRGs, PSO techniques and similarity measures between the subscripts of FSs for forecasting the TAIEX and the NTD/USD exchange rates to get higher forecasting accuracy rates than the ones of the existing fuzzy forecasting methods.

This paper is concerned with the stochastic stability and stabilization problem for a class of continuous-time semi-Markovian jump systems (S-MJSs) with mode transition-dependent sojourn-time distributions. In contrast to other approaches, this paper offers the possibility to explore more refined probability models on the sojourn-time by considering the mode transition-dependent sojourn-time distributions instead of mode-dependent ones. Here, to construct a finite set of linear matrix inequalities (LMIs) from sojourn-time-dependent matrix inequalities, a less conservative relaxation method is proposed in such a way that all available constraints on time-varying transition rates can be exploited. Simulation examples report the effectiveness of the proposed method.

Deep Neural Networks for image/video classification have obtained much success in various computer vision applications. Existing deep learning algorithms are widely used on RGB images or video data. Meanwhile, with the development of low-cost RGB-D sensors (such as Microsoft Kinect and Xtion Pro-Live), high-quality RGB-D data can be easily acquired and used to enhance computer vision algorithms [14]. It would be interesting to investigate how deep learning can be employed for extracting and fusing features from RGB-D data. In this paper, after briefly reviewing the basic concepts of RGB-D information and four prevalent deep learning models (i.e., Deep Belief Networks (DBNs), Stacked Denoising Auto-Encoders (SDAE), Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) Neural Networks), we conduct extensive experiments on five popular RGB-D datasets including three image datasets and two video datasets. We then present a detailed analysis about the comparison between the learned feature representations from the four deep learning models. In addition, a few suggestions on how to adjust hyper-parameters for learning deep neural networks are made in this paper. According to the extensive experimental results, we believe that this evaluation will provide insights and a deeper understanding of different deep learning algorithms for RGB-D feature extraction and fusion.

In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterization of the L -fuzzy tolerance relations and the L -fuzzy equivalence relations that a strict order relation is compatible with. In this paper, we extend the notion of clone relation to any binary relation. Although the definition of such extension is trivial, the corresponding properties significantly differ from those of the clone relation of a strict order relation. We analyse the most important ones among these properties, paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones.

In this paper, by considering the notion of equality algebra, which is introduced by Jenei in 18, as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras.

Decision evaluation functions in three-way decision spaces must meet three axioms, the minimum element axiom, the monotonicity axiom and the complement axiom. Maintaining the complement axiom of decision evaluation functions is crucial to three-way decisions to simplify the decision rules based only on the conditional probability and the loss functions. However, some handy functions do not satisfy the complement axiom. This paper introduces the notion of semi-decision evaluation functions not necessarily satisfying the complement axiom but the minimum element axiom and the monotonicity axiom, and presents some transformation methods from semi-decision evaluation functions to decision evaluation functions. Through numerous examples this paper demonstrates the existence of semi-decision evaluation functions and significance of the transformation methods.

Orthogonal moments play an important role in image analysis and other similar applications. However, existing orthogonal moments are restricted to integer order, and little investigation of non-integer order orthogonal moments has been conducted to date. In this paper, a general framework of real-order orthogonal moments, also known as fractional-order orthogonal moments, is proposed. In this general framework, fractional-order orthogonal moments can be defined in Cartesian and polar coordinate systems. Shifted Legendre polynomials are implemented in this paper to investigate the properties of fractional-order orthogonal moments. A series of experiments are performed, which demonstrate that fractional-order orthogonal moments are not only capable of region-of-interest (ROI) feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition.

Clustering analysis is a fundamental technique in machine learning, which is also widely used in information granulation. Multiple clustering systems granulate a data set into multiple granular structures. Therefore, clustering ensemble can serve as an important branch of multigranulation information fusion. Many approaches have been proposed to solve the clustering ensemble problem. This paper focuses on the direct approaches which involve two steps: finding cluster correspondence and utilizing a fusion strategy to produce a final result. The existing direct approaches mainly discuss the process of finding cluster correspondence, while the fusing process is simply done by voting. In this paper, we mainly focus on the fusing process and propose a Dempster-Shafer evidence theory-based clustering ensemble algorithm. The advantage of the algorithm is that the information of an object's surrounding cluster structure is taken into consideration by using its neighbors to describe it. First, we find neighbors of each object and generate its label probability outputs in every base partition. Second, these label probability outputs are integrated based on DS theory. Theoretically, our method is superior to other voting methods. Besides, several experiments show that the proposed algorithm is statistically better than seven other clustering ensemble methods.

Billions of resources, such as cars, clothes, household appliances and even food are being connected to the Internet forming the Internet of Things (IoT). Subsets of these resources can work together to create new self-regulating IoT applications such as smart health, smart communities and smart homes. However, several challenging issues need to be addressed before this vision of applications based on IoT concepts becomes a reality. Because many IoT applications will be distributed over a large number of interacting devices, centralized control will not be possible and so open problems will need to be solved that relate to building locally operating self-organizing and self-adaptive systems. As an initial step in creating IoT applications with these features, this paper presents a Framework for IoT (FIoT). The approach is based on Multi-Agent Systems (MAS) and Machine Learning Techniques, such as neural networks and evolutionary algorithms. To illustrate the use of FIoT, the paper contains two different IoT applications: (i) Quantified Things and (ii) Smart traffic control. We show how flexible points of our framework are instantiated to generate these IoT application.

In MMMF, ratings matrix with multiple discrete values is treated by specially extending hinge loss function to suit multiple levels.We view this process as analogous to extending two-class classifier to a unified multi-class classifier.Alternatively, multi-class classifier can be built by arranging multiple two- class classifiers in a hierarchical manner.In this paper, we investigate this aspect for collaborative filtering and propose an efficient and novel framework of multiple bi-level MMMFs.We compare our method with nine well-known algorithms on two benchmark datasets and show that our method outperforms these methods on NMAE measure. Maximum Margin Matrix Factorization (MMMF) has been a successful learning method in collaborative filtering research. For a partially observed ordinal rating matrix, the focus is on determining low-norm latent factor matrices U (of users) and V (of items) so as to simultaneously approximate the observed entries under some loss measure and predict the unobserved entries. When the rating matrix contains only two levels (1), rows of V can be viewed as points in k-dimensional space and rows of U as decision hyperplanes in this space separating +1 entries from 1 entries. When hinge/smooth hinge loss is the loss function, the hyperplanes act as maximum-margin separator. In MMMF, rating matrix with multiple discrete values is treated by specially extending hinge loss function to suit multiple levels. We view this process as analogous to extending two-class classifier to a unified multi-class classifier. Alternatively, multi-class classifier can be built by arranging multiple two-class classifiers in a hierarchical manner. In this paper, we investigate this aspect for collaborative filtering and propose an efficient and novel framework of multiple bi-level MMMFs. There is substantial saving in computational overhead. We compare our method with nine well-known algorithms on two benchmark datasets and show that our method outperforms these methods on NMAE measure. We also show that our method yields latent factors of lower ranks and the trade-off between empirical and generalization error is low.

This paper investigates a decentralized event-triggering communication scheme for large-scale systems under network environments. First, a decentralized event-triggering communication (DETC) scheme for large-scale systems is proposed, which does not require that all transmitted nodes are synchronous. Second, a heuristic algorithm is presented to optimize the parameters of DETC to reduce the occupancy of the network resources induced by DETC. Third, by constructing a novel LyapunovKrasovskii functional, a stability criterion and a stabilization criterion are derived for ensuring that the solution of studied system is uniformly ultimately bounded (UUB). Compared with some existing emulation-based methods, the controller gains in this paper are no longer required to be known a priori. Finally, an example is given to show the effectiveness of the proposed approach.

In this paper, we study the model-checking problem of linear-time properties in multi-valued systems. Safety properties, invariant properties , liveness properties , persistence and dual-persistence properties in multi-valued logic systems are introduced. Some algorithms related to the above multi-valued linear-time properties are discussed. The verification of multi-valued regular safety properties and multi-valued ω -regular properties using lattice-valued automata are thoroughly studied. Since the law of non-contradiction (i.e., a ∧ ¬ a = 0 ) and the law of excluded-middle (i.e., a ∨ ¬ a = 1 ) do not hold in multi-valued logic, the linear-time properties introduced in this paper have new forms compared to those in classical logic. Compared to those classical model-checking methods, our methods to multi-valued model checking are accordingly more direct: We give an algorithm for showing TS⊧P for a model TS and a linear-time property P, which proceeds by directly checking the inclusion Traces(TS) ⊆ P instead of T r a c e s ( T S ) ∩ ¬ P = ∅ . A new form of multi-valued model checking with membership degree is also introduced. In particular, we show that multi-valued model checking can be reduced to classical model checking. The related verification algorithms are also presented. Some illustrative examples and a case study are also provided.

We confirm that agent-ants can learn only via the pheromone trail.It is better to use both the heuristic function and the pheromone trail.The ACDT alg. makes it possible to optimize the construction of decision trees based on a heuristic.The pheromone map clearly present a data set as the solution space and pheromone trail values.Analysis of pheromone maps shows that the ACDT alg. searches different subspaces of the solution space. This paper considers the topic of cooperation between agent ants in an Ant Colony Optimization (ACO) algorithm that is used to construct decision trees (Ant Colony Decision Tree or ACDT). To follow a suitable methodology, the paper presents a formal definition of the ACDT algorithm with a focus on the influence that Ant Colony Optimization algorithms have on the obtained results. The aim of this paper is to provide the rationale for using swarm intelligence (i.e., ACO) in the process of constructing decision trees. Many experiments were conducted to provide a solid justification. These experiments tested cooperation between agent ants in ant colony algorithms with different ACO performance scenarios: the application of only a pheromone trail, the application of only a heuristic function, the application of both components, and the application of neither component. Additionally, different values of the pheromone trail were tested at various stages of the algorithm's operation and pheromone representations were presented. The experiments were conducted on 30 publicly available data sets; all observations were preceded by statistical tests. This paper confirms that it is reasonable to use the pheromone trail and balanced heuristics. Moreover, we found that, for the ACDT algorithm, good results can also be obtained without heuristics.

Over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand, evaluate, or compare them all. In principle, optimization methods, including the recently popular Evolutionary Computation or Swarm Intelligence-based ones, should be developed in order to solve real-world problems. Yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only, so their usefulness for various practical applications remains unverified. As a result, choosing the proper method for a particular real-world problem is a difficult task. This paper shows that such a choice is even more complicated if one wishes, with good reason, to use metaheuristics twice, once to find the best and then to find the worst solutions for the specific numerical real-world problem. It often occurs that for either case different optimizers are to be recommended. The above finding is based on testing 30 metaheuristics on numerical real-world problems from CEC2011. First we solve 22 minimization problems as defined for CEC2011. Then we reverse the objective function for each problem and search for its maximizing solution. We also observe that algorithms that are highly ranked on average may not perform best for any given specific problem. Rather, the highest average ranking may be achieved by methods that are never among the poorest ones. In other words, occasional winners may get less attention than rare losers.

In order to address the problem of retinal image registration, this paper proposes and analyzes a novel and general matching algorithm called Multi-Attribute-Driven Regularized Mixture Model (MAD-RMM). Mismatches removal can play a key role in image registration, which refers to establish reliable matches between two point sets. Here the presented approach starts from multi-feature attributes which are used to guide the feature matching to identify inliers (correct matches) from outliers (incorrect matches), and then estimates the spatial transformation. In this paper, motivated by the problem of feature matching that the initial correspondence is always contaminated by outliers, thereby we formulate this issue as a probability deformable mixture model which consists of Gaussian components for inliers and uniform components for outliers. Moreover, the algorithm takes full advantage of using multiple attributes for better general matching performance. Here we are assuming all inliers are mapped into a high-dimensional feature space, namely reproducing kernel Hilbert space (RKHS), and the closed-form solution to the mapping function is given by the representation theorem with L2 norm regularization under the Expectation-Maximization (EM) algorithm. Finally, we evaluate the performance of the algorithm by applying it to retinal image registration on several datasets, where experimental results demonstrate that the MAD-RMM outperforms current state-of-the-art methods and shows the robustness to outliers on real retinal images.

In recent years, there has been great progress in the wider use of three-dimensional (3D) technologies. With increasing sources of 3D content, a useful tool is needed to evaluate the perceived quality of the 3D videos/images. This paper puts forward a framework to evaluate the quality of stereoscopic images contaminated by possible symmetric or asymmetric distortions. Human visual system (HVS) studies reveal that binocular combination models and visual saliency are the two key factors for the stereoscopic image quality assessment (SIQA) metric. Therefore inspired by such findings in HVS, this paper proposes a novel saliency map in SIQA metric for the cyclopean image called "cyclopean saliency", which avoids complex calculations and produces good results in detecting saliency regions. Moreover, experimental results show that our metric significantly outperforms conventional 2D quality metrics and yields higher correlations with human subjective judgment than the state-of-art SIQA metrics. 3D saliency performance is also compared with "cyclopean saliency" in SIQA. It is noticed that the proposed metric is applicable to both symmetric and asymmetric distortions. It can thus be concluded that the proposed SIQA metric can provide an effective evaluation tool to assess stereoscopic image quality.

Rough set theory, as a new mathematical tool to handle uncertainty decision making problems, was used to study conflict analysis decision making in late90's, and then the Pawlak conflict analysis model was established. The approach of rough set provides a new perspective and also gives an effective tool to deal with conflict analysis decision making, both theoretically and practically. In this paper, we propose a new rough set model of conflict analysis: a conflict analysis decision model based on rough set theory over two universes. It is a natural extension of the Pawlak conflict analysis model. Subsequently, we define the conflict matrix and a consistent disagreement matrix on the basis of the model proposed in this paper. Then we can find the intrinsic reasons for conflict and attain a feasible strategy for a conflict situation. Furthermore, we define a positive alliance matrix and a negative alliance matrix for a conflict situation. These can help us analyze the opinions of different agents in the conflict situation. Moreover, we develop a matrix approach for a conflict analysis model based on rough set theory over two universes, which provides a convenient way to analyze and solve the conflict situation. Comparing to the Pawlak conflict analysis model, our proposed model not only could reveal the core causes for a conflict situation but also can find a possible optimal feasible consensus strategy to solve the conflict situation which satisfies the agents as much as possible. Finally, we illustrate the idea and the basic principles established in this paper by analyzing a conflict decision making scenario.

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms.

In this paper we propose a design for the kNN rule classifier based on GPU devices.This design overcomes the dependency between dataset size and GPU memory required.An efficient CPU-GPU communication scheme is designed.The carefully designed kernels for each step of the computation improve the run-time performance.An efficient selection algorithm replaces the sorting algorithm traditionally used to find the neighborhood. The k nearest neighbor (kNN) rule is one of the most used techniques in data mining and pattern recognition due to its simplicity and low identification error. However, the computational effort it requires is directly related to the dataset sizes, hence delivering a poor performance on large datasets. The use of graphics processing units (GPU) has improved the run-time performance of the kNN rule but the computational requirements of current approaches limit this performance as the dataset size increases.In this paper, we propose a new scalable and memory efficient design for a GPU-based kNN rule, called GPU-SME-kNN, that breaks the dependency between dataset size and memory footprint while delivering high performance. An experimental study of GPU-SME-kNN is presented showing a high performance, even in cases that other methods cannot address, while the computational requirements are suitable for most commercial GPU devices. Our design has also been applied to kNN-based lazy learning algorithms reducing run-times in a significant way.

This paper is concerned with the problem of stability and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional, sufficient conditions for ensuring the asymptotic stability and stabilization of the concerned fuzzy systems have been derived within the framework of linear matrix inequalities (LMIs). The advantage and effectiveness of the proposed criteria will be shown through the comparison of maximum delay bounds with some results obtained by recently published papers via four numerical examples.

This paper addresses a multi-resource-constrained flexible job shop scheduling problem with makespan criterion.A dynamic shuffled multi-swarm micro-migrating birds optimizer (MBO) is proposed.Advanced technologies including micro-MBO, multi-swarm parallel search, random shuffle process, diversity controlling strategy, and adaptive search operator are introduced.The proposed algorithm outperforms the existing state-of-art algorithms in terms of solution quality and computational efforts.9 out of 10 best known solutions for the benchmarks in the literature are improved. Scheduling problems with resource constraints have been a new research trend in recent years. This paper addresses a multi-resource-constrained flexible job shop scheduling problem that is very common in semiconductor manufacturing, precision engineering, and many other modern industries. To address this important problem, a novel algorithm called the shuffled multi-swarm micro-migrating birds optimization (SM2-MBO) algorithm is presented with a two-vector representation. The SM2-MBO forms a number of micro-swarms, each of which performs its own MBO independently. A random shuffle process applied to the entire population is invoked periodically to propagate the good information that is found in some of the micro-swarms. A diverse controlling strategy based on the aging phenomenon of life is proposed to diversify the population. An adaptive search operator based on a problem-specific crossover and a two-vector crossover helps to balance exploitation and exploration. Numerical experiments and comparisons are conducted against the best performing algorithms reported in the literature for the considered problem. The results demonstrate that the proposed SM2-MBO performs significantly better than the existing algorithms in solving the multi-resource-constrained flexible job shop scheduling problem with the makespan criterion. Furthermore, the proposed SM2-MBO can improve 9 out of 10 best known solutions for the benchmark instances in the literature.

A closed-form local adaptive contrast operation is proposed.The motion consistency characteristic is explored for the first time.Spatio-temporal saliency is specifically modeled for dim moving target detection.The proposed approach can outperform existing approaches remarkably. Dim moving target detection from infrared image sequences, which lags behind the visual perception ability of humans, has attracted considerable interest from researchers due to its crucial role in airborne surveillance systems. This paper proposes a novel spatio-temporal saliency model to cope with the infrared dim moving target detection problem. Based on a closed-form solution derived from regularized feature reconstruction, a local adaptive contrast operation is proposed, whereby the spatial saliency map and the temporal saliency map can be calculated on the spatial domain and the temporal domain. In order to depict the motion consistency characteristic of the moving target, this paper also proposes a transmission operation to generate the trajectory prediction map. The fused result of the spatial saliency map, the temporal saliency map, and the trajectory prediction map is called the "spatio-temporal saliency map" in this paper, from which the target of interest can be easily segmented. A diverse test dataset comprised of three infrared image sequences under different backgrounds was collected to evaluate the proposed model; and extensive experiments confirmed that the proposed spatio-temporal saliency model can achieve much better detection performance than the state-of-the-art approaches.

Estimation of Distribution Algorithms (EDAs) constitutes a class of evolutionary algorithms that can extract and exploit knowledge acquired throughout the optimization process. The most critical step in the EDAs is the estimation of the joint probability distribution associated to the variables from the most promising solutions determined by the evaluation function. Recently, a new approach to EDAs has been developed, based on copula theory, to improve the estimation of the joint probability distribution function. However, most copula-based EDAs still present two major drawbacks: focus on copulas with constant parameters, and premature convergence. This paper presents a new copula-based estimation of distribution algorithm for numerical optimization problems, named EDA based on Multivariate Elliptical Copulas (EDA-MEC). This model uses multivariate copulas to estimate the probability distribution for generating a population of individuals. The EDA-MEC differs from other copula-based EDAs in several aspects: the copula parameter is dynamically estimated, using dependence measures; it uses a variation of the learned probability distribution to generate individuals that help to avoid premature convergence; and uses a heuristic to reinitialize the population as an additional technique to preserve the diversity of solutions. The paper shows, by means of a set of parametric tests, that this approach improves the overall performance of the optimization process when compared with other copula-based EDAs and with other efficient heuristics such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES).

In this paper, we study a new type of fuzzy covering-based rough set model by introducing the notion of fuzzy β-minimal description. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-minimal description and study its properties. Then, we define a novel type of fuzzy covering-based rough set model and investigate the properties of this model. Furthermore, the axiomizations and matrix representations of the fuzzy covering lower and fuzzy covering upper approximations are the vital problems we investigate in this paper. Moreover, we explore the conditions under which two fuzzy β-coverings generate the same fuzzy covering lower or fuzzy covering upper approximations. Finally, we generalize the model to L-fuzzy covering-based rough set which is defined over fuzzy lattices. Similar to the fuzzy covering-based rough set model, we also address the issues mentioned above to the L-fuzzy covering-based rough set.