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Abstract: In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework. [Copyright &y& Elsevier]

Abstract: In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified. [Copyright &y& Elsevier]

This paper focuses on the problem of the fully distributed fixed-time bipartite output consensus tracking for nonlinear heterogeneous multiagent systems (MASs) via both state-feedback and output-feedback methods under the switching topology. The adaptive fully distributed state observers with quantization information are designed to eliminate the dependence on the Laplacian matrix. For MASs with unknown model matrix, a novel fixed-time observer-based regulator equation is employed, which avoids repeatedly getting the unnecessary solution of universal one in the time-varying cooperation-competition communication topology. In this case, both fixed-time state-feedback and output-feedback controllers are constructed such that the output consensus tracking is achieved regardless the state value is available or unavailable. Besides, the upper bound of convergence time can be adjusted only by parameters without initial states. Lyapunov functions are established to derive conditions of achieving consensus tracking by mathematical analysis. Eventually, the effectiveness of the proposed control strategy is manifested by simulation results. [ABSTRACT FROM AUTHOR]

• It is observed that regular convergence indicators are more focused on the convergence and may neglect the extent of the spread. • This paper designs an adaptive reference vector strategy, which is able to take into account the convergence and the extent of the spread, simultaneously. • A new algorithm is proposed and tested on multiple test suites.. Convergence is always a major concern for many-objective optimization problems. Over the past few decades, various methods have been designed for measuring the convergence. However, according to our mathematical and empirical analyses, most of these methods are more focused on the convergence, and may neglect the exploration of boundary solutions, resulting in the incomplete Pareto fronts and the poor extent of spread achieved among the obtained non-dominated solutions. Regarding this issue, this paper proposes a Many-Objective Evolutionary Algorithm with Adaptive Reference Vector (MaOEA-ARV). In MaOEA-ARV, an adaptive reference vector strategy is designed to dynamically adjust the reference vectors according to the current distribution of candidate solutions for ensuring the spread and convergence simultaneously. Additionally, a hierarchical clustering strategy is employed to adaptively partition candidate solutions into multiple clusters for the diversity of candidate solutions. Experimental results on DTLZ, BT, ZDT and WFG test suites with up to 12 objectives demonstrate the effectiveness of MaOEA-ARV. [ABSTRACT FROM AUTHOR]

• The paper is the first paper that provides a comprehensive theoretical analysis to the popular over-sampling method, SMOTE. • The theoretical and empirical analyses demonstrate the divergence of SMOTE patterns from the original minority distribution. • Our theoretical analysis applies to any data distribution, and we provide analysis for two examples of distributions. • We study the impact of number of minority patterns, dimensionality, and K of the KNN used in SMOTE, on SMOTE accuracy. • We study the impact of SMOTE in classification performance theoretically and empirically on LDA, KNN, and SVM classifiers. Imbalanced classification problems are often encountered in many applications. The challenge is that there is a minority class that has typically very little data and is often the focus of attention. One approach for handling imbalance is to generate extra data from the minority class, to overcome its shortage of data. The Synthetic Minority over-sampling TEchnique (SMOTE) is one of the dominant methods in the literature that achieves this extra sample generation. It is based on generating examples on the lines connecting a point and one its K -nearest neighbors. This paper presents a theoretical and experimental analysis of the SMOTE method. We explore the accuracy of how faithful it emulates the underlying density. To our knowledge, this is the first mathematical analysis of the SMOTE method. Moreover, we analyze the effect of the different factors on generation accuracy, such as the dimension, size of the training set and the considered number of neighbors K. We also provide a qualitative analysis that examines the factors affecting its accuracy. In addition, we explore the impact of SMOTE on classification boundary, and classification performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel method for 3D human joint estimation using part segmentation, and introduce an application for size measurement based on the obtained joints. A human segmentation dataset is first prepared as training set for the advanced neural network architecture. Different human parts yielded from the neural network are utilized to extract human joints. In the proposed method, the joints are categorized into the active joints and inert joints. In the extraction process of the active joints, the mathematical analysis method is adopted to calculate the joint positions. The geometric features of different human segments are further used to extract the inert joints. Moreover, we test on the dataset to compare its performance with our previous method based on geometrical features. The results show the average error of the joints is less than 4.2 cm, which is significantly improved from 5.8 cm demonstrated in our previous research. We also investigate the human size measurement. The distance between the joints is used to calculate the length, and the ellipse fitting method based on multi-frame point cloud is adapted to calculate the human girths. Compared with the manual measurement data, the size error is less than 4.1 cm. [ABSTRACT FROM AUTHOR]

Problems of anisotropic functionally graded media which are governed by the transient diffusion–convection–reaction equation of spatially varying coefficients are discussed in this paper. A mathematical analysis is used to transform the variable coefficient equation into a constant coefficient equation. A boundary-only integral equation is then derived from this constant coefficient equation after being Laplace transformed. Numerical solutions to the problems are sought by using a boundary element method (BEM) which is combined with the Stehfest formula for the numerical Laplace transform inversion. Some problems considered are those of compressible or incompressible flow, and of media which are quadratically, exponentially or trigonometrically graded materials. The results obtained show that the analysis used to transform the variable coefficients equation into the constant coefficients equation is valid, and the mixed LT-BEM is easy to implement and accurate for finding numerical solutions. The numerical solutions of some test problems are justified by showing their accuracy. Some non-test problems of geometrically symmetric systems are also considered to show the effect of the anisotropy and inhomogeneity of the material on the solutions by verifying the symmetry of solutions. In addition, the effect of boundary conditions is also exhibited. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As a typical methodology to deal with uncertain issues, the three-way decision (3WD) has been developed rapidly in nearly ten years, both in theories and applications. Three-way classification is one of the important research fields of 3WD, which utilizes the idea of 3WD to solve classification problems. In this paper, we focus on investigating the effectiveness of three-way classification through two evaluation indicators: the classification quality (Precision , Recall , Accuracy and F 1 ) and the decision cost. The comparisons between two-way classification and three-way classification are concretely analyzed, some mathematical properties, judging conditions and decision criteria of these two classification methods are also discussed in detail. Finally, the experimental results on eight UCI data sets validate the mathematical analysis, which reveal the effectiveness of three-way classification. [ABSTRACT FROM AUTHOR]

The Basic Uncertain Information (BUI) is a recently introduced type of uncertain data that has rapidly undergone development and practical application. The existing aggregation operators designed for BUI solely encompass the weighted mean and Choquet integral. The present study puts forth a set of general information fusion frameworks and methodologies aimed at gathering BUI granules. The first mode yields BUI granules as its output, whereas the subsequent two modes generate outputs in the form of interval values. The paper includes numerical examples and applications that correspond to the presented findings. The present study conducts an analysis of various mathematical properties pertaining to the three BUI fusion modes that have been proposed. These properties include idempotency, monotonicities, certainty derived inclusion, certainty monotonicity, homogeneities, non-symmetricity, comonotone additivities, and continuities. The proposals and analyses presented in this work are of a general nature and have the potential to inspire various practical specifications. [ABSTRACT FROM AUTHOR]

Formal concept analysis is a mathematical framework based on lattice theory that aims at representing the information contained in binary object-attribute datasets (called formal contexts) in the form of a lattice of so-called formal concepts. Since its introduction, it has been extended to more complex types of data. In this paper, we are interested in two of those extensions: relational concept analysis and polyadic concept analysis that allow to process, respectively, relational data and n -ary relations. We present a framework for polyadic relational concept analysis that extends relational concept analysis to relational datasets that are made of n -ary relations. We show its basic properties and that it is a valid extension of relational concept analysis. [ABSTRACT FROM AUTHOR]

In this paper the comparison of a proposed neural network with generalized type-2 fuzzy weights (NNGT2FW) with respect to the monolithic neural network (NN) and the neural network with interval type-2 fuzzy weights (NNIT2FW) is presented. Generalized type-2 fuzzy inference systems are used to obtain the generalized type-2 fuzzy weights and are designed by a strategy of increasing and decreasing an epsilon variable for obtaining the different sizes of the footprint of uncertainty (FOU) for the generalized membership functions. The proposed method is based on recent approaches that handle weight adaptation using type-1 and type-2 fuzzy logic. The approach is applied to the prediction of the Mackey–Glass time series, and results are shown to outperform the results produced by other neural models. Gaussian noise was applied to the test data of the Mackey–Glass time series for finding out which of the presented methods in this paper shows better performance and tolerance to noise. [ABSTRACT FROM AUTHOR]

The problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both NP-hard problems. This paper studies the relationship between the two problems. The vertex cover problem for graphs from the perspective of rough sets is first investigated. The attribute reduction of an information system is then studied in the framework of graph theory. The results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph. Conversely, the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph. Finally, a new algorithm for the vertex cover problem based on rough sets is presented. Furthermore, experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental measurements and their mathematical analysis. The decisive parameters (wave speed and damping coefficient) of a mathematical model of the acoustic wave are calibrated by comparing the measurement data with the numerically evaluated exact solution predicted by the mathematical model. The calibration is done both deterministically by minimizing the square error over time and stochastically by a Bayesian approach, implemented through the Metropolis-Hastings algorithm. The resulting posterior distribution of the parameters can be used to construct a Bayesian test for damage. [ABSTRACT FROM AUTHOR]

Possibility theory provides a good framework for dealing with merging problems when information is pervaded with uncertainty and inconsistency. Many merging operators in possibility theory have been proposed. This paper develops a new approach to merging uncertain information modeled by possibilistic networks. In this approach we restrict our attention to show how a "triangular norm" establishes a lower bound on the degree to which an assessment is true when it is obtained by a set of initial hypothesis represented by a joint possibility distribution. This operator is characterized by its high effect of reinforcement. A strongly conjunctive operator is suitable to merge networks that are not involved in conflict, especially those supported by both sources. In this paper, the Lukasiewicz t-norm is first applied to a set of possibility measures to combine networks having the same and different graphical structures. We then present a method to merge possibilistic networks dealing with cycles. [ABSTRACT FROM AUTHOR]

The theory of fuzzy implication algebras was proposed by Professor Wangming Wu in 1990. The present paper reviews the following two aspects of studies on FI-algebras: concepts, properties and some subclasses of FI-algebras; axiomatization of the class of FI-algebras and some of its important subclasses. The main results are summarized in the current paper, the relationships between FI-algebras and several classes of important fuzzy algebras are discussed, such as BL-algebras, MTL-algebras, and residuated lattices, and propositional calculus systems of several special classes of FI-algebras are shown. [ABSTRACT FROM AUTHOR]

• We develop a model of opinion formation that endows the heterogeneous HK dynamics with a time-varying communication topology. • Noise-induced synchronization of our model is rigorously investigated both mathematically and numerically. • We demonstrate that opinion formation is noise-synchronizable if and only if the switching communication topology is uniformly jointly connected. • Our model reveals that connected discourse topology in combination with noise can lead to a quasi-consensus that is inducible from any initial state or anyunderlying system size. • Our findings have profound implications for the design of future strategies for opinion control andoptimization. A fundamental question that arises in the analysis of the noise-based synchronization of opinion dynamics with bounded confidence (BC) is what opinion structures can be synchronized by noise. In the standard Hegselmann-Krause (HK) model, each agent examines the opinion values of all other agents and then selects neighbors who are appropriate for opinion updating in accordance with the BC scheme. In reality, however, people are more likely to exchange opinions with only a limited set of individuals, resulting in a predetermined local communication network as postulated in the DeGroot model. In this paper, we develop a new model of opinion formation that endows the heterogeneous HK dynamics with a time-varying communication topology, and we investigate its noise-induced synchronization both mathematically and numerically. We show that opinion dynamics in this model are noise-synchronizable if and only if the switching communication graph is uniformly jointly connected. Our rigorous mathematical analysis and simulation experiments demonstrate that connected discourse topology in combination with fair amounts of noise can lead to a quasi-consensus that is inducible from any initial state or any underlying system size. Our findings have profound implications for the design of future strategies of social control and global opinion optimization. [ABSTRACT FROM AUTHOR]

Three-way concept analysis is a mathematical theory, which combines formal concept analysis and three-way decision. The existing models, i.e., three-way concept lattices and three-way object oriented concept lattices, have been used successfully in many fields. However, these two models are established to cater some specific applications and cannot fulfill some special requirements such as the needs to seek potential collaborators in international import and export transactions. In this paper, a novel type of three-way concept lattices is presented based on dual concept analysis, which enables ones to characterize specific set by pointing out the attributes that are not possessed by at least one object in the complement of this specific set. And then, the connections between three-way dual concept lattices and classical dual concept lattices are explored. Besides, the relationships among four types of three-way concept analysis models, i.e., three-way concept lattices, three-way dual concept lattices, three-way object oriented concept lattices and three-way property oriented concept lattices, are investigated. [ABSTRACT FROM AUTHOR]

The relaxation of monotonicity requirements is a trend in the theory of aggregation functions. In the recent literature, we can find several relaxed forms of monotonicity, such as weak, directional, cone, ordered directional and strengthened directional monotonicity. All these forms of monotonicity are global properties in the sense that they are imposed for all the points in the domain of a function. In this work, we introduce a local notion of monotonicity called pointwise directional monotonicity, or directional monotonicity at a point. Based on this concept, we characterize all the previously defined notions of monotonicity and, in the final part of the paper, we present some geometric aspects of the global weaker forms of monotonicity, stressing their relations and singularities. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of ordering arc-reversal operations and breaking ties in cost measures when eliminating variables in Lazy AR Propagation (LPAR). In particular, the paper presents the BreakTies algorithm for breaking ties in cost measures when selecting the next arc to reverse in a variable elimination operation. BreakTies is based upon using a sequence of cost measures instead of randomly selecting an arc to reverse when multiple arcs share the same cost. The paper reports on an experimental evaluation of LPAR for belief update in Bayesian networks considering six sequences of five cost measures for breaking ties using BreakTies. The experimental results show that using BreakTies to select the next arc to reverse in a variable elimination operation can improve performance of LPAR. [Copyright &y& Elsevier]

Abstract: Graphical models are efficient and simple ways to represent dependencies between variables. We introduce in this paper the so-called belief causal networks where dependencies are uncertain causal links and where the uncertainty is represented by belief masses. Through these networks, we propose to represent the results of passively observing the spontaneous behavior of the system and also evaluate the effects of external actions. Interventions are very useful for representing causal relations, we propose to compute their effects using a generalization of the “do” operator. Even if the belief chain rule is different from the Bayesian chain rule, we show that the joint distributions of the altered structures to graphically describe interventions are equivalent. This paper also addresses new issues that are arisen when handling interventions: we argue that in real world applications, external manipulations may be imprecise and show that they have a natural encoding under the belief function framework. [Copyright &y& Elsevier]

Abstract: Interpolativity is one of the most important properties of a fuzzy inference system. It is well known that normal antecedent fuzzy sets forming a Ruspini partition constitute a practical setting ensuring interpolativity. In case of a fuzzy rule base expressing a monotone relationship, another desirable property is the monotonicity of the resulting function (after defuzzification). Unfortunately, this goal may often only be reached through the application of the at-least and/or at-most modifiers to the antecedent and consequent fuzzy sets. However, this approach does not seem compatible with the practical setting of a Ruspini partition. This paper shows that the situation is less conflicting than it seems, and that interpolativity can still be guaranteed, in the same practical setting, and, interestingly, from two different modeling points of view. This paper addresses the case of single-input single-output fuzzy rules. [Copyright &y& Elsevier]

Abstract: The paper deals with a simple and efficient procedure for the calculation of the transient impedance of the horizontal grounding electrode. This work represents an extension of a previous paper, published by the authors, on the antenna modeling of the grounding electrode with corresponding Pocklington integro-differential equation. The governing equation is solved in the frequency domain, both numerically and analytically, thus obtaining the solution for the current induced along the electrode. The numerical solution is undertaken via Galerkin–Bubnov scheme of the Indirect Boundary Element Method. Scattered voltage along the electrode is then calculated using Generalized Telegrapher׳s equation. Time domain scattered voltage is evaluated via the Inverse Fast Fourier Transform. Subsequently, transient impedance is determined as a ratio of time domain voltage and current at the feeding point. Results obtained via different methods seem to agree satisfactorily. [Copyright &y& Elsevier]

Abstract: The paper deals with the well-known notion of (dis)similarity measures between fuzzy sets. We provide three separate lists of axioms that fit with the respective notions of “general comparison measure”, “similarity measure” and “dissimilarity measure”. Then we review some of the most important axiomatic definitions of (dis)similarity measures in the literature, by referring to the axioms in those lists satisfied by each specific definition. This common framework will make our study about the formal relationships among different axiomatic definitions much easier: some of them, which are apparently different, do in fact share many commonalities. We provide a self-contained picture of these relationships, by providing formal results and counterexamples that reflect which of the (dis)similarity definitions in the literature are connected by implication relations and which of them are not. We finalize the paper with an in-depth study about the notion of “duality” between similarity and dissimilarity measures as well as with some concluding remarks. [Copyright &y& Elsevier]

Abstract: Several papers relate different alternative approaches to classical concept lattices: such as property-oriented and object-oriented concept lattices and the dual concept lattices. Whereas the usual approach to the latter is via a negation operator, this paper presents a fuzzy generalization of the dual concept lattice, the dual multi-adjoint concept lattice, in which the philosophy of the multi-adjoint paradigm is applied and no negation on the lattices is needed. [Copyright &y& Elsevier]

Abstract: In networked data, linked objects tend to belong to the same class, and densely linked subgraphs are often available. Based on these facts, this paper presents a regularization framework that consists of fitting and regularization terms for transductive learning in networked data. The desirable value of the fitting term is related to the number of labeled data, whereas that of the regularization term is dependent on the structure of the graph. The ratio of these two desirable values is essential for the estimation of the optimal regularization parameters, such as that proposed in our paper. Under the proposed regularization framework, an effective classification algorithm is developed. Two methods are also introduced to incorporate contents of objects into the proposed framework to ultimately improve classification accuracy. Promising experimental results are reported on a toy problem and a paper classification task. [Copyright &y& Elsevier]

Abstract: Recommender systems are very useful in domains in which a large amount of continuous information needs to be evaluated before a decision is made. Systems that permanently interact with users need to be adapted to changes in their interests. This paper proposes an algorithm that takes advantage of the preference information implicit in the actions of the user to dynamically adapt the user profile, in which user preferences are represented as fuzzy sets. The algorithm has been tested with real data extracted from the New York Times and has shown promising results. This paper presents the adaptation algorithm and discusses the influence of its basic parameters. [Copyright &y& Elsevier]

Abstract: Halfline tests studied in this paper are type tests for testing inequality constraints under the alternative hypothesis. An appealing example of such tests in the literature is to find a halfline in the restricted parameter space such that the resultant test is most stringent in terms of the minimization of the maximum shortcoming. However, there appears to be no generally applicable procedure available for implementing this test. This paper is to fill this gap. We also propose a halfline test which has a computational advantage. Simulation studies are conducted to compare the finite sample performance of halfline tests against some existing tests. The results of our simulation studies suggest that halfline tests can have a better finite sample power property and are more robust against the normality assumption compared to likelihood ratio-based tests. [Copyright &y& Elsevier]

Abstract: Industrial decision-makers often try to develop new products by reusing their past experience. Methods for obtaining feedback are available in knowledge management and produce tangible results in the industrial world. Nowadays, companies often consider employees’ knowledge as an asset. This approach is a potential answer for reusing knowledge acquired through experience. The Case-Based Reasoning (CBR) methodology, based on cognitive sciences, consists in solving new problems by reusing past experience. Case-Based Reasoning is an approach to solving a new problem by remembering and adapting a previous successful similar situation to the problem at hand. Of the four activities comprising CBR – Retrieve, Reuse, Revise, and Retain-this paper deals with the “Retrieve” phase. Consequently, we suggest using the Multi-Criteria Decisions concept in problem description to search for the solution in a case-based scenario. We show that Multi-Criteria Decisions and Case-Based Reasoning are complementary. This paper proposes using knowledge acquisition as a basis for seeking solutions from non-compensatory multi-criteria decision aids such as the ELECTRE-I and ELECTRE-II methods. We also carry out a robustness analysis at the end of this paper. We describe an industrial application with wire forming machines as an illustration of our recommendation. [Copyright &y& Elsevier]

Abstract: ross-entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain variables via uncertainty distributions, this paper aims at introducing the concept of cross-entropy for uncertain variables based on uncertain theory, as well as investigating some mathematical properties of this concept. Several practical examples are also provided to calculate uncertain cross-entropy. Furthermore, the minimum cross-entropy principle is proposed in this paper. Finally, a study of generalized cross-entropy for uncertain variables is carried out. [Copyright &y& Elsevier]

Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]

Abstract: This paper proposes a new type-2 fuzzy c-regression clustering algorithm for the structure identification phase of Takagi–Sugeno (T–S) systems. We present uncertainties with fuzzifier parameter “m”. In order to identify the parameters of interval type-2 fuzzy sets, two fuzzifiers “” and “” are used. Then, by utilizing these two fuzzifiers in a fuzzy c-regression clustering algorithm, the interval type-2 fuzzy membership functions are generated. The proposed model in this paper is an extended version of a type-1 FCRM algorithm , which is extended to an interval type-2 fuzzy model. The Gaussian Mixture model is used to create the partition matrix of the fuzzy c-regression clustering algorithm. Finally, in order to validate the proposed model, several numerical examples are presented. The model is tested on a real data set from a steel company in Canada. Our computational results show that our model is more effective for robustness and error reduction than type-1 NFCRM and the multiple-regression. [Copyright &y& Elsevier]

Abstract: This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set. It also presents basic ideas on fuzzy integrals defined using these fuzzy measures. Definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers. Several useful properties of fuzzy measures and fuzzy integrals are stated and proved. Definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral. [Copyright &y& Elsevier]

In the last decade, several new construction methods of fuzzy implication functions from one or more given ones have been proposed. Following this line of research, in our paper some construction methods based on polynomial functions of three variables are presented. Concretely, these methods provide a (possibly new) fuzzy implication function from a given one and a quadratic polynomial function. A complete characterization of those quadratic functions adequate to obtain a fuzzy implication function through this strategy is presented. Moreover, the invariant fuzzy implication functions with respect to this method are determined. Finally, some quadratic construction methods preserving some specific additional properties are analysed. [ABSTRACT FROM AUTHOR]

Abstract The main intention of the present work is to develop a numerical scheme based on radial basis functions (RBFs) to solve fractional stochastic integro-differential equations. In this paper, the solution of fractional stochastic integro-differential equation is approximated by using strictly positive definite RBFs such as Gaussian and strictly conditionally positive definite RBFs such as thin plate spline. Then, the quadrature methods are used to approximate the integrals which are appeared in this scheme. When we use thin plate spline to approximate the solution of mentioned equation, we encounter logarithm-like singular integrals which cannot be computed by common quadrature formula. To overcome this difficulty, we introduce the non-uniform composite Gauss–Legendre integration rule and employ it to estimate the singular logarithm integral appeared in this case. This method transforms the solution of linear fractional stochastic integro-differential equations to the solution of linear system of algebraic equations which can be easily solved. We also discuss the error analysis of the proposed method and demonstrate that the rate of convergence of this approach is arbitrary high for infinitely smooth RBFs. Finally, the efficiency and accuracy of the proposed method are checked by some numerical examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a meshless numerical wave flume, based on the generalized finite difference method (GFDM), is adopted to accurately and efficiently simulate the interactions of water waves and current. The GFDM, a newly-developed meshless method, is truly free from mesh generation and numerical quadrature. The proposed meshless numerical wave flume is the combination of the GFDM, the second-order Runge–Kutta method, the semi-Lagrangian approach, the sponge layer and the ramping function. The problems of wave-current interactions in flumes with horizontal and inclined bottoms are accurately and stably investigated by the proposed meshless scheme, respectively. The changes of waveform can be obviously found, while the cases of coplanar, opposing and no currents are stably simulated. Besides, the distribution of steady current in the flume with inclined bottom, which is governed by an inverse Cauchy problem, is acquired by the GFDM in a stable manner. Numerical results of wave-current interactions are compared with other solutions to verify the accuracy of the proposed meshless scheme. Additionally, different parameters of the proposed meshless numerical scheme are examined to validate the consistency and stability of the proposed numerical wave flume for solutions of wave-current interactions. [ABSTRACT FROM AUTHOR]

Abstract Fuzzy arithmetic operations are applied to mathematical equations that include fuzzy numbers, which are commonly used to represent non-probabilistic uncertainty in different applications. Although there are two mathematical approaches available in the literature for implementing fuzzy arithmetic (i.e., the α -cut approach, and the extension principle approach), the existing computational methods are mainly focused on implementing the α -cut approach due to its simplicity. However, this approach causes overestimation of uncertainty in the resulting fuzzy numbers, a phenomenon that reduces the interpretability of the results. This overestimation can be reduced by implementing fuzzy arithmetic using the extension principle; however, existing computational methods for implementing the extension principle approach are limited to the use of min and drastic product t -norms. Using the min t -norm produces the same result as the α -cuts and interval calculations approach, and the drastic product t -norm is criticized for producing resulting fuzzy numbers that are highly sensitive to the changes in the input fuzzy numbers. This paper presents original computational methods for implementing fuzzy arithmetic operations on triangular fuzzy numbers using the extension principle approach with product and Lukasiewicz t -norms. These computational methods contribute to the different applications of fuzzy arithmetic; they reduce the overestimation of uncertainty, as compared to the α -cut approach, and they reduce the sensitivity of the resulting fuzzy numbers to changes in the input fuzzy numbers, as compared to the extension principle approach using drastic product t -norm. [ABSTRACT FROM AUTHOR]

Abstract Neighborhood rough sets are widely used as an effective tool to deal with numerical data. However, most of the existing neighborhood granulation models cannot well describe the neighborhoods of category-mixed samples when they are used to characterize the classification ability of a subset of attributes. In this paper, we propose a new neighborhood rough set model called k -nearest neighborhood rough sets. This model combines the advantages of both δ -neighborhood and k -nearest neighbor, and has a better ability to deal with this type of heterogeneous data than the existing models. We employ an iterative strategy to define rough approximations of a decision and discuss their monotonicity. Furthermore, an attribute reduction algorithm based on this model is designed. Experimental analysis shows that the proposed algorithm has better performance than some existing algorithms, especially the δ -neighborhood rough set model and k -nearest neighbor rough set model. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the fuzzy extension of the weighted average operation. First, we study the convenient ways how uncertain weights and weighted values can be modeled by fuzzy vectors. We show that, in comparison to a tuple of fuzzy numbers that have been used for modeling uncertain values of particular weights and weighted values up to now, fuzzy vectors extend the possibilities of utilizing the vague expert information concerning the weights and weighted values. Next, we focus on computation of a fuzzy weighted average of a fuzzy vector of weighted values with a fuzzy vector of weights. We derive a general formula and we study its special forms. The advantage of the approach presented in the paper is that the resulting fuzzy weighted average is not overly imprecise since every available information about its variables is involved in computation. This fact is illustrated by several examples. Finally, we briefly discuss the problem of defuzzification of the resulting fuzzy weighted average. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a general principle for constructing robust and accurate viscous discretization, which is applicable to various discretization methods, including finite-volume, residual-distribution, discontinuous-Galerkin, and spectral-volume methods. The principle is based on a hyperbolic model for the viscous term. It is to discretize the hyperbolic system by an advection scheme, and then derive a viscous discretization from the result. A distinguished feature of the proposed principle is that it automatically introduces a damping term into the resulting viscous scheme, which is essential for effective high-frequency error damping and, in some cases, for consistency also. In this paper, we demonstrate the general principle for the diffusion equation on uniform grids in one dimension and unstructured grids in two dimensions, for node/cell-centered finite-volume, residual-distribution, discontinuous-Galerkin, and spectral-volume methods. Numerical results are presented to verify the accuracy of the derived diffusion schemes and to illustrate the importance of the damping term for highly-skewed typical viscous grids. [Copyright &y& Elsevier]

Abstract: The paper presents a method for evaluation of questionnaires supported by formal concept analysis. Formal concept analysis provides an expert with a structured view on the data contained in the questionnaires. The method results from experiments with IPAQ (International Physical Activity Questionnaire). The structured view on the data provided by the method suggests various hypotheses which can later be tested. In addition, the structured view on data itself proved to be sufficiently informative to the expert. In addition to the method, the paper presents experiments with evaluation of IPAQ. [Copyright &y& Elsevier]

Abstract: This paper presents a new method for reducing the number of sources of evidence to combine in order to reduce the complexity of the fusion processing. Such a complexity reduction is often required in many applications where the real-time constraint and limited computing resources are of prime importance. The basic idea consists in selecting, among all sources available, only a subset of sources of evidence to combine. The selection is based on an evidence supporting measure of similarity (ESMS) criterion which is an efficient generic tool for outlier sources identification and rejection. The ESMS between two sources of evidence can be defined using several measures of distance following different lattice structures. In this paper, we propose such four measures of distance for ESMS and we present in details the principle of Generalized Fusion Machine (GFM). Then we apply it experimentally to the real-time perception of the environment with a mobile robot using sonar sensors. A comparative analysis of results is done and presented in the last part of this paper. [Copyright &y& Elsevier]

Abstract: In this paper, three kinds of explicit local meshless methods are compared: the local method of approximate particular solutions (LMAPS), the local direct radial basis function collocation method (LDRBFCM) which are both first presented in this paper, and the local indirect radial basis function collocation method (LIRBFCM). In all three methods, the time discretization is performed in explicit way, the multiquadric radial basis functions (RBFs) are used to interpolate either initial temperature field and its derivatives or the Laplacian of the initial temperature field. The five-noded sub-domains are used in localization. Numerical results of simple diffusion equation with Dirichlet jump boundary condition are compared on uniform and random node arrangement, the accuracy and stabilities of these three local meshless methods are asserted. One can observe that the improvement of the accuracy with denser nodes and with smaller time steps for all three methods. All methods provide a similar accuracy in uniform node arrangement case. For random node arrangement, the LMAPS and the LDRBFCM perform better than the LIDRBFCM. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of combining belief functions obtained from not necessarily independent sources of information. It introduces two combination rules for the situation in which no assumption is made about the dependence of the information sources. These two rules are based on cautious combinations of plausibility and commonality functions, respectively. The paper studies the properties of these rules and their connection with Dempster’s rules of conditioning and combination and the minimum rule of possibility theory. [Copyright &y& Elsevier]

Abstract: The goal of the paper is twofold. The first is to show that some of the ideas for representation of multidimensional distributions in probability and possibility theories can be transferred into evidence theory. Namely, we show that multidimensional basic assignments can be rather efficiently represented in a form of so-called compositional models. These models are based on the iterative application of the operator of composition, whose definition for basic assignments as well as its properties are presented. We also prove that the operator of composition in evidence theory is in a sense generalization of its probabilistic counterpart. The second goal of the paper is to introduce a new definition of conditional independence in evidence theory and to show in what sense it is superior to that formerly introduced by other authors. [Copyright &y& Elsevier]

Abstract: This paper describes the application of an improved hybrid boundary node method (hybrid BNM) for solving steady fluid flow problems. The hybrid BNM is a boundary type meshless method, which combined the moving least squares (MLS) approximation and the modified variational principle. It only requires nodes constructed on the boundary of the domain, and does not require any ‘mesh’ neither for the interpolation of variables nor for the integration. As the variables inside the domain are interpolated by the fundamental solutions, the accuracy of the hybrid BNM is rather high. However, shape functions for the classical MLS approximation lack the delta function property. Thus in this method, the boundary condition cannot be enforced easily and directly, and its computational cost is high for the inevitable transformation strategy of boundary condition. In the method we proposed, a regularized weight function is adopted, which leads to the MLS shape functions fulfilling the interpolation condition exactly, which enables a direct application of essential boundary conditions without additional numerical effort. The improved hybrid BNM has successfully implemented in solving steady fluid flow problems. The numerical examples show the excellent characteristics of this method, and the computation results obtained by this method are in a well agreement with the analytical solutions, which indicate that the method we introduced in this paper can be implemented to other problems. [Copyright &y& Elsevier]

Abstract Information acquisition and communication play an important role in the field of information technology. Meanwhile, communication between fuzzy information systems is a basic problem in fuzzy systems. In this paper, we discuss the communication between fuzzy information systems by using fuzzy covering mappings and fuzzy covering-based rough sets, respectively. First, some properties of fuzzy covering mappings are investigated by Zadeh's extension principle. Then we address the communication between fuzzy information systems by using fuzzy covering mappings. Especially, by introducing some notions in fuzzy information system, we study the relationship between two fuzzy information systems which are defined in the same universe. Second, we propose a novel type of fuzzy covering-based rough set model in fuzzy information system. Some properties of this model are investigated. Finally, we study the communication between fuzzy information systems using fuzzy covering-based rough sets. [ABSTRACT FROM AUTHOR]

Abstract Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational closure according to the (propositional) KLM postulates. A well-known approach to lift this closure to DDLs is by so-called materialisation. Previously investigated algorithms for materialisation-based reasoning employ reductions to classical reasoning using all Boolean connectors. As a first result in this paper, we present a materialisation-based algorithm for the sub-Boolean DDL Image 2 , using a reduction to reasoning in classical Image 2 , rendering materialisation-based defeasible reasoning tractable. The main contribution of this article is a kind of canonical model construction, which can be used to decide defeasible subsumption and instance queries in Image 2 under rational and the stronger relevant entailment. Our so-called typicality models can reproduce the entailments obtained from materialisation-based rational and relevant closure and, more importantly, obtain stronger versions of rational and relevant entailment. These do not suffer from neglecting defeasible information for concepts appearing nested inside quantifications, which all materialisation-based approaches do. We also show the computational complexity of defeasible subsumption and instance checking in our stronger rational and relevant semantics. [ABSTRACT FROM AUTHOR]

Abstract The uncertainty of demands brings challenges for the private cloud providers, leading to low utilization of resources during periods of low-demand and low quality of service during periods of peak-demand, which has attracted much attention. In this paper, taking account into both uncertainty of demands and budget constraint, we design an online sequential procurement auctions of residual resources, which helps the busy cloud provider make an irrevocable decision about how to purchase resources during period of uncertain peak-demand. The crucial part of the mechanism is the seller accepting-rule based on a value-density threshold which is learned dynamically from the historical information. Given the condition that all the sellers are myopic, we prove that the mechanism is truthful, budget feasible and individual rational. Furthermore, we obtain the competitive ratio of the proposed mechanism when the demands of the BCP are δ -degree balance. Using real data from parallel computing centers, we construct 60 scenarios in six data settings, in which we compare our mechanism with average budget allocation and offline proportional sharing mechanism, the results show that in more than 85% scenarios the proposed mechanism has better performance than allocation with average budget, and it improves more than 20% valuation on average for the buyer, even if we use the estimate value of balance degree δ. Highlights • We present an online sequential procurement auctions of residual resources by taking account into both uncertainty of demands and budget constraint. • Given the condition that all the sellers are myopic, we prove that the mechanism is truthful, budget feasible and individual rational. • The results show that in more than 85% scenarios the proposed mechanism has better performance than allocation with average budget. [ABSTRACT FROM AUTHOR]

Abstract The axiomatization problems for generalized approximation operators are finding logical characters of these operators. Solving these problems is important not only for conceptual understanding generalized approximation operators, but also for theoretic discussing the properties of them. In recent years, many researchers explored and developed the axiomatic approach of generalized rough set theory and a lot of articles about axiomatizations of approximation operators were published. However, there are numbers of axiomatization problems for covering-based approximation operators are still open. In this article, we give axiomatic systems for several types of covering-based approximation operators. All the axiomatic systems given by us are original and one of our results answers an open problem raised by Zhu and Wang in 2007. We also discuss axiomatization problems for those covering-based approximation operators generated by irreducible coverings. We prove that for most types of operators, the axiomatic systems generated by irreducible coverings and by general coverings are the same. On the other hand, we show that for one type of operators, the axiomatic systems generated by irreducible coverings and by general coverings are different, and we give an axiomatic system for this type of operators generated by irreducible coverings. By several examples, we show that for each axiomatic system presented in this paper, conditions are independent of each other. [ABSTRACT FROM AUTHOR]