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Abstract This paper overviews the research investigations pertaining to impulsive control systems (ICSs). We focus on the fundamental results and recent progress of ICSs. After reviewing the relative literature, this paper will provide a comprehensive and intuitive overview of ICSs. Six aspects of ICSs are surveyed including basic theory, Lyapunov stability, delayed ICSs, input-to-state stability (ISS), finite-time control, and state-dependent impulses. Based on this, the paper provides a reference for further research on ICSs. [ABSTRACT FROM AUTHOR]

Highlights • A new construction method of fuzzy implication functions is presented. • The method is used to modify an implication to satisfy a desired property. • Many properties are preserved by the construction method. • The new constructed implications satisfy additional properties. Abstract One of the most important theoretical topics in the field of fuzzy implication functions is the study of how to construct new implication functions from given ones. In this line, the interest of a construction method mainly lies in the fact that the new obtained implication satisfies some desired property, specially in the case when the initial one does not satisfy it. This paper gives a new construction method of implication functions from an aggregation function F with F (0 , 1) = 1 , a fuzzy negation N , and an implication function I. After analysing some general properties preserved by this method, it is investigated how this method can be applied in such a way that the resulting implication satisfies some additional desired properties not satisfied by the initial implication function. Particular cases when the aggregation function F is a uninorm or a nullnorm are shown to be specially adequate for this purpose. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical method based on the dual reciprocity boundary elements method (DRBEM) to solve the stochastic partial differential equations (SPDEs). The concept of dual reciprocity method is used to convert the domain integral to the boundary. The conventional DRBEM starts with approximation of the source term of the original PDEs with radial basis functions (RBFs). Due to the fact that the nonhomogeneous term of SPDEs considered in this paper involves Wiener process, the traditional DRBEM cannot be applied. So a modification of it is suggested that has some advantages in comparison with the traditional DRBEM and can be developed for solving the SPDEs. The time evolution is discretized by using the finite difference method, while the modified DRBEM is proposed for spatial variations of field variables. The noise term is approximated at the collocation points at each time step. We employ the generalized inverse multiquadrics (GIMQ) RBFs to approximate functions in the presented technique. To confirm the accuracy of the new approach, several examples are employed and simulation results are reported. Also the convergence of the new technique is studied numerically. [ABSTRACT FROM AUTHOR]

Novel Evolutionary Algorithms are usually tested on sets of artificially-constructed benchmark problems. Such problems are often created to make the search of one global extremum (usually minimum) tricky. In this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially-created functions (with equal bounds and number of allowed function calls) may lead to very different ranking of tested algorithms. As Evolutionary Algorithms and other heuristic optimizers are developed in order to be applicable to real-world problems, such result may raise doubts on the practical meaning of benchmarking them on artificial functions, as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum. Thirty optimization heuristics, including a number of variants of Differential Evolution, as well as other kinds of Evolutionary Algorithms, Particle Swarm Optimization, Direct Search methods and – following the idea borrowed from No Free Lunch – pure random search are tested in the paper. Some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given. [ABSTRACT FROM AUTHOR]

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module Conical (Gil et al., 2012) for the computation of conical functions. Specifically, the module includes now a routine for computing the function R − 1 2 + i τ m ( x ) , a real-valued numerically satisfactory companion of the function P − 1 2 + i τ m ( x ) for x > 1 . In this way, a natural basis for solving Dirichlet problems bounded by conical domains is provided. The module also improves the performance of our previous algorithm for the conical function P − 1 2 + i τ m ( x ) and it includes now the computation of the first order derivative of the function. This is also considered for the function R − 1 2 + i τ m ( x ) in the extended algorithm. Program summary Program Title: Module Conical Program Files doi: http://dx.doi.org/10.17632/rpw5d8gdkg.1 Licensing provisions: CC by 4.0 Programming language: Fortran 90 External routines/libraries: The module Conical uses a Fortran 90 version of the routine dkia (developed by the authors) for computing the modified Bessel functions K i a ( x ) and its derivative. This routine is available at http://toms.calgo.org . Nature of problem: These functions are the natural function basis for solving, for example, the Laplace’s problem in spherical coordinates for two intersecting cones or for regions bounded by two intersecting spheres, or by one or two confocal hyperboloids of revolution when using toroidal coordinates. The conical function P − 1 2 + i τ m ( x ) is also used in the Mehler–Fock integral transform for problems in potential and heat theory, Solution method: The algorithm uses different methods of computation depending on the function under consideration ( P − 1 2 + i τ m ( x ) or R − 1 2 + i τ m ( x ) ) and the values of x , τ and m : numerical quadrature, asymptotic expansions in terms of elementary functions, asymptotic expansions in terms of Bessel functions, asymptotic expansions for tau large and backward/forward recursion of three-term recurrence relations. Restrictions: In order to avoid underflow/overflow problems in standard IEEE double precision arithmetic, the admissible parameter ranges for computing the conical function P − 1 2 + i τ m ( x ) in the routine conicp are: − 1 < x < 1 , 0 < τ < = 100 , 0 ≤ m ≤ 40 1 < x ≤ 100 , 0 < τ ≤ 100 , 0 ≤ m ≤ 100 . When using the routines conicr and conicpr , the admissible parameter ranges for computing the functions P − 1 2 + i τ m ( x ) and R − 1 2 + i τ m ( x ) are 1 < x ≤ 100 , 0 < τ ≤ 100 , 0 ≤ m ≤ 100 . [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel imaging and Doppler parameter estimation algorithm for ground maneuvering targets. Since the cross-track acceleration will induce the quadratic chirp rate (third-order phase) in the phase history, it may cause the maneuvering target severely smeared in the Doppler domain. To obtain a well-focused target imaging result, the quadratic chirp rate must be estimated accurately. Though cubic phase function (CPF) is efficient in estimating the parameters of a single maneuvering target, it may suffer from the identifiability problem when dealing with multiple maneuvering targets. To address these issues, an axis mapping (AM) based coherently integrated cubic phase function (CICPF) algorithm is proposed. This algorithm consists of two stages. Firstly, the linear chirp rate migration (i.e. quadratic chirp rate) of target in the time and chirp-rate domain is corrected by AM. After that, a dechirping technique is utilized to coherently integrate the auto-terms, and suppress the cross-terms and spurious peaks. Compared with several existing quadratic chirp rate estimation approaches, AM based CICPF (AMCICPF) algorithm can acquire lower signal-to-noise ratio threshold and estimate the centroid frequency, chirp rate and quadratic chirp rate of maneuvering target simultaneously. By compensating the chirp rate and quadratic chirp rate, a finely focused maneuvering target imaging can be obtained. Both simulated and real data processing results show that the AMCICPF algorithm serves as a good candidate for maneuvering target Doppler parameter estimation and imaging. [ABSTRACT FROM AUTHOR]

Abstract: Teaching–Learning-Based Optimization (TLBO) seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances. It is reported that it outperforms some of the well-known metaheuristics regarding constrained benchmark functions, constrained mechanical design, and continuous non-linear numerical optimization problems. Such a breakthrough has steered us towards investigating the secrets of TLBO’s dominance. This paper reports our findings on TLBO qualitatively and quantitatively through code-reviews and experiments, respectively. Our findings have revealed three important mistakes regarding TLBO: (1) at least one unreported but important step; (2) incorrect formulae on a number of fitness function evaluations; and (3) misconceptions about parameter-less control. Additionally, unfair experimental settings/conditions were used to conduct experimental comparisons (e.g., different stopping criteria). The experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy. The ultimate goal of this paper is to provide reminders for metaheuristics’ researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects, and to allow fair comparisons of the TLBO algorithm to be made with other metaheuristic algorithms. [Copyright &y& Elsevier]

Abstract: The results reported in this paper create a step toward the rough set-based foundations of data mining and machine learning. The approach is based on calculi of approximation spaces. In this paper, we present the summarization and extension of our results obtained since 2003 when we started investigations on foundations of approximation of partially defined concepts (see, e.g., ). We discuss some important issues for modeling granular computations aimed at inducing compound granules relevant for solving problems such as approximation of complex concepts or selecting relevant actions (plans) for reaching target goals. The problems discussed in this article are crucial for building computer systems that assist researchers in scientific discoveries in many areas such as biology. In this paper, we present foundations for modeling of granular computations inside of system that is based on granules called approximation spaces. Our approach is based on the rough set approach introduced by Pawlak . Approximation spaces are fundamental granules used in searching for relevant complex granules called as data models, e.g., approximations of complex concepts, functions or relations. In particular, we discuss some issues that are related to generalizations of the approximation space introduced in . We present examples of rough set-based strategies for the extension of approximation spaces from samples of objects onto a whole universe of objects. This makes it possible to present foundations for inducing data models such as approximations of concepts or classifications analogous to the approaches for inducing different types of classifiers known in machine learning and data mining. Searching for relevant approximation spaces and data models are formulated as complex optimization problems. The proposed interactive, granular computing systems should be equipped with efficient heuristics that support searching for (semi-)optimal granules. [Copyright &y& Elsevier]

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n -dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n -dimensional overlap and grouping functions. [ABSTRACT FROM AUTHOR]

Multi-class classification problems appear in a broad variety of real-world problems, e.g., medicine, genomics, bioinformatics, or computer vision. In this context, decomposition strategies are useful to increase the classification performance of classifiers. For this reason, in a previous work we proposed to improve the performance of FARC-HD (Fuzzy Association Rule-based Classification model for High-Dimensional problems) fuzzy classifier using One-vs-One (OVO) and One-vs-All (OVA) decomposition strategies. As a result of an exhaustive experimental analysis, we concluded that even though the usage of decomposition strategies was worth to be considered, further improvements could be achieved by introducing n -dimensional overlap functions instead of the product t-norm in the Fuzzy Reasoning Method (FRM). In this way, we can improve confidences for the subsequent processing performed in both OVO and OVA. In this paper, we want to conduct a broader study of the influence of the usage of n -dimensional overlap functions to model the conjunction in several Fuzzy Rule-Based Classification Systems (FRBCSs) in order to enhance their performance in multi-class classification problems applying decomposition techniques. To do so, we adapt the FRM of four well-known FRBCSs (CHI, SLAVE, FURIA, and FARC-HD itself). We will show that the benefits of the usage of n -dimensional overlap functions strongly depend on both the learning algorithm and the rule structure of each classifier, which explains why FARC-HD is the most suitable one for the usage of these functions. [ABSTRACT FROM AUTHOR]

In this paper, we study three selection mechanisms based on the maximin fitness function and we propose another one. These selection mechanisms give rise to the following MOEAs: “MC-MOEA”, “MD-MOEA”, “MH-MOEA” and “MAH-MOEA”. We validated them using standard test functions taken from the specialized literature, having from three up to ten objective functions. We compare these four MOEAs among them and also with respect to MOEA/D (which is based on decomposition), and to SMS-EMOA (which is based on the hypervolume indicator). Our preliminary results indicate that “MD-MOEA” and “MAH-MOEA” are promising alternatives for solving MOPs with either low or high dimensionality. [ABSTRACT FROM AUTHOR]

In this paper, we develop an equal norm based multiple scale Trefftz method (MSTM) to solve the Laplace equation subjected to large noisy boundary data. When the complicated geometry with noisy perturbation and ill-conditioned system by using higher-order T-complete functions are encountered, numerical convergence is hard to reach. To tackle these complicated problems, we adopt the MSTM combined with the vector regularization method (VRM) to eliminate the higher-order numerical oscillation phenomena. Due to the inclusion of the characteristic length in the scheme, the ill-posed problem of the constructed Vandermonde matrix is reduced, and the number of terms in the T-complete functions can be increased to stabilize the numerical calculations. More importantly, the proposed approach can successfully overcome the ill-posedness of severely ill-conditioned matrices appearing in linear equations and thus, obtain the accurate numerical solution under a serious noise disturbance. The results reveal that the method presents a simple and stable way to deal with the highly ill-posed problem. [ABSTRACT FROM AUTHOR]

Functionally-fitted methods generalize collocation techniques to integrate exactly a chosen set of linearly independent functions. In this paper, we propose a new type of functionally-fitted block methods for initial value problems of second order ordinary differential equations. The basic theory for the proposed methods is established. First, we present a sufficient condition for the existence of the functionally-fitted block methods. We then obtain some basic characteristics of the methods by Taylor series expansions, and show that the r -point functionally-fitted block method is convergent of order at least r for second order ordinary differential equations. Numerical experiments are conducted to demonstrate the validity and efficiency of the functionally-fitted block methods by comparison with some existing numerical methods. [ABSTRACT FROM AUTHOR]

We study the classical problem of high frequency scattering of an incident plane wave by a smooth convex two-dimensional body. We present a new integral representation of the leading order solution in the “Fock region”, i.e. the neighbourhood of a point of tangency between the incident rays and the scatterer boundary, from which the penumbra (light–shadow boundary) effects originate. The new representation, which is equivalent to the classical Fourier integral representation and its well-studied “forked contour” regularisation, reveals that the Pekeris caret function (sometimes referred to as a “Fock-type integral” or a “Fock scattering function”), a special function already known to describe the field in the penumbra, is also an intrinsic part of the solution in the inner Fock region. We also provide the correct interpretation of a divergent integral arising in the analysis of Tew et al. (2000), enabling the results of that paper to be used for quantitative calculations. [ABSTRACT FROM AUTHOR]

The rise of cloud computing and the proliferation of mobile devices make computation outsourcing popular. However, the servers are not fully trusted, and a critical problem is the verifiability and privacy of such computations. Although some computation outsourcing schemes provided a general method, the complicated cryptographic tools involved result in great inefficiency. The existing efficient computation outsourcing schemes however aim only at a specific computation task, lacking in generality. In this paper, we show how to construct a generic outsourcing computation scheme for inverting a class of homomorphic functions with computation disequilibrium. Extensive analysis shows that many cryptographic computations fall into this category. The formal security analysis proves that our scheme satisfies verifiability, input and output privacy in information-theoretic sense. Since the construction of our scheme tactfully takes advantage of the intrinsic property of the computation task being outsourced, no public key operations are used in the scheme, thus our solution clearly outperforms the existing schemes in terms of efficiency. In addition, we instantiate our generic construction with concrete examples, and the experimental result testifies the efficiency of our construction. [ABSTRACT FROM AUTHOR]

Abstract: Entity resolution is the problem of identifying the tuples that represent the same real world entity. In this paper, we propose a complete solution to the problem of entity resolution over probabilistic data (ERPD), which arises in many applications that have to deal with probabilistic data. To deal with the ERPD problem, we distinguish between two classes of similarity functions, i.e. context-free and context-sensitive. We propose a PTIME algorithm for context-free similarity functions, and an approximation algorithm for context-sensitive similarity functions. We validated our algorithms through experiments over both synthetic and real datasets. Our extensive performance evaluation shows the effectiveness of our algorithms. [Copyright &y& Elsevier]

Abstract: Capacitated Arc Routing Problem (CARP) has drawn much attention during the last few years. In addition to the goal of minimizing the total cost of all the routes, many real-world applications of CARP also need to balance these routes. The Multi-objective CARP (MO-CARP) commonly exists in practical applications. In order to solve MO-CARP efficiently and accurately, this paper presents a Multi-population Cooperative Coevolutionary Algorithm (MPCCA) for MO-CARP. Firstly, MPCCA applies the divide-and-conquer method to decompose the whole population into multiple subpopulations according to their different direction vectors. These subpopulations evolve separately in each generation and the adjacent subpopulations can share their individuals in the form of cooperative subpopulations. Secondly, multiple subpopulations are used to search different objective subregions simultaneously, so individuals in each subpopulation have a different fitness function, which can be modeled as a Single Objective CARP (SO-CARP). The advanced MAENS approach for single-objective CARP can be used to search each objective subregion. Thirdly, the internal elitism archive is used to construct evolutionary pool for each subregion, which greatly speeds up the convergence. Lastly, the fast nondominated ranking and crowding distance of NSGA-II are used for selecting the offspring and keeping the diversity. MPCCA is tested on 91 CARP benchmarks. The experimental results show that MPCCA obtains better generalization performance over the compared algorithms. [Copyright &y& Elsevier]

Abstract: This paper presents a series of score functions for hesitant fuzzy sets (HFSs) which provides us with a variety of new methods for ranking HFSs. The idea behind the methods is based on the score function for hesitant fuzzy elements (HFEs) that appears to be a subject worthy of further investigations in depth. The prominent characteristic of the HFS score-based method is that it can determine the priorities of the alternatives directly from the HFS score values. In a broad discussion, we describe a scheme for choosing an appropriate option from a set of HFS score-based methods according to what is expected from the score function and what is the nature of the values to be scored. Finally, the application of HFS ranking methods to multi-attribute decision making problems with hesitant fuzzy information is explained. [Copyright &y& Elsevier]

Abstract: Based on B-series theory, the order conditions of the multidimensional ARKN methods are presented for the general multi-frequency and multidimensional oscillatory second-order initial value problems by Wu et al. (2009). These multidimensional ARKN methods exactly integrate the multi-frequency and multidimensional unperturbed oscillators. In this paper, we pay attention to the analysis of the concrete multidimensional ARKN methods for the general multi-frequency oscillatory second-order initial value problems whose right-hand side functions depend on both and (the class of physical problems which fall within its scope is broader). Numerical experiments are carried out to show that the new multidimensional ARKN methods are more efficient compared with some well-known methods for dealing with the oscillatory problems in the scientific literature. [Copyright &y& Elsevier]

Abstract: Lo et al. (2011) proposed an efficient key assignment scheme for access control in a large leaf class hierarchy where the alternations in leaf classes are more frequent than in non-leaf classes in the hierarchy. Their scheme is based on the public-key cryptosystem and hash function where operations like modular exponentiations are very much costly compared to symmetric-key encryptions and decryptions, and hash computations. Their scheme performs better than the previously proposed schemes. However, in this paper, we show that Lo et al.’s scheme fails to preserve the forward security property where a security class can also derive the secret keys of its successor classes ’s even after deleting the security class from the hierarchy. We aim to propose a new key management scheme for dynamic access control in a large leaf class hierarchy, which makes use of symmetric-key cryptosystem and one-way hash function. We show that our scheme requires significantly less storage and computational overheads as compared to Lo et al.’s scheme and other related schemes. Through the informal and formal security analysis, we further show that our scheme is secure against all possible attacks including the forward security. In addition, our scheme supports efficiently dynamic access control problems compared to Lo et al.’s scheme and other related schemes. Thus, higher security along with low storage and computational costs make our scheme more suitable for practical applications compared to other schemes. [Copyright &y& Elsevier]

Abstract: In recent years, the Particle Swarm Optimization has rapidly gained increasing popularity and many variants and hybrid approaches have been proposed to improve it. In this paper, motivated by the behavior and the spatial characteristics of the social and cognitive experience of each particle in the swarm, we develop a hybrid framework that combines the Particle Swarm Optimization and the Differential Evolution algorithm. Particle Swarm Optimization has the tendency to distribute the best personal positions of the swarm particles near to the vicinity of problem’s optima. In an attempt to efficiently guide the evolution and enhance the convergence, we evolve the personal experience or memory of the particles with the Differential Evolution algorithm, without destroying the search capabilities of the algorithm. The proposed framework can be applied to any Particle Swarm Optimization algorithm with minimal effort. To evaluate the performance and highlight the different aspects of the proposed framework, we initially incorporate six classic Differential Evolution mutation strategies in the canonical Particle Swarm Optimization, while afterwards we employ five state-of-the-art Particle Swarm Optimization variants and four popular Differential Evolution algorithms. Extensive experimental results on 25 high dimensional multimodal benchmark functions along with the corresponding statistical analysis, suggest that the hybrid variants are very promising and significantly improve the original algorithms in the majority of the studied cases. [Copyright &y& Elsevier]

Abstract: Fuzzy data mining is used to extract fuzzy knowledge from linguistic or quantitative data. It is an extension of traditional data mining and the derived knowledge is relatively meaningful to human beings. In the past, we proposed a mining algorithm to find suitable membership functions for fuzzy association rules based on ant colony systems. In that approach, precision was limited by the use of binary bits to encode the membership functions. This paper elaborates on the original approach to increase the accuracy of results by adding multi-level processing. A multi-level ant colony framework is thus designed and an algorithm based on the structure is proposed to achieve the purpose. The proposed approach first transforms the fuzzy mining problem into a multi-stage graph, with each route representing a possible set of membership functions. The new approach then extends the previous one, using multi-level processing to solve the problem in which the maximum quantities of item values in the transactions may be large. The membership functions derived in a given level will be refined in the subsequent level. The final membership functions in the last level are then outputted to the rule-mining phase to find fuzzy association rules. Experiments are also performed to show the performance of the proposed approach. The experimental results show that the proposed multi-level ant colony systems mining approach can obtain improved results. [Copyright &y& Elsevier]

Abstract: In dealing with risk in real decision problems, decision-theoretic rough sets with loss functions aim to obtain optimization decisions by minimizing the overall risk with Bayesian decision procedures. Two parameters generated by loss functions divide the universe into three regions as the decision of acceptance, deferment and rejection. In this paper, we discuss the semantics of loss functions, and utilize the differences of losses replace actual losses to construct a new “four-level” approach of probabilistic rules choosing criteria. Ten types of probabilistic rough set models can be generated by the “four-level” approach and form two groups of models: two-way probabilistic decision models and three-way probabilistic decision models. A reasonable decision with these criteria is demonstrated by an illustration of oil investment. [Copyright &y& Elsevier]

Abstract: The purpose of this paper was to conduct a comparative study of score functions in multiple criteria decision analysis based on intuitionistic fuzzy sets. The concept of score functions has been conceptualized and widely applied to multi-criteria decision-making problems. There are several types of score functions that can identify the mixed results of positive and negative parts in a bi-dimensional framework of intuitionistic fuzzy sets. Considering various perspectives on score functions, the present study adopts an order of preference based on similarity to the ideal solution as the main structure to estimate the importance of different criteria and compute optimal multi-criteria decisions in intuitionistic fuzzy evaluation settings. An experimental analysis is conducted to examine the relationship between the results yielded by different score functions, considering the average Spearman correlation coefficients and contradiction rates. Furthermore, additional discussions clarify the relative differences in the ranking orders obtained from different combinations of numbers of alternatives and criteria as well as different importance conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider multipoint boundary value problem for third-order differential equations with p-Laplacian at resonancewhere is continuous function; is an integer, are constants satisfying and . Under various assumptions on the degree of the power with respect to the variables z in the function f(t, x, y, z), we obtain the existence of solutions for the problem. [Copyright &y& Elsevier]