on quick attribute reduction in decision theoretic rough set models compared with the pawlak rough set model decision theoretic rough set dtrs models have relatively powerful data processing capability for complex and low quality data however the non monotonicity of the criteria used in dtrs models causes many problems particularly the inefficiency of attribute reduction algorithms which greatly narrows their applications few systematic studies have been reported on how to construct efficient reduction methods for dtrs models this paper discusses this problem and constructs an efficient reduction algorithm for dtrs models incorporating three aspects taking advantage of common characteristics of data sets and employing division techniques a fast division approach to computing equivalence classes is proposed which is the most frequently used and the most time consuming basic operation in the reduction algorithm extracting a monotonic ingredient from decision systems an effective heuristic function is constructed for the reduction algorithm which can guide searches for the algorithm and has better ability to find shorter super reducts a novel algorithm is proposed to search the power set space of a given super reduct which has a shorter average search length than the existing backtracking methods finally the reduction algorithm is proposed that combines these improvements experimental results demonstrate that these improvements are effective and the proposed reduction algorithm is relatively efficient

an efficient high order nystrom scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface this text proposes a fast rapidly convergent nystrom method for the solution of the lippmann schwinger integral equation that mathematically models the scattering of time harmonic acoustic waves by inhomogeneous obstacles while allowing the material properties to jump across the interface the method works with overlapping coordinate charts as a description of the given scatterer in particular it employs partitions of unity to simplify the implementation of high order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations to deal with the discontinuous material interface in a high order manner a specialized quadrature is used in the boundary region the approach further utilizes an fft based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of o n log n for an n point discretization a detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance are presented in this paper

rules in incomplete information systems abstract a new method of computing all optimal certain rules from an incomplete information system is presented and proved the method does not require changing the size of the original incomplete system additionally several existing rough set methods of computing decision rules from incomplete information systems are analyzed and compared we show which of these methods are capable of generating all optimal certain rules or a class of optimal certain rules and which methods may lead to generation of false rules

the discrete fourier transform method of solving differential integral equations in scattering theory an accurate and efficient numerical method is presented for solving many differential integral equations arising from electromagnetic scattering theory it uses the discrete fourier transform technique to treat both the derivatives and the convolution integrals which often appear in these equations as a consequence this method is extremely simple to implement uses less computer memory than comparable methods and yields accurate predictions the differential integral equation is recast into a periodic form conducive to application of the discrete fourier convolution theorem the differential operators are approximated by appropriate finite difference and discrete convolution operators all these quantities are computed by using the fast fourier transform an approximate solution is obtained by using the conjugate gradient method results are compared to experimental data or analytical solutions for a 3 lambda 3 lambda metal plate where lambda is the wavelength a homogeneous and a layered infinite circular dielectric cylinder and a dielectric sphere the accuracy of the method is further illustrated by comparing predictions with independent measurements by r a ross 1966 on a 2 lambda 1 lambda metal plate at grazing incidence in all cases agreement is excellent

reducts and constructs in classic and dominance based rough sets approach abstract the idea of the reduct as defined in the classic rough sets approach crsa has proven to be inspiring enough to get into closely related theories including the dominance based rough sets approach drsa the procedure of reduction is generally similar to that of feature selection but narrower as it is the descriptive rather than the predictive aspect of data exploration that constitutes its principal goal crsa reducts are thus defined as minimal subsets of attributes that retain sufficiently high quality of object description developed within crsa the crsa reducts have given rise to the generalized notion of crsa constructs which have turned out to be superior to reducts in numerous practical experiments with real life data sets the generalization process is continued in this paper in which a definition of constructs in the context of drsa is introduced the definition fully analogous to that of crsa constructs differs only in that it is context based in drsa while context free in crsa consequently the presented drsa constructs are expected to have analogous properties to that of crsa constructs including superiority to drsa reducts in experiments with real life data sets

incremental rough set approach for hierarchical multicriteria classification abstract multicriteria classification refers to classify objects evaluated by a set of criteria to preference ordered decision classes dominance based rough set approach has been successfully introduced to express and reason inconsistencies with a dominance principle in multicriteria classification problems hierarchical attribute values exist extensively within many real world applications which provide a hierarchical form to organize view and analyze data from different perspectives for accommodating the preference variability in this study we consider an extension of dominance based rough set approach by applying an incremental learning technique for hierarchical multicriteria classification while attribute values dynamically vary across different levels of granulations we formalize the dynamic characteristics of knowledge granules with the cut refinement and coarsening through attribute value taxonomies in the hierarchical multicriteria decision systems in consequence incremental algorithms for computing dominance based rough approximations of preference ordered decision classes are developed by applying the resulted prior knowledge as the input and only recomputing those outputs which depend on the changed attribute values this paper presents the theoretical foundation of the proposed approach example analysis and experimental evaluation are also provided for illustration of the feasibility and efficiency

on the computation of power in volume integral equation formulations we present simple and stable formulas for computing power including absorbed radiated scattered and extinction power in current based volume integral equation formulations the proposed formulas are given in terms of vector matrix vector products of quantities found solely in the associated linear system in addition to their efficiency the derived expressions can guarantee the positivity of the computed power we also discuss the application of poynting s theorem for the case of sources immersed in dissipative materials the formulas are validated against results obtained both with analytical and numerical methods for scattering and radiation benchmark cases

current based volume integral equation formulation for bianisotropic materials the electric and magnetic current volume integral equation formulation is developed for the electromagnetic scattering analysis of arbitrarily shaped 3 d bianisotropic objects the eigenvalue spectrum of the operator is derived and analyzed in the case of bi isotropic media the effect of inhomogeneity and bianisotropy on the spectrum and convergence of iterative solutions is investigated numerically

on the relation between rough set reducts and jumping emerging patterns abstract this paper presents the relations between rough set reducts and jumping emerging patterns observations are introduced formally and supported by brief examples furthermore we propose practical applications of these observations to the minimal reduct problem and to testing whether a given attribute set is differentiating we believe that our study can be expanded so as to include other types of reducts and emerging patterns

on the generalization of directfn for singular integrals over quadrilateral patches a set of fully numerical algorithms for evaluating the 4 d singular integrals arising from galerkin surface integral equation methods over conforming quadrilateral meshes is presented this paper is an extension of directfn which was recently developed for the case of triangular patches utilizing in the same fashion a series of coordinate transformations together with appropriate integration reorderings and is applicable to coincident edge adjacent or vertex adjacent elements the resulting formulas consist of sufficiently smooth kernels and exhibit several favorable characteristics when compared with the vast majority of the methods currently available more specifically they can be applied without modifications to the following challenging cases 1 weakly and strongly singular kernels 2 basis and testing functions of arbitrary order 3 planar and curvilinear patches 4 problem specific green functions e g expressed in spectral integral form and 5 spectral convergence to machine precision finally we show that the overall performance of the fully numerical schemes can be further improved by a judicious choice of the integration order for each dimension

a fast approach to attribute reduction in incomplete decision systems with tolerance relation based rough sets efficient attribute reduction in large incomplete decision systems is a challenging problem existing approaches have time complexities no less than o c 2 u 2 this paper derives some important properties of incomplete information systems then constructs a positive region based algorithm to solve the attribute reduction problem with a time complexity no more than o c 2 u log u furthermore our approach does not change the size of the original incomplete system numerical experiments show that the proposed approach is indeed efficient and therefore of practical value to many real world problems the proposed algorithm can be applied to both consistent and inconsistent incomplete decision systems

an efficient accelerator for attribute reduction from incomplete data in rough set framework feature selection attribute reduction from large scale incomplete data is a challenging problem in areas such as pattern recognition machine learning and data mining in rough set theory feature selection from incomplete data aims to retain the discriminatory power of original features to address this issue many feature selection algorithms have been proposed however these algorithms are often computationally time consuming to overcome this shortcoming we introduce in this paper a theoretic framework based on rough set theory which is called positive approximation and can be used to accelerate a heuristic process for feature selection from incomplete data as an application of the proposed accelerator a general feature selection algorithm is designed by integrating the accelerator into a heuristic algorithm we obtain several modified representative heuristic feature selection algorithms in rough set theory experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

stochastic dominance based rough set model for ordinal classification in order to discover interesting patterns and dependencies in data an approach based on rough set theory can be used in particular dominance based rough set approach drsa has been introduced to deal with the problem of ordinal classification with monotonicity constraints also referred to as multicriteria classification in decision analysis however in real life problems in the presence of noise the notions of rough approximations were found to be excessively restrictive in this paper we introduce a probabilistic model for ordinal classification problems with monotonicity constraints then we generalize the notion of lower approximations to the stochastic case we estimate the probabilities with the maximum likelihood method which leads to the isotonic regression problem for a two class binary case the approach is easily generalized to a multi class case finally we show the equivalence of the variable consistency rough sets to the specific empirical risk minimizing decision rule in the statistical decision theory

attribute reduction of data with error ranges and test costs in data mining applications we have a number of measurement methods to obtain a data item with different test costs and different error ranges test costs refer to time money or other resources spent in obtaining data items related to some object observational errors correspond to differences in measured and true value of a data item in supervised learning we need to decide which data items to obtain and which measurement methods to employ so as to minimize the total test cost and help in constructing classifiers this paper studies this problem in four steps first data models are built to address error ranges and test costs second error range based covering rough set is constructed to define lower and upper approximations positive regions and relative reducts a closely related theory deals with neighborhood rough set which has been successfully applied to heterogeneous attribute reduction the major difference between the two theories is the definition of neighborhood third the minimal test cost attribute reduction problem is redefined in the new theory fourth both backtrack and heuristic algorithms are proposed to deal with the new problem the algorithms are tested on ten uci university of california irvine datasets experimental results show that the backtrack algorithm is efficient on rational sized datasets the weighting mechanism for the heuristic information is effective and the competition approach can improve the quality of the result significantly this study suggests new research trends concerning attribute reduction and covering rough set

quick attribute reduction in inconsistent decision tables this paper focuses on three types of attribute reducts in inconsistent decision tables assignment reduct distribution reduct and maximum distribution reduct it is quite inconvenient to judge these three types of reduct directly according to their definitions this paper proposes judgment theorems for the assignment reduct the distribution reduct and the maximum distribution reduct which are expected to greatly simplify the judging of these three types of reducts on this basis we derive three new types of attribute significance measures and construct the q ara quick assignment reduction algorithm the q dra quick distribution reduction algorithm and the q mdra quick maximum distribution reduction algorithm these three algorithms correspond to the three types of reducts we conduct a series of comparative experiments with twelve uci machine learning data repository university of california at irvine data sets including consistent and inconsistent decision tables to evaluate the performance of the three reduction algorithms proposed with the relevant algorithm quickreduct 9 34 the experimental results show that quickreduct possesses weak robustness because it cannot find the reduct even for consistent data sets whereas our proposed three algorithms show strong robustness because they can find the reduct for each data set in addition we compare the q dra quick distribution reduction algorithm with the cebarknc conditional entropy based algorithm for reduction of knowledge without a computing core 43 because both find the distribution reduct by using a heuristic search the experimental results demonstrate that q dra runs faster than cebarknc does because the distribution function of q dra has a lower calculation cost instructive conclusions for these reduction algorithms are drawn from the perspective of classification performance for the c4 5 and rbf svm classifiers last we make a comparison between discernibility matrix based methods and our algorithms the experimental results indicate that our algorithms are efficient and feasible

realization theory for rational systems the existence of rational realizations in this paper we solve the problem of the existence of rational realizations of response maps sufficient and necessary conditions for a response map to be realizable by a rational system are presented we provide also the characterization of the existence of rationally observable and canonical rational realizations for a given response map

minimum cost attribute reduction in decision theoretic rough set models in classical rough set models attribute reduction generally keeps the positive or non negative regions unchanged as these regions do not decrease with the addition of attributes however the monotonicity property in decision theoretic rough set models does not hold this is partly due to the fact that all regions are determined according to the bayesian decision procedure consequently it is difficult to evaluate and interpret region preservation attribute reduction in decision theoretic rough set models this paper provides a new definition of attribute reduct for decision theoretic rough set models the new attribute reduction is formulated as an optimization problem the objective is to minimize the cost of decisions theoretical analysis shows the meaning of the optimization problem both the problem definition and the objective function have good interpretation a heuristic approach a genetic approach and a simulated annealing approach to the new problem are proposed experimental results on several data sets indicate the efficiency of these approaches

incomplete information system andits optimal selections this paper deals with knowledge discovering in incomplete information systems iis by an iis we mean a system with unknown data or partly known data this kind of system can be regarded as a set valued system the selections of an iis are considered the relationships between the reducts in the source system and in its selections are investigated we also present the concept of maximum distribution reducts and optimal selections from which we provide an approach to acquire decision rules from incomplete decision tables idt

dominance based rough set approach to incomplete ordered information systems dominance based rough set approach has attracted much attention in practical applications ever since its inception this theory has greatly promoted the research of multi criteria decision making problems involving preferential information this paper mainly deals with approaches to attribute reduction in incomplete ordered information systems in which some attribute values may be lost or absent by introducing a new kind of dominance relation named the characteristic based dominance relation to incomplete ordered information systems we expand the potential applications of dominance based rough set approach to eliminate information that is not essential attribute reduction in the sense of reducing attributes is needed an approach on the basis of the discernibility matrix and the discernibility function to computing all relative reducts is investigated in incomplete ordered information systems consistent incomplete ordered decision tables to reduce the computational burden a heuristic algorithm with polynomial time complexity for finding a unique relative reduct is designed by using the inner and outer significance measures of each criterion candidate moreover some numerical experiments are employed to verify the feasibility and effectiveness of the proposed algorithms

the early days of geometric nonlinear control around 1970 the study of nonlinear control systems took a sharp turn in part this was driven by the hope for a more inclusive theory which would be applicable to various newly emerging aerospace problems lying outside the scope of linear theory and also by the gradual realization that tools from differential geometry and lie theory in particular could be seen as providing a remarkably nice fit with what seemed to be needed for the wholesale extension of linear control theory into a nonlinear setting this paper discusses an initial phase of the development of geometric nonlinear control including material on the broader context from which it emerged we limit our account to developments occurring up to the early 1980s not because the field stopped developing at that point but rather to limit the scope of the project to something manageable even so because of the volume and diversity of the literature we have had to be selective even within the given time frame

variable consistency dominance based rough set approach to preference learning in multicriteria ranking abstract we present a methodology for non statistical preference learning in multicriteria ranking based on variable consistency dominance based rough set approach vc drsa a finite set of objects to be ranked is evaluated by a set of criteria which are real valued functions with ordinal or cardinal scales given the statement of a multicriteria ranking problem the only objective information one can get is the dominance relation over the set of objects the dominance relation is however too poor because it leaves many objects incomparable to enrich this relation and make the objects more comparable a decision maker dm must supply some preference information revealing her his value system with respect to multicriteria evaluations we are considering a frequent case when the preference information has the form of pairwise comparisons of some objects relatively well known to the dm called reference objects this information is thus composed of some decision examples on the reference objects it is the input data for a method that learns the preferences of the dm since this information is prone to inconsistencies we propose to structure it using vc drsa then the pairs of objects that are sufficiently consistent serve as a basis for induction of a preference model this model has the form of a set of if then decision rules application of these rules on the whole set of objects to be ranked yields a fuzzy preference structure directed weighted graph this preference structure is then exploited using a ranking method so as to work out a final recommendation we propose a list of properties that helps to choose a proper ranking method the methodology is illustrated by an example

rough data deduction based on the upper approximation this paper describes how to construct a structure called a rough deduction space it is an extension of an approximation space and incorporates a deduction relation related to data connections in the rough deduction space a notion of data deduction is introduced and is referred to as rough data deduction based on integrated information of both the upper approximation and the deduction relation rough data deduction accomplishes deductions from data to data which is different from any logical deduction in mathematical logic research on rough data deduction covers two activities the rough data deduction with respect to an equivalence relation and rough data deductions with respect to different equivalence relations the activities also concern the relationship between rough data deduction and rough relations that are rough representations of the deduction relation this leads to properties involving approximate features implied by rough data deduction and reflecting the characteristic that rough data deduction can describe rough data connections in particular since the research correlates closely to granules it may offer an avenue of research on granular computing as an example a specific problem is modeled by a rough deduction space the rough data connections in the problem are described by use of rough data deduction

statistical inference of rough set dependence and importance analysis statistical inference about dependence degree dd and importance degree id of variables in an information system is crucial for variables appraisement and model reconstruction however in rough set data analysis rsda the literature is restricted to validate independence or test whether the degree is significantly big while the fixed value test and interval estimation for related measurements have been ignored because these important issues have not been addressed we cannot determine whether the data support expert opinions and compare the features in depth to enhance the integrity of statistical inference for dd and id in an rsda fixed value tests and interval estimations of dd and id are presented in this paper with multinomial distribution as the carrier for statistical information in the databases the fixed value test of dd is successfully transformed into a restricted estimation of multinomial distribution and a goodness of fit test for distributions the fixed value test and interval estimation algorithms for dd and id are then presented in detail and illustrated with examples explicit expressions for the dd and id interval estimation dd confidence curves and the limit theory for dd and id are shown furthermore the effectiveness and discrimination of the proposed algorithms are validated using the car evaluation tic tac toe endgame and fisher s iris databases

rough sets and intelligent data analysis rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and the bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

reduced order models for electromagnetic scattering problems we consider model order reduction of systems occurring in electromagnetic scattering problems where the inputs are current distributions operating in the presence of a scatterer and the outputs are their corresponding scattered fields using the singular value decomposition svd we formally derive minimal order models for such systems we then use a discrete empirical interpolation method deim to render the minimal order models more suitable to numerical computation these models consist of a set of elementary sources and a set of observation points both interior to the scatterer and located automatically by the deim a single matrix then maps the values of any incident field at the observation points to the amplitudes of the sources needed to approximate the corresponding scattered field similar to a green s function these models can be used to quickly analyze the interaction of the scatterer with other nearby scatterers or antennas

reference points and roughness in this paper we introduce the notion of a reference point and provide local approximations for a subset of the universe the notion of a reference point naturally gives rise to a rough approximations framework wherein several approximations are possible on the same set also we present an extension to the decision theoretic rough set model by using reference points

realizations of nonlinear control systems on time scales nonlinear partially defined systems on an arbitrary unbounded time scale are studied they include continuous time and discrete time systems the main problem is to find necessary and sufficient conditions for an abstract input output map to have a realization as a nonlinear system of a specific class on the time scale the obtained results extend criteria of realizability of continuous time polynomial systems a simple construction of a realization is provided

statistical inference in rough set theory based on kolmogorov smirnov goodness of fit test dependence degree dd and importance degree id of patterns are crucial for pattern appraisement and model reconstruction in rough set data analysis rsda dd and id lack robustness because the lower approximation set is terribly unstable under the indiscernibility relation perturbation statistical inference is a good way to deal with this instability however the fixed value hypothesis testing and interval estimation of dd and id were only discussed by the chi 2 test which merely suits for two contingency tables ct with the same number of elements and their nonzero elements must exist at the same positions these requirements are too strict for practical applications in this paper the kolmogorov smirnov k s goodness of fit test is introduced to generalize the statistical inferences of dd and id as the bridge between data and corresponding measures ct lies at the core of rsda by transforming ct to a random sample of a hypothesized random variable the elementary algorithm for the goodness of fit test of contingency tables and the advanced algorithm for the goodness of fit test of contingency tables are proposed based on k s statistic to implement goodness of fit tests of cts better than chi 2 test all cts even with different numbers and different positions of nonzero elements are permitted subsequently by generating a ct with expected dd value the fixed value hypothesis of dd is transformed to the goodness of fit test between the original and expected cts three algorithms i e hypothesis test of dependence degree based on the k s test region estimation of the dependence degree and significance test and region estimation of importance degree of attribute set are proposed as fixed value hypothesis tests and region estimations of dd and id these algorithms can be used to verify the importance of attributes and choose the attribute subset with the highest likelihood of maintaining the original discrimination ability experiments verify that the discrimination ability disturbance tolerance ability and stability under varying discretization strategies of dd and id are significantly enhanced by the proposed algorithms

existence of realizations of nonlinear analytic input output maps we are interested in the existence of realizations of nonlinear input output maps when they are defined for positive times and when the set of control values is finite first we give examples that point out the nature of the problems which may appear in the attempt to find global results in realization theory then we state a necessary and sufficient condition for the existence of realizations and we give a sketch of the proof

transverse electric scattering on inhomogeneous objects spectrum of integral operator and preconditioning the domain integral equation method with its fft based matrix vector products is a viable alternative to local methods in free space scattering problems however it often suffers from the extremely slow convergence of iterative methods especially in the transverse electric te case with large or negative permittivity we identify very dense line segments in the spectrum as being partly responsible for this behavior and the main reason why a normally efficient deflating preconditioner does not work we solve this problem by applying an explicit multiplicative regularizing operator which on the operator level transforms the system to the form identity plus compact on the matrix level this regularization reduces the length of the dense spectral segments roughly by a factor of four while preserving the ability to calculate the matrix vector products using the fft algorithm such a regularized system is then further preconditioned by deflating an apparently stable set of eigenvalues with largest magnitudes which results in a robust acceleration of the restarted gmres under constraint memory conditions

inner outer factorization of nonlinear operators abstract a fundamental result in the theory of hardy spaces of analytic matrix and operator valued functions on the unit disk is inner outer factorization for the case of rational matrix functions explicit formulas for the inner and outer factors have recently been obtained in these formulas the functions are presented in terms of a collection of finite matrices as the transfer function of a linear system the key ingredient in the construction is the solution of a linear matrix equation called a stein equation in this paper we obtain extensions of these results to the setting of input output maps of nonlinear discrete time systems a particaular computable class of examples is presented for illustration

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

some properties of l fuzzy approximation spaces based on bounded integral residuated lattices in this paper we present a general framework for the study of l fuzzy rough sets based on bounded integral residuated lattices we introduce and discuss the notions of l fuzzy topological spaces left right lower and left right upper l fuzzy approximation operators based on a complete bounded integral residuated lattice investigate union intersection and composition operations of l fuzzy approximation spaces and study some properties of the l fuzzy topologies generated by these l fuzzy rough approximation operators and the l relations induced by an l fuzzy topology

induction of ordinal classification rules from decision tables with unknown monotonicity abstract we are considering induction of ordinal classification rules which assign objects to preference ordered decision classes within the dominance based rough set approach in order to extract such rules it is necessary to define dominance inconsistencies with respect to a set of condition attributes containing at least one ordinal condition attribute furthermore it is also assumed that we know if there exist increasing or decreasing monotonicity relationships between the values of ordinal condition and decision attributes very often however this information is unknown a priori one solution to this issue is to transform the ordinal condition attributes with unknown directions of preference to pairs of attributes with supposed inverse monotonic relationships both local and global monotonicity relationships can be represented by decision rules induced from transformed decision tables however in some cases transforming a decision table in this way is overcomplex in this paper we propose the inconsistency rates based on dominance and fuzzy preference relations that have the capacity of discovering monotonic relationships directly from data rather than induced decision rules moreover we propose a refined transformation method by introducing an additional monotonicity checking using these inconsistency rates to determine whether an ordinal condition attribute should be cloned or not experiments are also provided to evaluate the usefulness of the refined transformation method

on the direct evaluation of weakly singular integrals in galerkin mixed potential integral equation formulations weakly singular integrals over coincident triangles arising in the galerkin discretization of mixed potential integral equation formulations are calculated using a direct evaluation method the proposed method utilizes a series of coordinate transformations together with a re ordering of the integrations in order to reduce the dimensionality of the original four dimensional 4d weakly singular integrals into 1d numerical integrations of smooth functions the final formulas can be easily evaluated with a standard gaussian quadrature rule resulting in a scheme with great accuracy and efficiency properties numerical results for the comparison of the proposed method with both singularity subtraction and singularity cancellation methods often used for the evaluation of multidimensional singular integrals are presented indicating the superior overall performance of the direct evaluation scheme

stable fft jvie solvers for fast analysis of highly inhomogeneous dielectric objects abstract a stable volume integral equation formulation based on equivalent volumetric currents is presented for modeling electromagnetic scattering of highly inhomogeneous dielectric objects the proposed formulation is numerically solved by means of galerkin method of moments on uniform grids allowing for acceleration of the matrix vector products associated with the iterative solver with the help of fft in addition the pertinent volume volume galerkin inner products are reduced to purely surface surface integrals with smoother kernels allowing for highly accurate and fast computation by readily available sophisticated cubatures numerical results demonstrate the convergence properties of the algorithm for scatterers with high dielectric contrast in addition we describe a road map for magnetic resonance specific volume integral equations fast solvers based on the proposed algorithm

reachability of linear switched systems differential geometric approach the paper investigates the structure of the reachable set of linear switched systems the structure of the reachable set is determined using techniques from classical nonlinear systems theory namely the theory of orbits developed by h sussman and the realization theory for nonlinear systems developed by b jakubczyk

set valued ordered information systems set valued ordered information systems can be classified into two categories disjunctive and conjunctive systems through introducing two new dominance relations to set valued information systems we first introduce the conjunctive disjunctive set valued ordered information systems and develop an approach to queuing problems for objects in presence of multiple attributes and criteria then we present a dominance based rough set approach for these two types of set valued ordered information systems which is mainly based on substitution of the indiscernibility relation by a dominance relation through the lower upper approximation of a decision some certain possible decision rules from a so called set valued ordered decision table can be extracted finally we present attribute reduction also called criteria reduction in ordered information systems approaches to these two types of ordered information systems and ordered decision tables which can be used to simplify a set valued ordered information system and find decision rules directly from a set valued ordered decision table these criteria reduction approaches can eliminate those criteria that are not essential from the viewpoint of the ordering of objects or decision rules

roughness bounds in rough set operations this paper presents some roughness bounds for rough set operations the results show that a bound of the set operation can be determined from their operand s roughnesses we prove also that this bound is not determined under some special operations

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

covering rough set structures for a locally finite covering approximation space abstract the purpose of this paper is to introduce the notion of locally finite covering approximation lfc for brevity space u c which is a generalization of a finite covering approximation space furthermore for a subset x of the universe u we develop two kinds of neighborhood systems derived from the covering c specifically k1 x and k2 x which are not comparable with each other next the paper establishes two topologies on u alexandroff and quasi discrete topologies generated by systems k1 x and k2 x as bases respectively after suggesting many examples explaining the above notions and systems we develop two new types of rough set structures an h rough set operator h h and a khalimsky k for short topological rough set operator d k d k the present paper investigates various properties of these operators and refers to certain advantages of them which can be used in applied science including digital geometry information geometry computer vision pattern recognition image processing and so on in order to accomplish this we use some tools such as granulations neighborhood systems typical pawlak s tools related topologies rough set structures associated with the k topology and so on furthermore through this work we can obtain strong connections between covering rough set theory and applied geometry in the present paper all sets u c and x u need not be finite

contingency matrix theory statistical dependence in a contingency table chance discovery aims at understanding the meaning of functional dependency from the viewpoint of unexpected relations one of the most important observations is that such a chance is hidden under a huge number of coocurrencies extracted from a given data on the other hand conventional data mining methods are strongly dependent on frequencies and statistics rather than interestingness or unexpectedness this paper discusses some limitations of ideas of statistical dependence especially focusing on the formal characteristics of simpson s paradox from the viewpoint of linear algebra theoretical results show that such a simpson s paradox can be observed when a given contingency table as a matrix is not regular in other words the rank of a contingency matrix is not full thus data ordered evidence gives some limitations which should be compensated by human oriented reasoning

existence and uniqueness of realizations of nonlinear systems necessary and sufficient conditions for the existence of either analytic or smooth symmetric realizations of nonlinear input output maps are given it is also shown that two minimal realizations are diffeomorphic

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

dominance based rough set approach and knowledge reductions in incomplete ordered information system many methods based on the rough set to deal with incomplete information systems have been proposed in recent years however they are only suitable for the incomplete systems with regular attributes whose domains are not preference ordered this paper thus attempts to present research focusing on a complex incomplete information system the incomplete ordered information system in such incomplete information systems all attributes are considered as criterions a criterion indicates an attribute with preference ordered domain to conduct classification analysis in the incomplete ordered information system the concept of similarity dominance relation is first proposed two types of knowledge reductions are then formed for preserving two different notions of similarity dominance relations with introduction of the approximate distribution reduct into the incomplete ordered decision system the judgment theorems and discernibility matrixes associated with four novel approximate distribution reducts are obtained a numerical example is employed to substantiate the conceptual arguments

a relative decision entropy based feature selection approach rough set theory has been proven to be an effective tool for feature selection to avoid the exponential computation in exhaustive methods many heuristic feature selection algorithms have been proposed in rough sets however these algorithms still suffer from high computational cost in this paper we propose a novel heuristic feature selection algorithm called fsmrde in rough sets to measure the significance of features in fsmrde we propose a new model of relative decision entropy which is an extension of shannon s information entropy in rough sets moreover to test the effectiveness of fsmrde we apply it to intrusion detection and other application domains experimental results show that by using the relative decision entropy based feature significance as heuristic information fsmrde is efficient for feature selection in particular fsmrde is able to achieve good scalability for large data sets highlightswe proposed a novel heuristic feature selection algorithm in rough sets we presented a new information entropy model relative decision entropy we proved that relative decision entropy is monotonic with respect to the partial order of partitions we applied our feature selection algorithm to intrusion detection the effectiveness of our algorithm was shown on kdd 99 data set and some other data sets

consistency of incomplete data consistency is well known for completely specified data sets a specified data set is defined as consistent when any pair of cases with the same attribute values belongs to the same concept in this paper we generalize the definition of consistency for incomplete data sets using rough set theory we discuss two types of missing attribute values lost values and do not care conditions for incomplete data sets there exist three definitions of approximations singleton subset and concept any approximation is lower or upper so we may define six types of consistencies we show that two pairs of such consistencies are equivalent hence there are only four distinct consistencies of incomplete data additionally we discuss probabilistic approximations and study properties of corresponding consistencies we illustrate the idea of consistency for incomplete data sets using experiments on many incomplete data sets derived from eight benchmark data sets

incomplete leaf multilevel fast multipole algorithm for multiscale penetrable objects formulated with volume integral equations recently introduced incomplete leaf il tree structures for multilevel fast multipole algorithm referred to as il mlfma is proposed for the analysis of multiscale inhomogeneous penetrable objects in which there are multiple orders of magnitude differences among the mesh sizes considering a maximum schaubert wilton glisson function population threshold per box only overcrowded boxes are recursively divided into proper smaller boxes leading to il tree structures consisting of variable box sizes such an approach 1 significantly reduces the cpu time for near field calculations regarding overcrowded boxes resulting a superior efficiency in comparison with the conventional mlfma where fixed size boxes are used and 2 effectively reduces the computational error of the conventional mlfma for multiscale problems where the protrusion of the basis testing functions from their respective boxes dramatically impairs the validity of the addition theorem moreover because il mlfma is able to use deep levels safely and without compromising the accuracy the memory consumption is significantly reduced compared with that of the conventional mlfma several examples are provided to assess the accuracy and the efficiency of il mlfma for multiscale penetrable objects

fuzzy rough attribute reduction with application to web categorization abstract due to the explosive growth of electronically stored information automatic methods must be developed to aid users in maintaining and using this abundance of information effectively in particular the sheer volume of redundancy present must be dealt with leaving only the information rich data to be processed this paper presents a novel approach based on an integrated use of fuzzy and rough set theories to greatly reduce this data redundancy formal concepts of fuzzy rough attribute reduction are introduced and illustrated with a simple example the work is applied to the problem of web categorization considerably reducing dimensionality with minimal loss of information experimental results show that fuzzy rough reduction is more powerful than the conventional rough set based approach classifiers that use a lower dimensional set of attributes which are retained by fuzzy rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method

a more efficient attribute self adaptive co evolutionary reduction algorithm by combining quantum elitist frogs and cloud model operators abstract in order to further improve the adaptability of attribute reduction and enhance its application performance in large scale attribute reduction a more efficient attribute self adaptive co evolutionary reduction algorithm by combining quantum elitist frogs and cloud model operators qecmascr is proposed in this paper firstly quantum chromosome is used to encode the evolutionary population and a multilevel elitist pool of quantum frogs is constructed in which quantum elitist frogs can fast guide the evolutionary population into the optimal area secondly a reversible cloud mode based on attribute entropy weight is designed to adjust the quantum cloud revolving angle so that the scope of search space can be adaptively controlled under the guidance of qualitative knowledge in addition both the quantum cloud mutation operator and quantum cloud entanglement operator are used to make quantum frogs be adaptive to get the optimal set of attribute reduction fast thirdly an improved decomposition framework of attribute self adaptive co evolution is adopted to capture interdependencies of decision variables it can decompose the large scale attribute set into reasonable scale subsets according to two kinds of the best performance fitness and assignment credit thus some optimal elitists in different memeplexes of multilevel elitist pool are selected out to evolve their representing attribute subsets which can increase the cooperation and efficiency of attribute reduction so the global minimum attribute reduction can be achieved steadily and efficiently experimental results indicate the proposed qecmascr algorithm achieves the better superior performance than existing representative algorithms moreover it is applied into mri segmentation and the effective and robust segmentation results further demonstrate its stronger applicability

gmres with deflated restarting a modification is given of the gmres iterative method for nonsymmetric systems of linear equations the new method deflates eigenvalues using wu and simon s thick restarting approach siam j matrix anal appl 22 2000 pp 602 616 it has the efficiency of implicit restarting but is simpler and does not have the same numerical concerns the deflation of small eigenvalues can greatly improve the convergence of restarted gmres also it is demonstrated that using harmonic ritz vectors is important because then the whole subspace is a krylov subspace that contains certain important smaller subspaces

sequential covering rule induction algorithm for variable consistency rough set approaches we present a general rule induction algorithm based on sequential covering suitable for variable consistency rough set approaches this algorithm called vc domlem can be used for both ordered and non ordered data in the case of ordered data the rough set model employs dominance relation and in the case of non ordered data it employs indiscernibility relation vc domlem generates a minimal set of decision rules these rules are characterized by a satisfactory value of the chosen consistency measure we analyze properties of induced decision rules and discuss conditions of correct rule induction moreover we show how to improve rule induction efficiency due to application of consistency measures with desirable monotonicity properties

complete semi analytical treatment of weakly singular integrals on planar triangles via the direct evaluation method keywords galerkin inner products method of moments mixed potential integral equations weakly singular integrals linear source distributions surface integrals potential integrals electromagnetic scattering numerical evaluation greens function shape transformation quadrature equations reference lema article 2010 007doi 10 1002 nme 2877view record in web of science record created on 2010 01 20 modified on 2016 08 08

a new effect based roughness measure for attribute reduction in information system roughness measure a quantitative index for processing uncertain information using fuzzy set theory is the basis of resource management system optimization and many other decision making problems the construction of a roughness measure which reflects different decision preferences has important theoretical and practical value in this paper we first analyze the characteristics and shortcomings of the existing methods for measuring roughness following this a new effect based roughness measure model is established using a combination of a basic measure factor the lower or upper accuracy of rough sets entitled the effective rough degree erd next the characteristics of erd are analyzed in combination with different synthesis functions and several further necessary and sufficient conditions are given finally we propose an erd based attribute reduction method abbreviated as erd rm and then discuss the differences and relationships between erd rm and existing reduction methods the theoretical analysis and practical applications show that erd has good structural features and interpretability and can integrate decision preference into the measure system in a straightforward manner

a rough margin based support vector machine by introducing the rough set theory into the support vector machine svm a rough margin based svm rmsvm is proposed to deal with the overfitting problem due to outliers similar to the classical svm the rmsvm searches for the separating hyper plane that maximizes the rough margin defined by the lower and upper margin in this way more data points are adaptively considered rather than the few extreme value points used in the classical svm in addition different support vectors may have different effects on the learning of the separating hyper plane depending on their positions in the rough margin points in the lower margin have more effects than those in the boundary of the rough margin from experimental results on six benchmark datasets the classification accuracy of this algorithm is improved without additional computational expense compared with the classical n svm

rough fuzzy rule interpolation abstract fuzzy rule interpolation forms an important approach for performing inference with systems comprising sparse rule bases even when a given observation has no overlap with the antecedent values of any existing rules fuzzy rule interpolation may still derive a useful conclusion unfortunately very little of the existing work on fuzzy rule interpolation can conjunctively handle more than one form of uncertainty in the rules or observations in particular the difficulty in defining the required precise valued membership functions for the fuzzy sets that are used in conventional fuzzy rule interpolation techniques significantly restricts their application in this paper a novel rough fuzzy approach is proposed in an attempt to address such difficulties the proposed approach allows the representation handling and utilisation of different levels of uncertainty in knowledge this allows transformation based fuzzy rule interpolation techniques to model and harness additional uncertain information in order to implement an effective fuzzy interpolative reasoning system final conclusions are derived by performing rough fuzzy interpolation over this representation the effectiveness of the approach is illustrated by a practical application to the prediction of diarrhoeal disease rates in remote villages it is further evaluated against a range of other benchmark case studies the experimental results confirm the efficacy of the proposed work

rough set approach to incomplete information systems abstract in the paper we present rough set approach to reasoning in incomplete information systems we propose reduction of knowledge that eliminates only that information which is not essential from the point of view of classification or decision making in our approach we make only one assumption about unknown values the real value of a missing attribute is one from the attribute domain however we do not assume which one we show how to find decision rules directly from such an incomplete decision table which are as little non deterministic as possible and have minimal number of conditions

rough sets and boolean reasoning abstract in this article we discuss methods based on the combination of rough sets and boolean reasoning with applications in pattern recognition machine learning data mining and conflict analysis

α dominance relation and rough sets in interval valued information systems though rough set has been widely used to study systems characterized by insufficient and incomplete information its performance in dealing with initial interval valued data needs to be seriously considered for improving the suitability and scalability the aim of this paper is to present a parameterized dominance based rough set approach to interval valued information systems first by considering the degree that an interval valued data is dominating another one we propose the concept of dominance relation second we present the dominance based rough set model in interval valued decision systems finally we introduce lower and upper approximate reducts into dominance based rough set for simplifying decision rules we also present the judgement theorems and discernibility functions which describe how lower and upper approximate reducts can be calculated this study suggests potential application areas and new research trends concerning rough set approach to interval valued information systems

mining incomplete data with singleton subset and concept probabilistic approximations abstract rough set theory provides a very useful idea of lower and upper approximations for inconsistent data for incomplete data these approximations are not unique in this paper we investigate properties of three well known generalizations of approximations singleton subset and concept these approximations were recently further generalized as to include an additional parameter interpreted as a probability in this paper we report novel properties of singleton subset and concept probabilistic approximations additionally we validated such approximations experimentally our main objective was to test which of the singleton subset and concept probabilistic approximations are the most useful for data mining our conclusion is that for a given incomplete data set all three approaches should be applied and the best approach should be selected as a result of ten fold cross validation finally we conducted experiments on complexity of rule sets and the total number of singleton subset and concept approximations

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

three way decisions with probabilistic rough sets the rough set theory approximates a concept by three regions namely the positive boundary and negative regions rules constructed from the three regions are associated with different actions and decisions which immediately leads to the notion of three way decision rules a positive rule makes a decision of acceptance a negative rule makes a decision of rejection and a boundary rule makes a decision of abstaining this paper provides an analysis of three way decision rules in the classical rough set model and the decision theoretic rough set model the results enrich the rough set theory by ideas from bayesian decision theory and hypothesis testing in statistics the connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications

rudiments of rough sets abstract worldwide there has been a rapid growth in interest in rough set theory and its applications in recent years evidence of this can be found in the increasing number of high quality articles on rough sets and related topics that have been published in a variety of international journals symposia workshops and international conferences in recent years in addition many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs rough set theory has led to many interesting applications and extensions it seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences especially in research areas such as machine learning intelligent systems inductive reasoning pattern recognition mereology knowledge discovery decision analysis and expert systems in the article we present the basic concepts of rough set theory and point out some rough set based research directions and applications

feature selection for monotonic classification monotonic classification is a kind of special task in machine learning and pattern recognition monotonicity constraints between features and decision should be taken into account in these tasks however most existing techniques are not able to discover and represent the ordinal structures in monotonic datasets thus they are inapplicable to monotonic classification feature selection has been proven effective in improving classification performance and avoiding overfitting to the best of our knowledge no technique has been specially designed to select features in monotonic classification until now in this paper we introduce a function which is called rank mutual information to evaluate monotonic consistency between features and decision in monotonic tasks this function combines the advantages of dominance rough sets in reflecting ordinal structures and mutual information in terms of robustness then rank mutual information is integrated with the search strategy of min redundancy and max relevance to compute optimal subsets of features a collection of numerical experiments are given to show the effectiveness of the proposed technique

minimal state space realization in linear system theory an overview we give a survey of the results in connection with the minimal state space realization problem for linear time invariant systems we start with a brief historical overview and a short introduction to linear system theory next we present some of the basic algorithms for the reduction of nonminimal state space realizations and for the minimal state space realization of infinite or finite sequences of markov parameters of linear time invariant systems finally we discuss some extensions of this problem to other classes of systems and point out some related problems

the superiority of three way decisions in probabilistic rough set models three way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier this paper compares probabilistic three way decisions probabilistic two way decisions and qualitative three way decisions of the standard rough set model it is shown that under certain conditions when considering the costs of different types of miss classifications probabilistic three way decisions are superior to the other two

method for the global analysis of non linear parametrized systems a method for the global analysis of non linear systems is presented which provides a framework for the analysis of both continuous and discrete time non linear systems for the diverse range of model types by extending a numerical approach to enable the analysis of non linear parametrized non linear systems a global perspective is achieved that is difficult to obtain using analytical methods alone simple examples are used to illustrate how the method characterizes the system stability at the same time as detecting typical qualitative bifurcation phenomena a non linear feedback system is analysed in order to show how the approach provides both qualitative and quantitative information over a defined region of the system parameter space the method proves to be a powerful tool which can be used to probe the non linear characteristics of a system

covering based rough set approximations we propose a framework for the study of covering based rough set approximations three equivalent formulations of the classical rough sets are examined by using equivalence relations partitions and s algebras respectively they suggest the element based the granule based and the subsystem based definitions of approximation operators covering based rough sets are systematically investigated by generalizing these formulations and definitions a covering of universe of objects is used to generate different neighborhood operators neighborhood systems coverings and subsystems of the power set of the universe they are in turn used to define different types of generalized approximation operators within the proposed framework we review and discuss covering based approximation operators according to the element granule and subsystem based definitions

approximate distribution reducts in inconsistent interval valued ordered decision tables abstract many methods based on the rough set theory to deal with information systems have been proposed in recent decades in practice some information systems are based on dominance relations and may be inconsistent because of various factors moreover taking the imprecise evaluations and assignments in the description of objects into account single valued information systems have been generalized to interval valued information systems in this paper by introducing a dominance relation to interval valued ordered information systems we establish a dominance based rough set approach which is mainly based on substitution of the indiscernibility relation by the dominance relation to extract the minimal decision rules approximate distribution reducts are proposed in inconsistent interval valued ordered decision tables this paper presents a theoretical method based on the discernibility matrix to enumerate all reducts and a practical approach on the basis of significance to find one reduct and two equivalent definitions of approximate distribution reducts are also introduced in addition numerical examples are employed to examine the validity of the approaches proposed in this paper

a weighted rough set based method developed for class imbalance learning in this paper we introduce weights into pawlak rough set model to balance the class distribution of a data set and develop a weighted rough set based method to deal with the class imbalance problem in order to develop the weighted rough set based method we design first a weighted attribute reduction algorithm by introducing and extending guiasu weighted entropy to measure the significance of an attribute then a weighted rule extraction algorithm by introducing a weighted heuristic strategy into lem2 algorithm and finally a weighted decision algorithm by introducing several weighted factors to evaluate extracted rules furthermore in order to estimate the performance of the developed method we compare the weighted rough set based method with several popular methods used for class imbalance learning by conducting experiments with twenty uci data sets comparative studies indicate that in terms of auc and minority class accuracy the weighted rough set based method is better than the re sampling and filtering based methods and is comparable to the decision tree and svm based methods it is therefore concluded that the weighted rough set based method is effective for class imbalance learning

comparison of lpv and nonlinear system theory a realization problem abstract the paper explores the utilization of the nonlinear realization theory to address the problem of transforming linear parameter varying input output lpv io equations into a state space form with static dependence on the so called scheduling parameter the necessary and sufficient solvability conditions are given and three additional subclasses of lpv io equations are suggested that are guaranteed to have a realization of the considered type

fliess operators on lp spaces convergence and continuity fliess operators as input output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory in the classical analysis of these operators certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence provided every input is uniformly bounded by some 4xed upperbound in some emerging applications however it is more natural to consider other classes of inputs in this paper lp function spaces are considered in particular it is shown that the classic growth conditions also provide su3cient conditions for convergence and continuity when the admissible inputs are from a ball in lp t0 t 0 t where t is bounded and p 1 in addition stronger global growth conditions are given that apply even for the case where t is unbounded when the coe3cients of a fliess operator have a state space representation it is shown that the state space model will always locally realize the correspondinginput output map on lp t0 t 0 t for su3ciently small t 0 if certain well posedness conditions are satis4ed then the state space model will globally realized the input output mapping for unbounded t when the coe3cients satisfy the global growth condition c 2002 elsevier science b v all rights reserved

adjoint polynomial formulas for nonlinear state space realization this paper focuses on computational aspects of the realization of nonlinear multi input multi output systems instead of the algorithmic solutions provided in earlier works the explicit formulas are presented which enable to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system the solution is based on the concept of adjoint polynomials and requires a minimal amount of computations the formulas are implemented in computer algebra system mathematica and made available online via web mathematica tools

nonconformal discretization of electric current volume integral equation with higher order hierarchical vector basis functions a nonconformal discretization of the electric current volume integral equation jvie is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects this jvie is based on higher order geometrical and current modeling where curved tetrahedral elements and higher order hierarchical vector hohv basis functions are adopted in order to implement the nonconformal discretization the half face based hohv basis function is introduced to address the nonconformal volumetric elements compared to the conventional low order conformal nonconformal vie our nonconformal hohv based jvie has the advantage of improving the computational efficiency and accuracy compared to the previous vie discretized by other higher order functions our nonconformal jvie is based on the higher order geometric modeling and the hohv bases in order to improve the efficiency the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling moreover the flexibility of basis order selection is further enhanced by the mixed order schemes numerical results are given to demonstrate its accuracy efficiency and flexibility

evidential weights of multiple preferences for competitiveness the alternative selections or feasible sets in multi attribute utility theory usually face problems of inaccuracy or inconsistency in weighting evidential weight and weight of evidence still have not resolved these problems in an efficient manner this research proposes evidential weights of multiple preferences by using evidence and inference based on the rough set theory an evidential probability is constructed to resolve this weight technically the evidential probability is required to satisfy the following conditions uniqueness independence and consistency to identify various evidence and noise and to provide quantities of certain evidence to resolve weights empirically the resolved weights are fused into competitiveness utility for verification a practical case successfully classifies dominating nations of world competitiveness yearbook another case analyzes the competitiveness trends of china during 1997 to 2012 predicting china will continue rising in near future

a cost sensitive decision tree algorithm based on weighted class distribution with batch deleting attribute mechanism minimal cost classification is an important issue in data mining and machine learning recently many enhanced algorithms based on the c4 5 algorithm have been proposed to tackle this issue one disadvantage in these methods is that they are inefficient for medium or large data sets to overcome this problem we present a cost sensitive decision tree algorithm based on weighted class distribution with a batch deleting attribute mechanism bdadt in the bdadt algorithm a heuristic function is designed for evaluating attributes in node selection this contains a weighted information gain ratio a test cost and a user specified non positive parameter for adjusting the effect of the test cost meanwhile a batch deleting attribute mechanism is incorporated into our algorithm this mechanism deletes redundant attributes according to the values of the heuristic function in the process of assigning nodes to improve the efficiency of decision tree construction experiments are conducted on 20 uci data sets with representative test cost normal distribution to evaluate the proposed bdadt algorithm the experimental results show that the average total costs obtained by the proposed algorithm are smaller than the existing cs c4 5 and cs gainratio algorithms furthermore the proposed algorithm significantly increases the efficiency of cost sensitive decision tree construction