om3 ordered maxitive minitive and modular aggregation operators axiomatic and probabilistic properties in an arity monotonic setting the recently introduced om3 aggregation operators fulfill three appealing properties they are simultaneously minitive maxitive and modular among the instances of om3 operators we find e g owmax and owmin operators the famous hirsch h index and all its natural generalizations in this paper the basic axiomatic and probabilistic properties of extended i e in an arity dependent setting om3 aggregation operators are studied we illustrate the di culties one is inevitably faced with when trying to combine the quality and quantity of numeric items into a single number the discussion on such aggregation methods is particularly important in the information resources producers assessment problem which aims to reduce the negative e ects of information overload it turns out that the hirsch like indices of impact do not fulfill a set of very important properties which puts the sensibility of their practical usage into question moreover thanks to the probabilistic analysis of the operators in an i i d model we may better understand the relationship between the aggregated items quality and their producers productivity

owa generation function and some adjustment methods for owa operators with application we propose the concept of ordered weighted averaging owa generation function with some properties illustrative examples and usages a number of new properties of owa operators and relations between some well known owa operators are proposed and proved using owa generation functions we discuss some orness andness adjustment methods for a predetermined owa operator a practical application about investment prediction problem is given with detailed illustration and analysis which can show the advantages of the adjustment methods proposed in this paper in particular the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties

capacities and overlap indexes with an application in fuzzy rule based classification systems in this work we introduce a method for constructing capacities using overlap indexes between the fuzzy sets which are generated from the inputs of the considered problem we also use these capacities to aggregate information by means of the choquet integral in a fuzzy rule based classifier we observe that with these capacities the obtained results are better than those obtained with other measures

bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations in this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra necessary and sufficient conditions are obtained for the matrix equation ax c and the following systemsa 1x c 1 a 1x c 1 xb 3 c 3 a 2x c 2 to have bisymmetric solutions and the systema 1x c 1 a 3xb 3 c 3 to have centrosymmetric solutions the expressions of such solutions of the matrix and the systems mentioned above are also given moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over are also mentioned

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

generalized ordered modular averaging operator and its application to group decision making in this paper we propose a new class of operators called the ordered quasi modular averaging oqma operators based on the ordered modular averaging oma operators it is shown that the oqma operators are monotonic bounded idempotent commutative and quasi comonotone modular moreover we introduce the generalized ordered modular averaging goma operator which is a special case of the oqma operator some special cases of the goma operator are discussed an orness measure to reflect the or like degree of the goma operator is proposed we further extend the goma operator to the generalized ordered hybrid modular gohm operator which focuses not only on the degree of importance with respect to input arguments but also their serial positions finally a new method based on the gohm operator for multi attribute group decision making is presented and a numerical example shows that the developed approach is feasible

causal path local time stepping in the discontinuous galerkin method for maxwell s equations we introduce a novel local time stepping technique for marching in time algorithms the technique is denoted as causal path local time stepping cplts and it is applied for two time integration techniques fourth order low storage explicit runge kutta lserk4 and second order leap frog lf2 the cplts method is applied to evolve email protected s curl equations using a discontinuous galerkin dg scheme for the spatial discretization numerical results for lf2 and lserk4 are compared with analytical solutions and the email protected s lf2 technique the results show that the cplts technique improves the dispersive and dissipative properties of lf2 lts scheme

generalizations of owa operators owa operators can be seen as symmetrized weighted arithmetic means as choquet integrals with respect to symmetric measures or as comonotone additive functionals following these three different looks on owas we discuss several already known generalizations of owa operators including gowa iowa oma operators as well as we propose new types of such generalizations

more on maximal and minimal ranks of schur complements with applications the maximal and minimal ranks of the schur complement d cgb are determined with respect to generalized inverse g of a matrix a where g is taken respectively as least squares g inverse a 1 3 minimum norm g inverse a 1 4 as well as a 1 2 3 a 1 2 4 and a 1 3 4 various consequences are also presented

generalized cf1f2 integrals from choquet like aggregation to ordered directionally monotone functions abstract this paper introduces the theoretical framework for a generalization of c f 1 f 2 integrals a family of choquet like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems the proposed generalization called by g c f 1 f 2 integrals is based on the so called pseudo pre aggregation function pairs f 1 f 2 which are pairs of fusion functions satisfying a minimal set of requirements in order to guarantee that the g c f 1 f 2 integrals to be either an aggregation function or just an ordered directionally increasing function satisfying the appropriate boundary conditions we propose a dimension reduction of the input space in order to deal with repeated elements in the input avoiding ambiguities in the definition of g c f 1 f 2 integrals we study several properties of g c f 1 f 2 integrals considering different constraints for the functions f 1 and f 2 and state under which conditions g c f 1 f 2 integrals present or not averaging behaviors several examples of g c f 1 f 2 integrals are presented considering different pseudo pre aggregation function pairs defined on e g t norms overlap functions copulas that are neither t norms nor overlap functions and other functions that are not even pre aggregation functions

optimal discontinuous galerkin methods for wave propagation we have developed and analyzed a new class of discontinuous galerkin methods dg which can be seen as a compromise between standard dg and the finite element fe method in the way that it is explicit like standard dg and energy conserving like fe in the literature there are many methods that achieve some of the goals of explicit time marching unstructured grid energy conservation and optimal higher order accuracy but as far as we know only our new algorithms satisfy all the conditions we propose a new stability requirement for our dg the stability analysis is based on the careful selection of the two fe spaces which verify the new stability condition the convergence rate is optimal with respect to the order of the polynomials in the fe spaces moreover the convergence is described by a series of numerical experiments

time series smoothing and owa aggregation in this paper an overview of the time series smoothing problem is provided and the role of data aggregation is described using a weighted average of the past observations two important features associated with this smoothing process are introduced one is the average age of the data and other is the expected variance it is noted how both of these are defined in terms of the associated weights we show the fundamental conflict between trying to keep the variance small while simultaneously using the freshest data we study the moving average and exponential smoothing methods focusing on the aggregation aspect of the data smoothing problem allows us to draw upon the work done with the ordered weighted averaging aggregation operators to suggest new methods for developing smoothing techniques a new class of smoothing operators based on the use of linearly decaying weights is introduced and is shown to have some better features than either exponential smoothing or the moving average other classes of smoothing operators are introduced we introduce the idea of an operational estimate that involves adjusting a smoothed value by other considerations

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

high order leap frog based discontinuous galerkin method for the time domain maxwell equations on non conforming simplicial meshes a high order leap frog based non dissipative discontinuous galerkin time domain method for solving maxwell s equations is introduced and analyzed the proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements with a nth order leap frog time scheme moreover the interpolation degree is defined at the element level and the mesh is refined locally in a non conforming way resulting in arbitrary level hanging nodes the method is proved to be stable under some cfl like condition on the time step the convergence of the semi discrete approximation to maxwell s equations is established rigorously and bounds on the global divergence error are provided numerical experiments with high order elements show the potential of the method

a note on cc integral abstract recently choquet like copula based aggregation functions were introduced and discussed by lucca et al afterwards cmin integral i e a choquet like minimum based operator was examined by dimuro et al we show the link of these aggregation functions with universal integrals of klement et al in particular cmin integral is shown to be an alternative approach to the sugeno integral assuming symmetry an axiomatic characterization of the discussed aggregation functions is given and their coincidence with ordered modular averages in short oma operators is shown

extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications abstract assume that the linear quaternion matrix expression f x 1 x 2 a a 3 x 1 b 3 a 4 x 2 b 4 where x 1 x 2 are variant quaternion matrices in this paper we derive the maximal and minimal ranks of f x 1 x 2 subject to consistent systems of quaternion matrix equations a 1 x 1 c 1 x 1 b 1 c 2 and a 2 x 2 c 3 x 2 b 2 c 4 moreover corresponding results on some special cases are presented as applications we give necessary and sufficient conditions for the existence of solutions to some systems of quaternion matrix equations some previous known results can be regarded as the special cases of this paper

right eigenvalue equation in quaternionic quantum mechanics we study the right eigenvalue equation for quaternionic and complex linear matrix operators defined in n dimensional quaternionic vector spaces for quaternionic linear operators the eigenvalue spectrum consists of n complex values for these operators we give a necessary and sufficient condition for the diagonalization of their quaternionic matrix representations our discussion is also extended to complex linear operators whose spectrum is characterized by 2n complex eigenvalues we show that a consistent analysis of the eigenvalue problem for complex linear operators requires the choice of a complex geometry in defining inner products finally we introduce some examples of the left eigenvalue equations and highlight the main difficulties in their solution

using stress functions to obtain owa operators the ordered weighted averaging operator attempts to provide a user friendly class of mean type aggregation operators by allowing a user to easily and naturally go from a mental model of a desired type of aggregation to its formal realization our objective in this paper is to support this agenda by providing a new methodology to help a user describe the type of aggregation they desire using the idea of a stress function with this stress function a user can stress which argument values they want to give more weight in the aggregation an important feature of this stress function is that it is only required to be nonnegative function on the unit interval this allows a user to completely focus on the issue of where to put the stress in the aggregation without having to consider satisfaction of any other requirements

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

quaternions and matrices of quaternions abstract we give a brief survey on quaternions and matrices of quaternions present new proofs for certain known results and discuss the quaternionic analogues of complex matrices the methods of converting a quaternion matrix to a pair of complex matrices and homotopy theory are emphasized

the ordered modular averages ordered modular averages omas generalize ordered weighted averages operators with the replacement of the additivity property by the modularity omas can be seen as a symmetrized idempotent modular aggregation functions characterized by comonotone modularity each oma can be seen also as a copula based integral with respect to a symmetric capacity special omas are characterized such as associative operators operators with neutral element or operators with an annihilator some construction methods for omas are also discussed

the owa aggregation with uncertain descriptions on weights and input arguments since the ordered weighted averaging owa operator was introduced by yager to provide a method for aggregating multiple inputs that lie between the max and min operators much research that deals with uncertain information on input arguments instead of numerical values has been conducted due to the fact that information provided by human beings is in fact often vague and imprecise in this paper the owa operators with uncertain weights such as interval or weak ordinal descriptions coupled with interval input arguments are presented in order to identify the superior course of action among a multitude of courses of action with the help of relaxation of information representation a burden of information specification imposed on decision maker can be to some extent relieved and thus with regard to the parameters we can obtain a less specific expression that renders human judgments readily available to perform the owa aggregation we take into account the strength of preference based on a probabilistic measure and present a way of ordering the input arguments specified by interval numbers as well as two heuristic algorithms to allocate uncertain weights to the ordered input arguments for prioritizing the courses of action

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

discontinuous galerkin methods for dispersive and lossy maxwell s equations and pml boundary conditions in this paper we will present a unified formulation of discontinuous galerkin method dgm for maxwell s equations in linear dispersive and lossy materials of debye type and in the artificial perfectly matched layer pml regions an auxiliary differential equation ade method is used to handle the frequency dependent constitutive relations with the help of auxiliary polarization currents in the computational and pml regions the numerical flux for the dispersive lossy maxwell s equations with the auxiliary polarization current variables is derived various numerical results are provided to validate the proposed formulation

the matrix equations ax c xb d for the pair of matrix equations ax c xb d this paper gives common solutions of minimum possible rank and also other feasible specified ranks

axiomatizations of lovasz extensions of pseudo boolean functions three important properties in aggregation theory are investigated namely horizontal min additivity horizontal max additivity and comonotonic additivity which are defined by certain relaxations of the cauchy functional equation in several variables we show that these properties are equivalent and we completely describe the functions characterized by them by adding some regularity conditions these functions coincide with the lovasz extensions vanishing at the origin which subsume the discrete choquet integrals we also propose a simultaneous generalization of horizontal min additivity and horizontal max additivity called horizontal median additivity and we describe the corresponding function class additional conditions then reduce this class to that of symmetric lovasz extensions which includes the discrete symmetric choquet integrals

on the matrix equation ax b with applications to the generators of a controllability matrix abstract given two matrices a and b over an arbitrary field for which ax b is consistent we determine all possible ranks for solutions x of ax b given one solution x we furthermore determine all possible ranks of other solutions of this matrix equation we then apply the results to determine when a given n nm matrix a with first m columns b occurs as a controllability matrix a b ab a n 1 b for some a we determine all matrices a that generate a and find all their possible ranks and some bounds on their sparsity structure

a spatial high order hexahedral discontinuous galerkin method to solve maxwell s equations in time domain in this paper we present a non dissipative spatial high order discontinuous galerkin method to solve the maxwell equations in the time domain the non intuitive choice of the space of approximation and the basis functions induce an important gain for mass stiffness and jump matrices in terms of memory this spatial approximation combined with a leapfrog scheme in time leads also to a fast explicit and accurate method a study of the dispersive error is carried out and a stability condition for the proposed scheme is established some comparisons with other schemes are presented to validate the new scheme and to point out its advantages finally in order to improve the efficiency of the method in terms of cpu time on general unstructured meshes a strategy of local time stepping is proposed

weighted fuzzy pattern matching the fuzzy pattern matching technique has been developed in the framework of fuzzy set and possibility theory in order to take into account the imprecision and the uncertainty pervading values which have to be compared in a matching process this technique has proved very useful for implementing patterns of approximate reasoning in expert system inference engines and for designing retrieval systems capable of managing incomplete and fuzzy information data bases and vague queries in this paper the fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern matching indices are obtained using weighted versions of the minimum and maximum operations of fuzzy set theory this approach is extended to the case of variable weights and is related to aggregation schemes proposed by yager when modeling soft quantified statements such as most of the criteria must be met a notion of soft partial matching is thus modelled

on the relationship between symmetric maxitive minitive and modular aggregation operators in this paper the relationship between symmetric minitive maxitive and modular aggregation operators is considered it is shown that the intersection between any two of the three discussed classes is the same moreover the intersection is explicitly characterized it turns out that the intersection contains families of aggregation operators such as owmax owmin and many generalizations of the widely known hirsch s h index often applied in scientific quality control

completing triangular block matrices with maximal and minimal ranks abstract this paper considers two completion problems on block matrices with maximal and minimal ranks let a a ij be an n n block matrix where a ij n i j 1 is given and a ij 1 i is a variant block entry then determine all these variant block entries such that a a ij has maximal and minimal possible ranks respectively by making use of the theory of generalized inverses of matrices we present complete solutions to these two problems as applications we also determine maximal and minimal ranks of the matrix expression a bxc when x is a variant triangular block matrix and then present a necessary and sufficient condition for the matrix equation bxc a to have a triangular block solution