an approach for finding the most preferred alternative in the presence of multiple criteria abstract an interactive approach for discrete multiple criteria decision making problems is developed the approach requires the decision maker to compare pairs of presented alternatives these alternatives may be existing alternatives or dummy alternatives created from existing alternatives inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses the approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function the aim is to keep the number of pairwise comparisons required of the decision maker as small as possible computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches

the regularizing properties of anisotropic radial basis functions in the present work we consider the problem of interpolating scattered data using radial basis functions rbf in general it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution the work focuses on a metric regularization approach based on a new class of rbf called anisotropic rbf the work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric supporting it by numerical examples

consistency of finite systems of convex inequalities we give necessary and sufficient conditions for the existence of a convex functionu which satisfies a finite list of inequalities of the typeu a u b oru a u b wherea b are finite dimensional vectors

an efficient algorithm for building locally refined hp adaptive h pcfe application to uncertainty quantification abstract hybrid polynomial correlated function expansion h pcfe is a novel metamodel formulated by coupling polynomial correlated function expansion pcfe and kriging unlike commonly available metamodels h pcfe performs a bi level approximation and hence yields more accurate results however till date it is only applicable to medium scaled problems in order to address this apparent void this paper presents an improved h pcfe referred to as locally refined hp adaptive h pcfe the proposed framework computes the optimal polynomial order and important component functions of pcfe which is an integral part of h pcfe by using global variance based sensitivity analysis optimal number of training points are selected by using distribution adaptive sequential experimental design additionally the formulated model is locally refined by utilizing the prediction error which is inherently obtained in h pcfe applicability of the proposed approach has been illustrated with two academic and two industrial problems to illustrate the superior performance of the proposed approach results obtained have been compared with those obtained using hp adaptive pcfe it is observed that the proposed approach yields highly accurate results furthermore as compared to hp adaptive pcfe significantly less number of actual function evaluations are required for obtaining results of similar accuracy

solving the discrete multiple criteria problem using linear prospect theory abstract prospect theory developed by kahneman and tversky is a popular model of choice in decision problems under uncertainty prospect theory has recently been extended to multiple criteria choice problems in this paper an interactive method for solving discrete multiple criteria decision problems based on prospect theory type value functions has been developed piecewise linear marginal value functions are assumed to approximate the s shaped value functions of prospect theory therefore the proposed procedure is valid only for convex preferences

coloring non gaussian sequences we propose a novel method for generating random sequences matching both a target non gaussian distribution and a target autocorrelation in the proposed scheme samples matching the target distribution are drawn independently and then suitably rearranged to match the target autocorrelation our method overcomes the difficulties of the standard method in generating sequences with unknown inverse distribution many examples are included

approximate implicitization of parametric surfaces by using compactly supported radial basis functions in this paper a new approach is proposed to solve the approximate implicitization of parametric surfaces it is primarily based on multivariate interpolation of scattered data by using compactly supported radial basis functions experimental results are provided to illustrate the proposed method is flexible and effective

reliability analysis of randomly vibrating structures with parameter uncertainties the problem of reliability analysis of randomly driven stochastically parametered vibrating structures is considered the excitation components are assumed to be jointly stationary gaussian random processes the randomness in structural parameters is modelled through a vector of mutually correlated non gaussian random variables the structure is defined to be safe if a set of response quantities remain within prescribed thresholds over a given duration of time an approximation for the failure probability conditioned on structure randomness is first formulated in terms of recently developed multivariate extreme value distributions an estimate of the unconditional failure probability is subsequently obtained using a method based on taylor series expansion this has involved the evaluation of gradients of the multivariate extreme value distribution conditioned on structure random variables with respect to the basic variables analytical and numerical techniques for computing these gradients have been discussed issues related to the accuracy of the proposed method have been examined the proposed method has applications in reliability analysis of vibrating structural series systems where different failure modes are mutually dependent illustrative examples presented include the seismic fragility analysis of a piping network in a nuclear power plant

interpolation and approximation of 3 d and 4 d scattered data abstract given a set of 3 d or 4 d scattered data methods are presented that yield a bivariate or trivariate function that interpolate or approximate the given data the subroutine package includes hardy s multiquadric interpolant and multistage methods with many options available to the user thus several different interpolation and approximation methods can be generated the options available in the multistage methods can be effectively used if the data set is noisy rapidly varying or nonuniformly distributed the computational and storage requirements for the multistage methods are linear in the number of data points thus they are efficient on large data sets

a rank based approach to the sequential selection and assignment problem abstract in the classical sequential assignment problem machines are to be allocated sequentially to jobs so as to maximize the expected total return where the return from an allocation of job j to machine k is the product of the value xj of the job and the weight pk of the machine the set of m machines and their weights are given ahead of time but n jobs arrive in sequential order and their values are usually treated as independent identically distributed random variables from a known univariate probability distribution with known parameter values in the paper we consider a rank based version of the sequential selection and assignment problem that minimizes the sum of weighted ranks of jobs and machines the so called secretary problem is shown to be a special case of our sequential assignment problem i e m 1 due to its distribution free property our rank based assignment strategy can be successfully applied to various managerial decision problems such as machine scheduling job interview kidney allocations for transplant and emergency evacuation plan of patients in a mass casualty situation

regression based inverse distance weighting with applications to computer experiments inverse distance weighting idw is a simple method for multivariate interpolation but has poor prediction accuracy in this article we show that the prediction accuracy of idw can be substantially improved by integrating it with a linear regression model this new predictor is quite flexible computationally efficient and works well in problems having high dimensions and or large datasets we also develop a heuristic method for constructing confidence intervals for prediction this article has supplementary material online

an interactive evolutionary multi objective optimization algorithm with a limited number of decision maker calls this paper presents a preference based method to handle optimization problems with multiple objectives with an increase in the number of objectives the computational cost in solving a multi objective optimization problem rises exponentially and it becomes increasingly difficult for evolutionary multi objective techniques to produce the entire pareto optimal front in this paper an evolutionary multi objective procedure is combined with preference information from the decision maker during the intermediate stages of the algorithm leading to the most preferred point the proposed approach is different from the existing approaches as it tries to find the most preferred point with a limited budget of decision maker calls in this paper we incorporate the idea into a progressively interactive technique based on polyhedral cones the idea is also tested on another progressively interactive approach based on value functions results are provided on two to five objective unconstrained as well as constrained test problems

a new approach for shape preserving interpolating curves in this paper we present an new approach to construct the so called shape preserving interpolation curves the basic idea is first to approximate the set of interpolated points with a class of mq quasi interpolation operators and then pass through the set with the use of multivariate interpolation by using compactly supported radial basis functions this approach possesses the advantages of certain shape preserving and good approximation behaviors the proposed algorithm is easy to implement

generation of a random sequence having a jointly specified marginal distribution and autocovariance we consider the problem of generating a random sequence with a specified marginal distribution and autocovariance the proposed scheme for generating such a sequence consists of a white gaussian noise source input to a linear digital filter followed by a zero memory nonlinearity zmnl the zmnl is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated both analytic results and examples are included the proposed scheme should prove useful in simulations involving non gaussian processes

a meshless interpolation algorithm using a cell based searching procedure in this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets it is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell based searching procedure more precisely we construct a cell structure which partitions the domain and strictly depends on the dimension of the subdomains thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in allasia et al 2011 and cavoretto and de rossi 2010 2012 in fact this efficient algorithm and in particular the new searching procedure enable us a fast computation also in several applications where the amount of data to be interpolated is often very large up to many thousands or even millions of points analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm this is also supported by numerical experiments

computer experiments with both qualitative and quantitative variables computer experiments have received a great deal of attention in many fields of science and technology most literature assumes that all the input variables are quantitative however researchers often encounter computer experiments involving both qualitative and quantitative variables bqqv in this article a new interface on design and analysis for computer experiments with bqqv is proposed the new designs are one kind of sliced latin hypercube designs with points clustered in the design region and possess good uniformity for each slice for computer experiments with bqqv such designs help to measure the similarities among responses of different level combinations in the qualitative variables an adaptive analysis strategy intended for the proposed designs is developed the proposed strategy allows us to automatically extract information from useful auxiliary responses to increase the precision of prediction for the target response the interface between the proposed design and the analysis strategy

a trivariate interpolation algorithm using a cube partition searching procedure in this paper we propose a fast algorithm for trivariate interpolation which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube partition searching procedure more precisely we construct a cube structure which partitions the domain and strictly depends on the size of its subdomains so that the new searching procedure and accordingly the resulting algorithm enable us to efficiently deal with a large number of nodes complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

cut a multicriteria approach for concavifiable preferences we consider the problem of helping a decision maker dm choose from a set of multiattributed objects when her preferences are concavifiable i e representable by a concave value function we establish conditions under which preferences or preference intensities are concavifiable we also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the dm this can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure we report on the practical use of this procedure with several dms for a flat choice problem and its computational performance on a set of project portfolio selection problem instances the use of preference intensities is found to provide significant improvements to the performance of the procedure

multi attribute sequential decision problem with optimizing and satisficing attributes abstract we deal with the multi attribute decision problem with sequentially presented decision alternatives our decision model is based on the assumption that the decision maker has a major attribute that must be optimized and minor attributes that must be satisficed in the vendor selection problem for example the product price could be the major factor that should be optimized while the product quality and delivery time could be the minor factors that should satisfy certain aspiration levels we first derive the optimal selection strategy for the discrete time case in which one alternative is presented at each time period the discrete time model is then extended to the continuous time case in which alternatives are presented sequentially at random times a numerical example is used to analyze the effects of the satisficing condition and the uncertainty on the optimal selection strategy

representation and generation of non gaussian wide sense stationary random processes with arbitrary psds and a class of pdfs a new method for representing and generating realizations of a wide sense stationary non gaussian random process is described the representation allows one to independently specify the power spectral density and the first order probability density function of the random process the only proviso is that the probability density function must be symmetric and infinitely divisible the method proposed models the sinusoidal component frequencies as random variables a key departure from the usual representation a of wide sense stationary random process by the spectral theorem ergodicity in the mean and autocorrelation is also proven under certain conditions an example is given to illustrate its application to the k distribution which is important in many physical modeling problems in radar and sonar

statistical properties and uses of the wavelet variance estimator for the scale analysis of time series abstract many physical processes are an amalgam of components operating on different scales and scientific questions about observed data are often inherently linked to understanding the behavior at different scales we explore time scale properties of time series through the variance at different scales derived using wavelet methods the great advantage of wavelet methods over ad hoc modifications of existing techniques is that wavelets provide exact scale based decomposition results we consider processes that are stationary nonstationary but with stationary dth order differences and nonstationary but with local stationarity we study an estimator of the wavelet variance based on the maximal overlap undecimated discrete wavelet transform the asymptotic distribution of this wavelet variance estimator is derived for a wide class of stochastic processes not necessarily gaussian or linear the variance of this distribution is estimated using spectral methods simulations confirm the theoretical result

stochastic differential equations an approach to the generation of continuous non gaussian processes the generation of continuous random processes with jointly specified probability density and covariation functions is considered the proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system excited by white gaussian noise and described by a system of a first order stochastic differential equations sde the authors explore how the statistical characteristics of the equation s solution depends on the form of its operator and on the intensity of the input noise some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non gaussian continuous processes are considered the approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its markov model as well as in simulation of continuous correlated processes with the known probability density function

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

multichannel detection for correlated non gaussian random processes based on innovations the paper addresses the problem of multichannel signal detection in additive correlated non gaussian noise using the innovations approach although this problem has been addressed extensively for the case of additive gaussian noise the corresponding problem for the non gaussian case has received limited attention this is due to the fact that there is no unique specification for the joint probability density function pdf of n correlated non gaussian random variables the authors overcome this problem by using the theory of spherically invariant random processes sirps and derive the innovations based detector it is found that the optimal estimators for obtaining the innovations processes are linear and that the resulting detector is canonical for the class of pdfs arising from sirps the authors also present a performance analysis of the innovations based detector for the case of a k distributed sirp

quasi interpolation scheme for arbitrary dimensional scattered data approximation based on natural neighbors and rbf interpolation abstract a local quasi interpolation scheme is presented in the paper which can be applied to arbitrary dimensional scattered data approximation with high accuracy high efficiency and high stability under our new quasi interpolation scheme we treat the natural neighbor set of the point to be estimated in a given scattered node set as a local interpolation node set based on the local node set a local radial basis function interpolation with algebraic precision of any degree is constructed through a modified taylor expansion of sampled function at each natural neighbor to compute approximate values given the exclusion of the point to be estimated from its natural neighbor set i e interpolation node set the interpolation scheme we construct is a local quasi interpolation scheme and its approximation error is given the numerical experimental results show that when the derivative information is unavailable our method outperforms the famous natural neighbor interpolation method in both approximation accuracy and efficiency as algebraic precision increases the approximation accuracy can be further improved

radial basis functions for the multivariate interpolation of large scattered data sets an efficient method for the multivariate interpolation of very large scattered data sets is presented it is based on the local use of radial basis functions and represents a further improvement of the well known shepard s method although the latter is simple and well suited for multivariate interpolation it does not share the good reproduction quality of other methods widely used for bivariate interpolation on the other band radial basis functions which have proven to be highly useful for multivariate scattered data interpolation have a severe drawback they are unable to interpolate large sets in an efficient and numerically stable way and maintain a good level of reproduction quality at the same time both problems have been circumvented using radial basis functions to evaluate the nodal function of the modified shepard s method this approach exploits the flexibility of the method and improves its reproduction quality the proposed algorithm has been implemented and numerical results confirm its efficiency

polyharmonic splines an approximation method for noisy scattered data of extra large size the aim of this paper is to provide a fast method with a good quality of reproduction to recover functions from very large and irregularly scattered samples of noisy data which may present outliers to the given sample of size n we associate a uniform grid and around each grid point we condense the local information given by the noisy data by a suitable estimator the recovering is then performed by a stable interpolation based on isotropic polyharmonic b splines due to the good approximation rate we need only m n degrees of freedom to recover the phenomenon faithfully

adaptive thinning for bivariate scattered data this paper studies adaptive thinning strategies for approximating a large set of scattered data by piecewise linear functions over triangulated subsets our strategies depend on both the locations of the data points in the plane and the values of the sampled function at these points adaptive thinning all our thinning strategies remove data points one by one so as to minimize an estimate of the error that results by the removal of a point from the current set of points this estimate is termed anticipated error the thinning process generates subsets of most significant points such that the piecewise linear interpolants over the delaunay triangulations of these subsets approximate progressively the function values sampled at the original scattered points and such that the approximation errors are small relative to the number of points in the subsets we design various methods for computing the anticipated error at reasonable cost and compare and test the performance of the methods it is proved that for data sampled from a convex function with the strategy of convex triangulation the actual error is minimized by minimizing the best performing measure of anticipated error it is also shown that for data sampled from certain quadratic polynomials adaptive thinning is equivalent to thinning which depends only on the locations of the data points nonadaptive thinning based on our numerical tests and comparisons two practical adaptive thinning algorithms are proposed for thinning large data sets one which is more accurate and another which is faster

memoryless discrete time signal detection in long range dependent noise the problem of designing optimum memoryless detectors for known signals in long range dependent lrd noise is considered in particular under the performance criterion of asymptotic relative efficiency are optimum memoryless detection in lrd noise is investigated by exploiting the hermite expansions the detectors considered have the form of a nonlinearity followed by an accumulator and threshold comparator it is shown that when the noise is lrd and gaussian all nonlinearities with hermite rank one are asymptotically equivalent in terms of efficiency and are most powerful moreover the optimum nonlinearities with hermite rank greater than one are given by the corresponding hermite polynomials the case of non gaussian lrd noise that can be derived by nonlinear transformation of gaussian noise is also considered in this case the globally optimum nonlinearity is very difficult to obtain in general instead we proposed a suboptimal nonlinearity which is given by a linear combination of the corresponding locally optimum detector and the inverse of the transform function generating the noise simulations show that the proposed detector outperforms the locally optimal detector for lrd non gaussian noise

sequential experimental design based generalised anova over the last decade surrogate modelling technique has gained wide popularity in the field of uncertainty quantification optimization model exploration and sensitivity analysis this approach relies on experimental design to generate training points and regression interpolation for generating the surrogate in this work it is argued that conventional experimental design may render a surrogate model inefficient in order to address this issue this paper presents a novel distribution adaptive sequential experimental design da sed the proposed da sed has been coupled with a variant of generalised analysis of variance g anova developed by representing the component function using the generalised polynomial chaos expansion moreover generalised analytical expressions for calculating the first two statistical moments of the response which are utilized in predicting the probability of failure have also been developed the proposed approach has been utilized in predicting probability of failure of three structural mechanics problems it is observed that the proposed approach yields accurate and computationally efficient estimate of the failure probability

data driven pod galerkin reduced order model for turbulent flows abstract in this work we present a reduced order model which is specifically designed to deal with turbulent flows in a finite volume setting the method used to build the reduced order model is based on the idea of merging combining projection based techniques with data driven reduction strategies in particular the work presents a mixed strategy that exploits a data driven reduction method to approximate the eddy viscosity solution manifold and a classical pod galerkin projection approach for the velocity and the pressure fields respectively the newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with reynolds up to r e o 10 5

fast and accurate interpolation of large scattered data sets on the sphere in this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented the solution method is local and involves a modified spherical shepard s interpolant which uses zonal basis functions as local approximants the associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere specifically this technique is mainly based on the partition of the sphere in a suitable number of spherical zones the construction of spherical caps as local neighbourhoods for each node and finally the employment of a spherical zone searching procedure computational cost and storage requirements of the spherical algorithm are analyzed moreover several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm

a new laplace second order autoregressive time series model nlar 2 a time series model for laplace double exponential variables having second order autoregressive structure nlar 2 is presented the model is markovian and extends the second order process in exponential variables near 2 to the case where the marginal distribution is laplace the properties of the laplace distribution make it useful for modeling in some cases where the normal distribution is not appropriate the time series model has four parameters and is easily simulated the autocorrelation function for the process is derived as well as third order moments to further explore dependency in the process the model can exhibit a broad range of positive and negative correlations and is partially time reversible joint distributions and the distribution of differences are presented for the first order case nlar 1

generation and analysis of non gaussian markov time series correlated non gaussian markov sequences can be considered as filtered white noise independent identically distributed sequences of random variables the filter being a nonlinear system in general the authors discuss the applicability of linear models and nonlinear methods based on the diagonal series expansion of bivariate densities for analyzing this system non gaussian sequences exhibit different properties in the forward and backward directions of time the authors explore the connection to system modeling of this temporal asymmetry and some of its consequences as an example they analyze a first order linear autoregressive model with hyperbolic secant amplifier distribution at its output

multistep scattered data interpolation using compactly supported radial basis functions a hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support a nested sequence of subsets of the data is computed efficiently using successive delaunay triangulations the scale of the basis function at each level is determined from the current density of the points using information from the triangulation the method is rotationally invariant and has good reproduction properties moreover the solution can be calculated and evaluated in acceptable computing time

scattered and track data interpolation using an efficient strip searching procedure abstract a new local algorithm for bivariate interpolation of large sets of scattered and track data is presented the method which changes partially depending on the kind of data is based on the partition of the interpolation domain in a suitable number of parallel strips and starting from these on the construction for any data point of a square neighbourhood containing a convenient number of data points then the well known modified shepard s formula for surface interpolation is applied with some effective improvements the proposed algorithm is very fast owing to the optimal nearest neighbour searching and achieves good accuracy computational cost and storage requirements are analyzed moreover the efficiency and reliability of the algorithm are shown by several numerical tests also performed by renka s algorithm for a comparison

shape preserving surface reconstruction using locally anisotropic radial basis function interpolants in this paper we deal with the problem of reconstructing surfaces from unorganized sets of points while capturing the significant geometry details of the modelled surface such as edges flat regions and corners this is obtained by exploiting the good approximation capabilities of the radial basis functions rbf the local nature of the method proposed in 1 and introducing information on shape features and data anisotropies detected from the given surface points the result is a shape preserving reconstruction given by a weighted combination of locally aniso tropic interpolants for each local interpolant the anisotropy is obtained by replacing the euclidean norm with a suitable metric which takes into account the local distribution of the points thus hyperellipsoid basis functions named anisotropic rbfs are defined results from the application of the method to the reconstruction of object surfaces in 3 are presented confirming the effectiveness of the approach

fast computation of triangular shepard interpolants abstract in this paper we present an efficient algorithm for the computation of triangular shepard interpolation method more precisely it is well known that the triangular shepard method reaches an approximation order better than the shepard one dellaccio et al 2016 but it needs to identify useful general triangulation of the node set here we propose a searching technique used to detect and select the nearest neighbor points in the interpolation scheme cavoretto et al 2016 2017 it consists in determining the closest points belonging to the different neighborhoods and subsequently applies to the triangulation based approach numerical experiments and some geological applications show efficiency and accuracy of the interpolation procedure

testing the efficiency of pairwise comparison methods in discrete multiple criteria problems we test the efficiency of two pairwise comparison methods the methods studied are salminen s piecewise linear prospect theory plp method and the convex cone method by korhonen wallenius and zionts kwz the plp method is based on a piecewise linear difference function the kwz method assumes a quasi concave utility or value function these methods are tested using randomly generated data sets with 50 100 150 and 200 alternatives and from 2 up to 6 criteria the dm s preference statements are simulated using linear quadratic and chebycheff value functions and piecewise linear difference functions both methods lose their efficiency very rapidly with increasing number of criteria our results indicate that pairwise comparison methods are not as efficient as reported in literature

interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions in this paper we develop interactive approaches for the discrete alternative multiple criteria decision making problem we develop an algorithm that finds the most preferred alternative of a decision maker dm assuming only that the dm has a monotonic utility function the algorithm divides the criteria space into a number of smaller subspaces and then uses the ideal points of these subspaces to eliminate alternatives we also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function we present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm we then develop a general algorithm that first identifies the type of the dm s utility function and then employs the approach that is compatible with the identified utility function type we also present computational results for the general algorithm

a bi reference procedure for interactive multiple criteria programming the paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem the procedure requires the decision maker to specify the worst outcome then the ideal outcome is identified and the improvement direction from the worst to ideal outcomes is constructed a trial solution is found by moving from a current solution along the improvement direction while maximizing the step size for a trial solution the decision maker is requested to partition the set of objective functions into three categories those to be improved those which may remain unchanged those which may be relaxed based on this partition the procedure displaces the worst and ideal outcomes calculates the new improvement direction and the entire process is repeated the method terminates when two successive trial solutions are reasonably similar

on the generation of the baseband and narrowband non gaussian processes one of the widely used classifications of random processes implies their separation from the baseband and narrowband ones exponent and exponentially decaying cosine waves represent the most popular approximations of the observed processes autocovariation functions acf we consider the generation of such processes with any specified marginal probability density function pdf the approach is based on the representation of the process considered to be a stationary solution of certain stochastic differential equations sde with the white gaussian noise in the right hand side it removes the known pearson restrictions on the kind of available process pdf and in the part related to the generation of the processes with strictly exponential acf is very close to that considered by haddad 1970 concerning the generation of the narrowband non gaussian processes with the exact exponential envelope of its acf synthesis of the corresponding sde may be considered to be principally novel several examples of nonlinear dynamical systems generating baseband and narrowband stationary continuous processes with the given pdf are considered some aspects of the sde numerical simulation are presented the generation method proposed may be useful in communication and signal processing applications where a proper interference simulation appears to be really important

a progressive algorithm for modeling and solving multiple criteria decision problems we consider a decision maker dm who has a set of possible decision alternatives from which one a best is to be chosen however all decision alternatives are not at the dm s disposal initially nor is full knowledge of his her utility value function therefore the dm evaluates only the available subset of all decision alternatives from which he she chooses a most preferred one obviously this decision is not necessarily globally best two natural questions arise how good is the most preferred solution what are the chances of finding better solutions by considering additional alternatives we describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically

on condition numbers associated with radial function interpolation abstract estimates on spectral condition numbers for scattered data interpolation matrices associated with a certain class of conditionally positive definite radial functions of order 0 including the gaussians are provided in addition lp condition number estimates with 1 p are discussed the estimates on the spectral condition numbers lead to necessary and sufficient conditions for such condition numbers to be independent of the number of data sites

rate distortion bound for a class of non gaussian sources with memory the rate distortion performance of a class of non gaussian source with memory is studied the source model is generated from a correlated gaussian source through a memoryless transform which actually constitutes a special class of the frequently used gibbs model in speech and image processing applications its entropy and a rate distortion bound are evaluated to obtain further insights into this class of source models several examples are also given to illustrate the usefulness and tightness of the rate distortion bound

fast exact synthesis of gaussian and nongaussian long range dependent processes 1 f noise and statistically self similar random processes such as fractional brownian motion fbm and fractional gaussian noise fgn are fundamental models for a host of real world phenomena from network traffic to dna to the stock market synthesis algorithms play a key role by providing the feedstock of data necessary for running complex simulations and accurately evaluating analysis techniques unfortunately current algorithms to correctly synthesize these long range dependent lrd processes are either abstruse or prohibitively costly which has spurred the wide use of inexact approximations to fill the gap we develop a simple fast o n log n operations for a length n signal framework for exactly synthesizing a range of gaussian and nongaussian lrd processes as a bonus we introduce and study a new bi scaling fbm process featuring a kinked correlation function that exhibits distinct scaling laws at coarse and fine scales

arma signals with specified symmetric marginal probability distribution except in the case of normal i e gaussian distribution it is very difficult to calculate the marginal probability distribution of arma signals by using a particular form of modeling such signals with random coefficients we show that the problem can be solved and we present an algorithm allowing the numerical generation of arma signals with arbitrary specified marginal distribution function their properties are analyzed in computer experiments the experimental results show in general a very good agreement with theoretical calculations

symmetric binary random signals with given spectral properties the usual known methods for generating signals with given marginal probability and spectral properties cannot be applied to binary signals widely used in theoretical problems and communications systems to overcome this difficulty we first present some structural properties of power spectral densities enabling the precise definition of the concept of spectral properties this allows us to introduce a new method valid for symmetric binary random signals this method uses some specific properties of filters with random impulse responses results of computer simulations show clearly the good performance of this method some extensions by using random thinning can further improve its performance

an adaptive method for computing invariant manifolds in non autonomous three dimensional dynamical systems abstract we present a computational method for determining the geometry of a class of three dimensional invariant manifolds in non autonomous aperiodically time dependent dynamical systems the presented approach can be also applied to analyse the geometry of 3d invariant manifolds in three dimensional time dependent fluid flows the invariance property of such manifolds requires that at any fixed time they are given by surfaces in r 3 we focus on a class of manifolds whose instantaneous geometry is given by orientable surfaces embedded in r 3 the presented technique can be employed in particular to compute codimension one invariant stable and unstable manifolds of hyperbolic trajectories in 3d non autonomous dynamical systems which are crucial in the lagrangian transport analysis the same approach can also be used to determine evolution of an orientable material surface in a fluid flow these developments represent the first step towards a non trivial 3d extension of the so called lobe dynamics a geometric invariant manifold based framework which has been very successful in the analysis of lagrangian transport in unsteady two dimensional fluid flows in the developed algorithm the instantaneous geometry of an invariant manifold is represented by an adaptively evolving triangular mesh with piecewise c 2 interpolating functions the method employs an automatic mesh refinement which is coupled with adaptive vertex redistribution a variant of the advancing front technique is used for remeshing whenever necessary such an approach allows for computationally efficient determination of highly convoluted evolving geometry of codimension one invariant manifolds in unsteady three dimensional flows we show that the developed method is capable of providing detailed information on the evolving lagrangian flow structure in three dimensions over long periods of time which is crucial for a meaningful 3d transport analysis

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

modified virtual grid difference for discretizing the laplace beltrami operator on point clouds we propose a new and simple discretization named the modified virtual grid difference mvgd for numerical approximation of the laplace beltrami lb operator on manifolds sampled by point clouds the key observation is that both the manifold and a function defined on it can both be parametrized in a local cartesian coordinate system and approximated using least squares based on the above observation we first introduce a local virtual grid with a scale adapted to the sampling density centered at each point then we propose a modified finite difference scheme on the virtual grid to discretize the lb operator instead of using the local least squares values on all virtual grid points like the typical finite difference method we use the function value explicitly at the grid located at the center coinciding with the data point the new discretization provides more diagonal dominance to the resulting linear system and improves its conditioning we show that the linear system can be robustly efficientl