preference modeling experiments with surrogate weighting procedures for the promethee method abstract one of the main tasks in a multi criteria decision making process is to define weights for the evaluation criteria however in many situations the decision maker dm may not be confident about defining specific values for these weights and may prefer to use partial information to represent the values of such weights with surrogate weights although for the additive model the use of surrogate weighting procedures has been already explored in the literature there is a gap with regard to experimenting with such kind of preference modeling in outranking based methods such as promethee for which there already are applications with surrogate weights in the literature thus this paper presents an experimental study on preference modeling based on simulation so as to increase understanding and acceptance of a recommendation obtained when using surrogate weights within the promethee method the main approaches to surrogate weights in the literature ew rs rr and roc have been evaluated for choice and ranking problematics throughout statistical procedures including kendall s tau coefficient the surrogate weighting procedure that most faithfully represents a dm s value system according to this analysis is the roc procedure

tools for interactive multiattribute decisionmaking with incompletely identified information abstract the aim of this paper is to present tools or techniques for an interactive multiattribute decisionmaking with the decision maker s incomplete information that is 1 we formally describe mathematical models under certainty and uncertainty for establishing pairwise dominance where the incomplete information becomes the set of constraints in the model 2 we present a description on styles of incomplete parameter value information 3 the characteristic of a weak dominance is described when the decision maker is not willing or able to provide more information on parameters the weak dominance technique is useful for a final choicemaking 4 we propose a dominance graph and also present an algorithm of generating the dominance graph based on the information of pairwise dominance the dominance graph compactly displays the dominance structure of all alternatives thus it can be used for aiding the selection of preferable alternatives

wave field separation in two dimensional anisotropic media until recently the term elastic usually implied two dimensional 2 d and isotropic in this limited context the divergence and curl operators have found wide use as wave separation operators for example mora 1987 used them in his inversion method to allow separate correlation of p and s arrivals although the separation is buried in the math and not obvious clayton 1981 used them explicitly in several modeling and inversion methods devaney and oristaglio 1986 used closely related operators to separate p and s arrivals in elastic vsp data

2d and 3d elastic wavefield vector decomposition in the wavenumber domain for vti media a pragmatic decomposition of a vector wavefield into p and s waves is based on the helmholtz theory and the christoffel equation it is applicable to vti media when the plane wave polarization is continuous in the vicinity of a given wavenumber and is uniquely defined by that wavenumber except for the kiss singularities on the vti symmetry axis unlike divergence and curl which separate the wavefield into a scalar and a vector field the decomposed p and s wavefields are both vector fields with correct amplitude phase and physical units if the vector components of decomposed wavefields are added they reconstruct those of the original input wavefield wavefield propagation in any portions of a vti medium that have the same polarization distribution i e the same eigenvector in the wavenumber domain have the same decomposition operators and can be recon structed with a single 3d fourier transform for each operator e g one for p waves and one for s waves this applies to isotropic wavefields a

ranking with partial information a method and an application a method is presented for ranking multiattributed alternatives using a weighted additive evaluation function with partial information about the weighting scaling constants the method is applied to evaluate materials for use in nuclear waste containment the paper derives conditions to determine whether a pair of alternatives can be ranked given the partial information about weighting constants and presents an algorithm that partially rank orders the complete set of alternatives based on the pairwise ranking information

an analytic approach for obtaining maximal entropy owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem in this paper using the method of lagrange multipliers we shall solve this constrained optimization problem analytically and derive a polynomial equation which is then solved to determine the optimal weighting vector

fast algorithms for elastic wave mode separation and vector decomposition using low rank approximation for anisotropic media abstractwave mode separation and vector decomposition are significantly more expensive than wavefield extrapolation and are the computational bottleneck for elastic reverse time migration in heterogeneous anisotropic media we have expressed elastic wave mode separation and vector decomposition for anisotropic media as space wavenumber domain operations in the form of fourier integral operators and developed fast algorithms for their implementation using their low rank approximations synthetic data generated from 2d and 3d models demonstrated that these methods are accurate and efficient

on the properties of owa operator weights functions with constant level of orness the result of aggregation performed by the ordered weighted averaging owa operator heavily depends upon the weighting vector used a number of methods have been presented for obtaining the associated weights in this paper we present analytic forms of owa operator weighting functions each of which has properties of rank based weights and a constant level of orness irrespective of the number of objectives considered these analytic forms provide significant advantages for generating the owa weights over previously reported methods first the owa weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program moreover convex combinations of these specific owa operators can be used to generate the owa operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker those weights have a property of constant level of orness as well finally the owa weights generated at a predefined value of orness make almost no numerical difference with maximum entropy owa weights in terms of dispersion

an experimental comparison of different approaches to determining weights in additive utility models several studies this past decade have examined differences between holistic and decomposed approaches to determining weights in additive utility models some have argued that it matters little which procedure is used whereas others strongly favored particular methods in this paper we address this controversy experimentally by comparing five conceptually different approaches in terms of their weights and predictive ability the five methods are 1 multiple linear and non linear regression analyses of ten and fifteen holistic assessments 2 direct decomposed tradeoffs as proposed by keeney and raiffa keeney r l h raiffa 1977 decisions with multiple objectives wiley new york 3 a recent eigen vector technique of saaty saaty t l 1977 a scaling method for priorities in hierarchical structures j math psych 15 3 234 281 involving redundant pairwise comparisons of attributes 4 a straightforward allocation of hundred importance points and 5 unit weighting i e equal weighting after standardizing the attributes the decision task involved college admissions subjects were asked to evaluate hypothetical college applicants on the basis of verbal sat quantitative sat high school grade point average and a measure of extra curricular activity linear as well as nonlinear attribute utility functions were used in constructing the additive models the nonlinear functions were specified graphically by the subjects through selection from five different shapes i e one per attribute to test the predictive ability of the various models each subject made twenty separate pairwise comparisons of alternatives including direction and strength of preference the prediction criteria were percentage correct predictions as well as correlations using these twenty pairs seventy subjects were tested using an order controlled within subject design in comparing the different methods of weight determination monetary incentives were used to enhance motivation in terms of findings the methods generally differed systematically concerning the weights given to the various attributes as well as the variances of the resulting predictions on average however the methods predicted about equally well except for unit weighting which was clearly inferior the findings differ in this regard from the general literature furthermore nonlinear models were found to be inferior to linear ones finally subjects judged the methods to differ significantly in difficulty and trustworthiness which were found to correlate inversely the overall results raise various applied and theoretical issues which are discussed

on obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

compatible weighting method with rank order centroid maximum entropy ordered weighted averaging approach in a situation where imprecise attribute weights such as a rank order are captured various approximate weighting methods have been proposed to aid multiattribute decision analysis among others it is well known that the rank order centroid roc weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights in this paper we aim to reinterpret the meaning of the roc weights and to develop a compatible weighting method that is based on other well established academic disciplines the ordered weighted averaging owa method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process some interesting semantics can be attached to the approximate weights in view of the measure developed in the owa method furthermore the weights generated by the maximum entropy method show equally compatible performance with the roc weights under some condition which is demonstrated by theoretical and simulation analysis

scalar reverse time depth migration of prestack elastic seismic data reflected p to p and p to s converted seismic waves in a two component elastic common source gather generated with a p wave source in a two dimensional model can be imaged by two independent scalar reverse time depth migrations the inputs to migration are pure p and s waves that are extracted by divergence and curl calculations during shallow extrapolation of the elastic data recorded at the earth s surface for both p to p and p to s converted reflected waves the imaging time at each point is the p wave traveltime from the source to that point the extracted p wave is reverse time extrapolated and imaged with a p velocity model using a finite difference solution of the scalar wave equation the extracted s wave is reverse time extrapolated and imaged similarly but with an s velocity model converted s wave data requires a polarity correction prior to migration to ensure constructive interference between data from adjacent sources synthetic examples show that the algorithm gives satisfactory resul

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

nonliner inversion of seismic reflection data in a laterally invariant medium interpretation of seismic waveforms can be expressed as an optimization problem based on a non linear least squares criterion to find the model which best explains the data an initial model is corrected iteratively using a gradient method conjugate gradient at each iteration computation of the direction of the model perturbation requires the forward propagation of the actual sources and the reverse time propagation of the residuals misfit between the data and the synthetics the two wave fields thus obtained are then correlated an extra forward propagation is required to compute the amplitude of the perturbation along the conjugate gradient direction the number of propagations to be simulated numerically in each iteration equals three times the number of shots since a 2 d finite difference code is employed to solve forward and backward propagation problems the method is general and can handle arbitrary 2 d source receiver configurations and lateral heterogeneities using conventional velocity

the possibilities of compressed sensing based kirchhoff prestack migration an approximate subsurface reflectivity distribution of the earth is usually obtained through the migration process however conventional migration algorithms including those based on the least squares approach yield structure descriptions that are slightly smeared and of low resolution caused by the common migration artifacts due to limited aperture coarse sampling band limited source and low subsurface illumination to alleviate this problem we use the fact that minimizing the l1 norm of a signal promotes its sparsity thus we formulated the kirchhoff migration problem as a compressed sensing cs basis pursuit denoise problem to solve for highly focused migrated images compared with those obtained by standard and least squares migration algorithms the results of various subsurface reflectivity models revealed that solutions computed using the cs based migration provide a more accurate subsurface reflectivity location and amplitude we applied the cs algorithm to image synthetic data from a fault model using dense and sparse acquisition geometries our results suggest that the proposed approach may still provide highly resolved images with a relatively small number of measurements we also evaluated the robustness of the basis pursuit denoise algorithm in the presence of gaussian random observational noise and in the case of imaging the recorded data with inaccurate migration velocities

2d frequency domain elastic full waveform inversion using time domain modeling and a multistep length gradient approach abstractto decouple the parameters in elastic full waveform inversion fwi we evaluated a new multistep length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction to perform wavefield extrapolations for the inversion we used parallelized high precision finite element fe modeling in the time domain the inversion was implemented in the frequency domain the data were obtained at every subsurface grid point using the discrete fourier transform at each time domain extrapolation step we also used frequency selection to reduce cycle skipping time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data and source wavelet estimation at the receivers over the full frequency spectrum by using a fast fourier transform in the inversion the velocity and density reconstructions behaved differently as a low wavenumber tomography for v

multiscale adjoint waveform difference tomography using wavelets abstractfull waveform seismic inversions based on minimizing the distance between observed and predicted seismograms are in principle able to yield better resolved earth models than those minimizing misfits derived from traveltimes alone adjoint based methods provide an efficient way of calculating the gradient of the misfit function via a sequence of forward modeling steps which using spectral element codes can be carried out in realistically complex media convergence and stability of full waveform difference adjoint schemes are greatly improved when data and synthetics are progressively presented to the algorithms in a constructive multiscale approximation using a bi orthogonal wavelet transform wavelets provide the nonredundant spectral decomposition that paves the way for the inversion to proceed successively from long wavelength fitting to detailed exploration of the phases in the seismogram the choice of wavelet class and type the initial depth of the multiscale decomposition and the min

implementation of the centroid method of solymosi and dombi multiple objective decision support either for selection among finite alternatives or for combining multiple functions in mathematical programming often involves estimating a set of weights of relative importance recently solymosi and dombi proposed a means of estimating such weights based upon ordinal preference information this method relies upon the centroid of bounded weights analytic hierarchy process uses ratio estimates of pairwise comparisons using only ordinal information the centroid of weights is developed as an alternative means of weighting hierarchical elements these weights could be used in selection among alternatives directly in concordance analysis or in multiple objective linear programming formulation for the centroid of feasible weight values is presented with a table of values for cases where the preference ranking includes no ties comparison of the technique on a student job selection decision indicates slight but insignificant decline in accuracy relative to the analytic hierarchy based method

multiscale seismic waveform inversion iterative inversion methods have been unsuccessful at inverting seismic data obtained from complicated earth models e g the marmousi model the primary difficulty being the presence of numerous local minima in the objective function the presence of local minima at all scales in the seismic inversion problem prevent iterative methods of inversion from attaining a reasonable degree of convergence to the neighborhood of the global minimum the multigrid method is a technique that improves the performance of iterative inversion by decomposing the problem by scale at long scales there are fewer local minima and those that remain are further apart from each other thus at long scales iterative methods can get closer to the neighborhood of the global minimum we apply the multigrid method to a subsampled low frequency version of the marmousi data set although issues of source estimation source bandwidth and noise are not treated results show that iterative inversion methods perform much better when employed with a decomposition by scale furthermore the method greatly reduces the computational burden of the inversion that will be of importance for 3 d extensions to the method

phase correction in separating p and s waves in elastic data two dimensional elastic data containing reflected p waves and converted s wave generated by a p source may be separated using dilatation and rotation calculation sun 1999 the algorithm is a combination of elastic full wavefield extrapolation sun and mcmechan 1986 chang and mcmechan 1987 1994 and wave type separation using dilatation divergence and rotation curl calculations dellinger and etgen 1990 it includes 1 downward extrapolating the multicomponent elastic data in an elastic velocity model using the elastic wave equation 2 calculating the dilatation to represent pure p waves and calculating the rotation to represent pure s waves at some depth and 3 upward extrapolating the dilatation in a p velocity model and upward extrapolating the rotation in an s velocity model using the acoustic wave equation for each

revising the owa operator for multi criteria decision making problems under uncertainty abstract multi criteria decision making mcdm problems are usually under uncertainty one of these uncertain parameters is the decision maker dm s degree of optimism which has an important effect on the results fuzzy linguistic quantifiers are used to obtain the assessments of this parameter from dm and then because of its uncertainty it is assumed to have stochastic nature a new approach entitled fsrowa is introduced to combine the fuzzy and stochastic features into a revised owa operator if the dm is not aware of the risk in decision then the decision objective is to maximize the expected combined goodness measure if the dm cares only about the risk then minimizing the variance of the combined goodness measure is his her objective the results of the fsrowa provide the expected value and the variance of the combined goodness measure for each alternative in order to combine these two attributes a composite goodness measure is introduced this measure gives more robust decision outcomes the theoretical results are illustrated in a watershed management problem

comparison of two algorithms for isotropic elastic p and s vector decomposition the research leading to this paper is supported by the sponsors of the ut dallas geophysical consortium a portion of the computations was done at the texas advanced computing center this paper is contribution no 1270 from the department of geosciences at the university of texas at dallas special thanks go to j brown a shabelansky and two anonymous reviewers for their useful comments and encouragements

amplitude balancing in separating p and s waves in 2d and 3d elastic seismic data the reflected p and s waves in elastic displacement component data recorded at the earth s surface are separated by reverse time downward extrapolation of the data in an elastic computational model followed by calculations to give divergence dilatation and curl rotation at a selected reference depth the surface data are then reconstructed by separate forward time upward scalar extrapolations from the reference depth of the magnitude of the divergence and curl wavefields and extraction of the separated p and s waves respectively at the top of the models a p wave amplitude will change by a factor that is inversely proportional to the p velocity when it is transformed from displacement to divergence and an s wave amplitude will change by a factor that is inversely proportional to the s velocity when it is transformed from displacement to curl consequently the ratio of the p to the s wave amplitude the p s amplitude ratio in the form of divergence and curl postseparation is different

nonlinear transformation on the transfer entropy of financial time series abstract transfer entropy te now is widely used in the data mining and economic field however te itself demands that time series intend to be stationary and meet markov condition naturally we are interested in investigating the effect of the nonlinear transformation of the two series on the te therefore the paper is designed to study the te of five nonlinear volatile transformations based on the data which are generated by the linear modeling and the logistic maps modeling as well as the dataset that come from financial markets with only one of the te of nonlinear transformations fluctuating around the te of original series the te of others all have increased with different degrees

a hierarchical elastic full waveform inversion scheme based on wavefield separation and the multistep length approach abstractelastic full waveform inversion fwi updates model parameters by minimizing the residuals of the p and s wavefields resulting in more local minima and serious nonlinearity in addition the coupling of different parameters degrades the inversion results to address these problems we have developed a hierarchical elastic fwi scheme based on wavefield separation and a multistep length gradient approach first we have derived the gradients expressed by different wave modes analyzed the crosstalk between various parameters and evaluated the sensitivity of separated p wave separated s wave and p and s wave misfit functions then a practical four stage inversion workflow was developed in the first stage conventional fwi is used to achieve rough estimates of the p and s wave velocities in the second stage we only invert the p wave velocity applying the separated p wavefields when strong s wave energy is involved or we merely update the s wave velocity by matching the separated s wavefiel

improving the efficiency of elastic wave mode separation for heterogeneous tilted transverse isotropic media wave mode separation for ti transversely isotropic models can be carried out by nonstationary filtering the elastic wavefields with localized filters these filters are constructed based on the polarization vectors obtained by solving the christoffel equation using local medium parameters this procedure although accurate is computationally expensive especially in 3d we develop an efficient method for wave mode separation which exploits the same general idea of projecting wavefields onto polarization vectors the method consists of two steps 1 separate wave modes in the wavenumber domain at a number of reference models to obtain the same number of partially separated wavefields then transform all the wavefields to the space domain 2 interpolate the wavefields obtained in step 1 in the space domain using the spatially variable model parameters the new method resembles the phaseshift plus interpolation pspi technique which interpolates the wavefields that are reconstructed at several reference velocities synthetic examples indicate that the separation followed by interpolation is effective for models with complex geology the new technique has the benefits of speed and accuracy

which data residual norm for robust elastic frequency domain full waveform inversion elastic full waveform inversion is an ill posed data fitting procedure that is sensitive to noise inaccuracies of the starting model definitionofmultiparameterclasses andinaccuratemodeling of wavefield amplitudes we have investigated the performance of different minimization functionals as the least squares norm 2 the least absolute values norm 1 and combinations of both the huber and so called hybrid criteria with reference to twonoisyoffshorevalhallmodelandonshoreoverthrustmodel synthetic data sets the four minimization functionals were implemented in 2d elastic frequency domain full waveform inversion fwi where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies for the offshore and onshore case studies the 1 norm provided the most reliable models for p and s wave velocities vp and vs even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data the 2 norm can provide reliable results in the presence of uniform white noise for vp and vs if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency the 1 norm and the huber and hybrid criteria unlike the 2 norm allowforsuccessfulimagingofthevsmodelfromnoisydataina soft seabed environment where the p to s waves have a small footprint in the data however the huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial and error investigations for reliable estimation the 1 norm provides a robust alternativetothe2 normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency domainfwi

conditioning the full waveform inversion gradient to welcome anisotropy abstractmultiparameter full waveform inversion fwi suffers from complex nonlinearity in the objective function compounded by the eventual trade off between the model parameters a hierarchical approach based on frequency and arrival time data decimation to maneuver the complex nonlinearity associated with this problem usually falls short in anisotropic media in place of data decimation i use a model gradient filter approach to access the parts of the gradient more suitable to combat the potential nonlinearity and parameter trade off the filter is based on representing the gradient in the time lag normalized domain in which small scattering angles of the gradient update are initially muted out the model update hierarchical filtering strategy include applying varying degrees of filtering to the different anisotropic parameter updates a feature not easily accessible to simple data decimation using fwi and reflection based fwi when the modeled data are obtained with the single scattering theory al

improvements to elastic full waveform inversion using cross gradient constraints seismic full waveform inversion fwi is potentially a powerful method for obtaining high resolution subsurface images but the results are often distorted by non linear effects and parameter trade offs such distortions can be particularly severe in the case of multi parameter fwi such as elastic fwi where inversion is performed simultaneously for p and s wave velocities and density the problem can be alleviated by adding additional constraints in form of plausible a priori information a usually well justified constraint includes the structural similarity of different model parameters that is an anomalous body likely exhibits variations in all elastic properties although their magnitudes may be different to consider such type of a priori information we have developed a structurally constrained elastic fwi which is based on minimization of cross products of gradients of different model parameters our synthetic 2d experiments show that the structurally constrained fwi can significantly improve mo

a strategy for nonlinear elastic inversion of seismic reflection data the problem of interpretation of seismic reflection data can be posed with sufficient generality using the concepts of inverse theory in its roughest formulation the inverse problem consists of obtaining the earth model for which the predicted data best fit the observed data if an adequate forward model is used this best model will give the best images of the earth s interior three parameters are needed for describing a perfectly elastic isotropic earth the density x and the lame parameters x and x or the density x and the p wave and s wave velocities x and x the choice of parameters is not neutral in the sense that although theoretically equivalent if they are not adequately chosen the numerical algorithms in the inversion can be inefficient in the long spatial wavelengths of the model adequate parameters are the p wave and s wave velocities while in the short spatial wavelengths p wave impedance s wave impedance and density are adequate the problem of inversion o

elastic full waveform inversion using the second generation wavelet and an adaptive operator length scheme abstractelastic full waveform inversion fwi can generally yield subsurface model parameters of high spatial resolution however the computational and storage burden is tremendous to mitigate this problem we developed the following three strategies first we derived a time space domain adaptive staggered grid finite difference method the size of the calculation was reduced by using smaller operator lengths for high s wave velocities second we evaluated a multiscale elastic fwi scheme based on the second generation wavelet by which scale decompositions of data and model space were implemented with the scale increasing spatial sampling intervals and time steps became larger therefore the minimum computational cost could be achieved by combining the variable operator length scheme with the multiscale scheme third to economize the memory consumption we extended the efficient boundary storage and checkpointing schemes into elastic fwi only wavefields of several parts in the boundary area betwe

approximate gauss newton methods for nonlinear least squares problems the gauss newton algorithm is an iterative method regularly used for solving nonlinear least squares problems it is particularly well suited to the treatment of very large scale variational data assimilation problems that arise in atmosphere and ocean forecasting the procedure consists of a sequence of linear least squares approximations to the nonlinear problem each of which is solved by an inner direct or iterative process in comparison with newton s method and its variants the algorithm is attractive because it does not require the evaluation of second order derivatives in the hessian of the objective function in practice the exact gauss newton method is too expensive to apply operationally in meteorological forecasting and various approximations are made in order to reduce computational costs and to solve the problems in real time here we investigate the effects on the convergence of the gauss newton method of two types of approximation used commonly in data assimilation first we examine truncated gauss newton methods where the inner linear least squares problem is not solved exactly and second we examine perturbed gauss newton methods where the true linearized inner problem is approximated by a simplified or perturbed linear least squares problem we give conditions ensuring that the truncated and perturbed gauss newton methods converge and also derive rates of convergence for the iterations the results are illustrated by a simple numerical example a practical application to the problem of data assimilation in a typical meteorological system is presented

decision making with incomplete information abstract decision situations with incomplete information are characterized by a decision maker without a precisely defined stable preference structure by probability distributions not known completely or by an inexact evaluation of consequences within the paper a general framework for decision making with incomplete information is presented which shows how to solve problems from descriptive as well as prescriptive decision theory based on this framework an overview of existing methods which are particularly suitable for handling incomplete information is given

analytic properties of maximum entropy owa operators we discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging owa aggregation operator the resulting weights are called the meowa weights using the method of lagrange multipliers we obtain an analytic form for these weights and describe some of their properties the concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker s degree of optimism this transformation which is affected by an owa operator is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the meowa weights

generalized mixture operators using weighting functions a comparative study with wa and owa abstract in the context of multiple attribute decision making we present an aggregation scheme based on generalized mixture operators using weighting functions and we compare it with two standard aggregation methods weighted averaging and ordered weighted averaging specifically we consider linear and quadratic weight generating functions that penalize bad attribute performances and reward good attribute performances an illustrative example borrowed from the literature is used to perform the operators comparison we believe that this comparative study will highlight the potential and flexibility of generalized mixture operators using weighting functions that depend on attribute performances

soft computing based aggregation methods for human resource management abstract we are interested in the personnel selection problem we have developed a flexible decision support system to help managers in their decision making functions this dss simulates experts evaluations using ordered weighted average owa aggregation operators which assign different weights to different selection criteria moreover we show an aggregation model based on efficiency analysis to put the candidates into an order

decision quality using ranked attribute weights three published approximation formulae for selecting the best multiattribute alternative based on rank ordered weights are evaluated all formulae are surprisingly efficacious in determining the best multiattribute alternative rank order centroid roc weights are more accurate than the other rank based formulae furthermore the roc formula generalizes to incorporate both other forms of partial information about attribute weights and partial rank order information as well because a roc based analysis is so straightforward and efficacious it provides an appropriate implementation tool