set choice problems with incomplete information about the preferences of the decision maker we consider the problem of selecting a predetermined number of objects from a given finite set it is assumed that the preferences of the decision maker on this set are only partially known our solution approach is based on the notions of optimal and non dominated subsets the properties of such subsets and the objects they contain are investigated the implementation of the developed approach is discussed and illustrated by various examples

ordinal regression revisited multiple criteria ranking using a set of additive value functions abstract we present a new method called utagms for multiple criteria ranking of alternatives from set a using a set of additive value functions which result from an ordinal regression the preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ar a called reference alternatives the preference model built via ordinal regression is the set of all additive value functions compatible with the preference information using this model one can define two relations in the set a the necessary weak preference relation which holds for any two alternatives a b from set a if and only if for all compatible value functions a is preferred to b and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b these relations establish a necessary and a possible ranking of alternatives from a being respectively a partial preorder and a strongly complete relation the utagms method is intended to be used interactively with an increasing subset ar and a progressive statement of pairwise comparisons when no preference information is provided the necessary weak preference relation is a weak dominance relation and the possible weak preference relation is a complete relation every new pairwise comparison of reference alternatives for which the dominance relation does not hold is enriching the necessary relation and it is impoverishing the possible relation so that they converge with the growth of the preference information distinguishing necessary and possible consequences of preference information on the complete set of actions utagms answers questions of robustness analysis moreover the method can support the decision maker when his her preference statements cannot be represented in terms of an additive value function the method is illustrated by an example solved using the utagms software some extensions of the method are also presented

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

interactive group decision making procedure under incomplete information this paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers multiple criteria group decision making mcgdm are involved usually decision makers dms are willing or able to provide only incomplete information because of time pressure lack of knowledge or data and their limited expertise related with problem domain there have been just a few studies considering incomplete information in group settings this incompletely specified information constructs region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings hence to handle this difficulty we suggest a method utilizing individual decision results to form group consensus final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings using individual decision results under group members possibly different weight constraints

robustness and information levels in case based multiple criteria sorting abstract case based preference elicitation methods for multiple criteria sorting problems have the advantage of posing rather small cognitive demands on a decision maker but they may lead to ambiguous results when preference parameters are not uniquely determined we use a simulation approach to determine the extent of this problem and to study the impact of additional case information on the quality of results our experiments compare two decision analysis tools case based distance sorting and the simple additive weighting method in terms of the effects of additional case information on sorting performance depending on problem dimension number of groups number of criteria etc our results confirm the expected benefit of additional case information on the precision of estimates of the decision maker s preferences problem dimension however has some unexpected effects

decision making under uncertainty with unknown utility function and rank ordered probabilities abstract we consider the ranking of decision alternatives in decision analysis problems under uncertainty under very weak assumptions about the type of utility function and information about the probabilities of the states of nature namely the following two assumptions are required for the suggested method the utility function is in the class of increasing continuous functions and the probabilities of the states of nature are rank ordered we develop a simple analytical method for the partial ranking of decision alternatives under the stated assumptions this method does not require solving optimization programs and is free of the rounding errors

non dominance and potential optimality for partial preference relations abstract in this paper we obtain new theoretical results relating the notions of potential optimality and non dominance without an assumption that a value function exists in particular we investigate a decision problem involving the choice of single or multiple best objects our results show that the notions of potential optimality and non dominance are equivalent in a special case of preferences of the decision maker expressed by partial quasi orders

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

cumulative dominance and heuristic performance in binary multiattribute choice we study the effectiveness of simple heuristics in multiattribute decision making we consider the case of an additive separable utility function with nonnegative nonincreasing attribute weights in this case cumulative dominance ensures that the so called cumulative dominance compliant heuristics will choose a best alternative for the case of binary attribute values and under two probabilistic models of the decision environment generalizing a simple bernoulli model we obtain the probabilities of simple and cumulative dominance in contrast with the probability of simple dominance the probability of cumulative dominance is shown to be large in many cases explaining the effectiveness of cumulative dominance compliant heuristics in those cases additionally for the subclass of the so called fully cumulative dominance compliant heuristics we obtain an upper bound for the expected loss that only depends on the weights being nonnegative and nonincreasing the low values of the upper bound for cases in

deriving rankings from incomplete preference information a comparison of different approaches abstract volume based methods for decision making under incomplete information like the smaa family of methods provide rich probabilistic information to support decision making however they usually do not directly generate a unique ranking of alternatives methods to create such a unique ranking from incomplete preference information typically select one parameter vector either by mathematical programming approaches or by averaging and then apply a preference model using this parameter vector in the present paper we develop several models to infer a complete ranking or a complete preorder of alternatives directly from the probabilistic information provided by volume based methods without singling out a specific parameter vector we compare the results obtained by these models to those obtained with a single parameter approach in a computational study results indicate small but significant differences in the performance of methods as well as in the probability that additional preference information might worsen rather than improve the results

the aspiration level interactive method aim reconsidered robustness of solutions abstract in this paper we explore theory and practice for the aspiration level interactive model aim a useful decision tool that takes advantage of the concepts of satisficing as well as other concepts of multiple criteria decision making mcdm we examine the relationship between aspiration levels and their mapped to solutions in the mcdm context using aim we extend the concept of robustness in decision making by defining a solution to be robust if many suitably defined aspiration levels map to it we use simulation to help explore robustness by generating three groups of random test problems each problem has twenty alternatives for each group of problems the top 5 most mapped to alternatives out of 20 are mapped to by at least 50 of the aspiration levels we also relate the concept of robustness in decision making to the ideas of simply ranking alternatives using equal weights there is a strong correlation between the robustness ranking and the equal weights ranking based on our analyses we then randomly generate additional problems to explore certain other factors we also discuss practical aspects of robustness

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

the utility efficient set and its interactive reduction we assume a decision situation under risk with incomplete information on preferences modelled as a vector utility function we consider an additive aggregation of its components and partial information on the scaling constants we develop the concept of utility efficiency to identify efficient strategies in discrete problems when the information about the scaling constants of the decision maker is in the form of a polyhedral cone a characterization of the utility efficient set provides a practical way to compute such efficient strategies we then discuss an interactive method based on the assessment of the scaling constants via an interactive paired comparison with its convergence the method is complemented by a procedure to reduce the utility efficient set to aid in the process of reaching a final strategy

linearly implicit all mach number shock capturing schemes for the euler equations abstract we propose a family of simple second order accurate schemes for the numerical solution of euler equation of gas dynamics that are linearly implicit in the acoustic waves eliminating the acoustic cfl restriction on the time step the general idea is that explicit differential operators in space relative to convective or material speeds are discretised by upwind schemes or local lax friedrics fluxes and the linear implicit operators pertaining to acoustic waves are discretised by central differences we have compared the results of such schemes on a series of one and two dimensional test problems including classical shock tube configurations also we have considered low mach number acoustic wave propagation tests as well as nozzle flows in various mach regimes the results show that these schemes do not introduce excessive numerical dissipation at low mach number providing an accurate solution in such regimes they perform reasonably well also when the mach number are not too small

an asymptotic preserving all speed scheme for the euler and navier stokes equations we present an asymptotic preserving all speed scheme for the simulation of compressible flows valid at all mach numbers ranging from very small to order unity the scheme is based on a semi implicit discretization which treats the acoustic part implicitly and the convective and diffusive parts explicitly this discretization which is the key to the asymptotic preserving property provides a consistent approximation of both the hyperbolic compressible regime and the elliptic incompressible regime the divergence free condition on the velocity in the incompressible regime is respected and an the pressure is computed via an elliptic equation resulting from a suitable combination of the momentum and energy equations the implicit treatment of the acoustic part allows the time step to be independent of the mach number the scheme is conservative and applies to steady or unsteady flows and to general equations of state one and two dimensional numerical results provide a validation of the asymptotic preserving all speed properties

an aggregation disaggregation approach to obtain robust conclusions with electre tri electre tri is a well known method to assign a set of alternatives to a set of predefined categories considering multiple criteria using this method requires setting many parameters which is often a difficult task we consider the case where the decision makers dms in the decision process are unsure of which values should each parameter take which may result from uncertain imprecise or inaccurately determined information as well as from lack of consensus among them this paper discusses the synergy between two approaches developed independently to deal with this difficulty the first approach infers the value of parameters from assignment examples provided by the dms as an elicitation aid each assignment example originates mathematical constraints that the parameter values should satisfy the second approach considers a set of constraints on the parameter values reflecting the imprecise information that the dms are able to provide then it computes the best and worst categories for each alternative compatible with constraints in order to present robust conclusions both approaches avoid asking for precise values for the parameters rather they proceed to solve the problem in a way that requires from the dms much less effort by integrating these two approaches this paper proposes a new interactive approach where the insight obtained during robustness analyses guides the dms during the elicitation phase

decision network polynomials and the sensitivity of decision support models abstract decision makers benefit from the utilization of decision support models in several applications obtaining managerial insights is essential to better inform the decision process this work offers an in depth investigation into the structural properties of decision support models we show that the input output mapping in influence diagrams decision trees and decision networks is piecewise multilinear the conditions under which sensitivity information cannot be extracted through differentiation are examined in detail by complementing high order derivatives with finite change sensitivity indices we obtain a systematic approach that allows analysts to gain a wide range of managerial insights a well known case study in the medical sector illustrates the findings

rank inclusion in criteria hierarchies this paper presents a method called rank inclusion in criteria hierarchies rich for the analysis of incomplete preference information in hierarchical weighting models in rich the decision maker is allowed to specify subsets of attributes which contain the most important attribute or more generally to associate a set of rankings with a given set of attributes such preference statements lead to possibly non convex sets of feasible attribute weights allowing decision recommendations to be obtained through the computation of dominance relations and decision rules an illustrative example on the selection of a subcontractor is presented and the computational properties of rich are considered

an all speed second order well balanced imex relaxation scheme for the euler equations with gravity abstract we present an implicit explicit well balanced finite volume scheme for the euler equations with a gravitational source term which is able to deal also with low mach flows to visualize the different scales we use the non dimensionalized equations on which we apply a pressure splitting and a suliciu relaxation on the resulting model we apply a splitting of the flux into a linear implicit and an non linear explicit part that leads to a scale independent time step the explicit step consists of a godunov type method based on an approximative riemann solver where the source term is included in the flux formulation we develop the method for a first order scheme and give an extension to second order both schemes are designed to be well balanced preserve the positivity of density and internal energy and have a scale independent diffusion we give the low mach limit equations for well prepared data and show that the scheme is asymptotic preserving these properties are numerically validated by various test cases

generalized polynomial decomposable multiple attribute utility functions for ranking and rating multiple criteria discrete alternatives1all rights reserved this study or parts thereof may not be reproduced in any form without the written permission of the authors 1 this paper describes a class of nonlinear polynomial functions which are far more complex than linear and additive functions and other types of well known utility functions although the assessment of such nonlinear polynomial functions may require more time and possibly more cognitive burden the advantage of using more complex and nonlinear functions is that more complex preferential behaviors can be represented and hence a larger set of decision problems can be solved in this paper we develop a generalized decomposable multiattribute utility function gdmauf for representing the decision maker s dm s preferential behavior we show that any polynomial function can be represented by the gdmauf and that such a function can be assessed to represent the dm s behavioral preferences or so called the utility function our approach is based on the use of holistic responses numerical rankings and rating of alternatives from which we assess the gradients of the dm s unknown utility function from assessed gradients we then construct a generalized decomposable multiattribute utility function that mimics and represent the dm s preferential behavior this assessed generalized decomposable multiattribute utility function can be used directly to rank and rate all alternatives without any further interaction from the dm we also demonstrate that the generalized utility function gdmauf is more general and flexible than some other well known utility structures such as additive multiplicative multilinear quasi concave and quasi convex the underlying assumptions for gdmauf are that it is differentiable and that it can be expressed in a polynomial form some classes extensions and properties of the generalized utility function are explored to simplify its assessment several examples and experimental results are provided

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

preference assessment by imprecise ratio statements the pairs method developed in this paper introduces imprecise preference statements into value trees the assessment of attribute weights in pairs extends the well known smart technique so that in addition to exact statements the decision maker can enter interval judgments which indicate ranges for the relative importance of the attributes the interval judgments and the possibly range valued information about the outcomes of the alternatives are processed with linear programming into value intervals and dominance relations as the decision maker refines the description of his preferences either by entering new statements or by tightening his earlier judgments these results become more detailed and convey more information about which alternatives are preferred throughout the interactive refinement process pairs supports the decision maker by deriving and displaying the consequences of his earlier judgments

multi attribute decision aid under incomplete information and hierarchical structure abstract this paper presents methods for dealing with incomplete information about both attribute weights and values under a hierarchically structured value tree incomplete information in this paper covers arbitrary linear inequalities and is hence to treat a more general situation than a previous restrictive definition of incomplete information that typically includes interval judgment this may give decision makers chances that is enhanced freedom of choice and comforts of specification we propose two techniques for prioritizing alternatives by strict dominance relationship one is the extension of a previous method for operating flat structured value trees to hierarchical ones the other approach propagates pairwise dominance values from leaf nodes to topmost node consecutively which is also an extension of a previous method because the strict dominance rule fails to fully prioritize alternatives as is usual the case under incomplete information we suggest a new method a measure of preference strength which can provide decision makers with a single optimal alternative or full rank of alternatives without any further interaction with decision makers

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

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

decision theory and strict ranking of probabilities abstract this paper is concerned with the derivation of guides to decision making in a set of circumstances intermediate between the classic extremes of pure risk and pure uncertainty it is assumed that the decision maker can specify a subjective strict ranking of the probabilities of states of nature in which case given knowledge of the payoffs of a strategy it is possible to find in a straightforward fashion maximum and minimum expected payoffs for the strategy if the information contained in the strict ranking is available to the decision maker then to fail to take it into account must adversely affect the quality of decision making the paper discusses both the interpretation and the possible practical uses of extreme expected values in decision making and includes a numerical example based on an investment decision problem to demonstrate the ease of use of the results obtained

establishing dominance between alternatives with incomplete information in a hierarchically structured attribute tree abstract a model for establishing dominance with incomplete information is proposed in a hierarchically structured attribute tree the linear additive value function under certainty is used in the model the model allows the decision maker to provide any type of linear partial information on the attribute weights and the alternative values the incompletely specified information constructs a feasible region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable non linear programming hence to handle this difficulty we propose a solution technique also to handle the tree structure we break down the attribute tree into sub trees due to the recursive structure of the solution technique the optimization results from sub trees can be utilized in computing the value interval on the topmost attribute based on the solution technique an algorithm for obtaining the value interval is proposed and dominance relation is established

hierarchical multi objective decision making this paper proposes a hierarchical procedure for solving decision problems with multiple objectives the procedure consists of two levels a top and a base level the main idea is that the top level only provides general preference information taking this information into account the base level then determines a compromise solution for a multi objective linear program it will be shown how such a hierarchical procedure can be structured by deriving weight restrictions from the general preference information of the top level and by using the interactive modm procedure of zionts and wallenius on the base level

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

a weakly asymptotic preserving low mach number scheme for the euler equations of gas dynamics we propose a low mach number godunov type finite volume scheme for the numerical solution of the compressible euler equations of gas dynamics the scheme combines klein s non stiff stiff decomposition of the fluxes j comput phys 121 1995 pp 213 237 with an explicit implicit time discretization f cordier p degond and a kumbaro j comput phys 231 2012 pp 5685 5704 for the split fluxes this results in a scalar second order partial differential equation pde for the pressure which we solve by an iterative approximation due to our choice of a crucial reference pressure the stiff subsystem is hyperbolic and the second order pde for the pressure is elliptic the scheme is also uniformly asymptotically consistent numerical experiments show that the scheme needs to be stabilized for low mach numbers unfortunately this affects the asymptotic consistency which becomes nonuniform in the mach number and requires an unduly fine grid in the small mach number limit on the other han

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

study of a new asymptotic preserving scheme for the euler system in the low mach number limit this article deals with the discretization of the compressible euler system for all mach numbers regimes for highly subsonic flows since acoustic waves are very fast compared to the velocity of the fluid the gas can be considered as incompressible from the numerical point of view when the mach number tends to zero the classical godunov type schemes present two main drawbacks they lose consistency and they suffer of severe numerical constraints for stability to be guaranteed since the time step must follow the acoustic waves speed in this work we propose and analyze a new unconditionally stable an consistent scheme for all mach number flows from compressible to incompressible regimes stability being only related to the flow speed a stability analysis and several one and two dimensional simulations confirm that the proposed method possesses the sought characteristics 1 introduction almost all fluids can be said to be compressible however there are many situations in which the changes in density are so small to be considered negligible we refer to these situations saying that the fluid is in an incompressible regime from the mathematical point of view the difference between compressible and incompressible situations is that in the second case the equation for the conservation of mass is replaced by the constraint that the divergence of the velocity should be zero this is due to the fact that when the mach number tends to zero the pressure waves can be considered to travel at infinite speed from the theoretical point of view researchers try to fill the gap between those two different descriptions by determining in which sense compressible equations tend to incompressible ones 2 20 21 22 33 in this article we are interested in the numerical solution of the euler system when used to describe fluid flows where the mach number strongly varies this causes the gas to pass from compressible to almost incompressible situations and consequently it causes most of the numerical methods build for solving compressible euler equations to fail in fact when the mach number tends to zero it is well known that classical godunov type schemes do not work anymore indeed they lose consistency in the incompressible limit this means that when close to the limit the accuracy of theses schemes is not sufficient to describe the flow many efforts have been done in the recent past in order to correct this main drawback of godunov schemes for instance by using preconditioning methods 34 or by splitting and correcting the pressure on the collocated meshes 5 9 10 12 13 14 30 15 23 24 26 27 28 or instead by using staggered grids like in the famous mac scheme see for instance 3 16 17 18 19 31 unfortunately even if these approaches permit to bypass the consistency problem of godunov methods they all need to resolve the scale of the acoustic waves in the fluid in order to remain stable this means that they suffer from a restrictive cfl courant frierichs levy condition which is inversely proportional to the mach number value in this work we derive a method which

compressible multiphase semi implicit method with moment of fluid interface representation a unified method for simulating multiphase flows using an exactly mass momentum and energy conserving cell integrated semi lagrangian advection algorithm is presented the deforming material boundaries are represented using the moment of fluid method the new algorithm uses a semi implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed the asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods shocks are captured and material discontinuities are tracked without the aid of any approximate or exact riemann solvers simulations of underwater explosions and fluid jetting in one two and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large impedance mismatch

generalized chebychev inequalities theory and applications in decision analysis in many decision analysis problems we have only limited information about the relevant probability distributions in problems like these it is natural to ask what conclusions can be drawn on the basis of this limited information for example in the early stages of analysis of a complex problem we may have only limited fractile information for the distributions in the problem what can we say about the optimal strategy or certainty equivalents given these few fractiles this paper describes a very general framework for analyzing these kinds of problems where given certain moments of a distribution we can compute bounds on the expected value of an arbitrary objective function by suitable choice of moment and objective functions we can formulate and solve many practical decision analysis problems we describe the general framework and theoretical results discuss computational strategies and provide specific results for examples in dynamic programming decision analysis with incomplete information bayesian statistics and option pricing

asymptotic preserving imex finite volume schemes for low mach number euler equations with gravitation in this paper we will present and analyze a new class of the imex finite volume schemes for the euler equations with a gravity source term we will in particular concentrate on a singular limit of weakly compressible flows when the mach number m1 in order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non stiff nonlinear part that models nonlinear advection effects for time discretization we use a special class of the so called globally stiffly accurate imex schemes and approximate the stiff linear operator implicitly and the non stiff nonlinear operator explicitly for spatial discretization the finite volume approximation is used with the central and rusanov laxfriedrichs numerical fluxes for the linear and nonlinear subsystem respectively in the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small mach number we also analyze experimentally convergence rates in the singular limit when the mach number tends to zero

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

modelling pairwise comparisons on ratio scales abstract many real world decision problems have multiple criteria on qualitative domains given the expectation that more and more of such problems will be modelled as mcdm problems involving scoring on subjective qualitative domains then there is a class of significant problems for which the evaluator will require an evaluation framework which handles occurrences of seeming intransitivity and inconsistency these phenomena are likely to appear in qualitative subjective domains where the decision making environment is characterized by ambiguity and vagueness in this paper we present a model for exploring the implications of pairwise comparisons on ratio scales this model provides a mathematical explanation for the phenomena of intransitivity and inconsistency that sometimes appear in situations involving scoring on a subjective qualitative domain using this framework we develop methods for generating consistent intervals on ratio scales we also present a two stage action learning process for generating consistent points on ratio scales that provides both behavioral and mathematical convergence

weighted sum model with partial preference information application to multi objective optimization multi objective optimization problems often lead to large nondominated sets as the size of the problem or the number of objectives increases generating the whole nondominated set requires significant computation time while most of the corresponding solutions are irrelevant to the decision maker dm optimizing an aggregation function reduces the computation time and produces one or a very limited number of more focused solutions this requires however the elicitation of precise preference parameters which is often difficult and partly arbitrary and might discard solutions of interest an intermediate approach consists in using partial preference information with an aggregation function in this work we present a preference relation based on the weighted sum aggregation where weights are not precisely defined we give some properties of this preference relation and define the set of preferred points as the set of nondominated points with respect to this relation we provide an efficient and generic way of generating this preferred set using any standard multi objective optimization algorithm this approach shows competitive performances both on computation time and quality of the generated preferred set

an all speed relaxation scheme for gases and compressible materials abstract we present a novel relaxation scheme for the simulation of compressible material flows at all speeds an eulerian model describing gases fluids and elastic solids with the same system of conservation laws is adopted the proposed numerical scheme is based on a fully implicit time discretization easily implemented thanks to the linearity of the transport operator in the relaxation system the spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in all different mach regimes the scheme is validated by simulating gas and liquid flows with different mach numbers the simulation of the deformation of compressible solids is also approached assessing the ability of the scheme in approximating material waves in hyperelastic media

extreme point based multi attribute decision analysis with incomplete information abstract in this paper we present a simple method for finding the extreme points of various types of incomplete attribute weights incomplete information about attribute weights is transformed by a sequence of change of variables to a set whose extreme points are readily found this enhanced method fails to derive the extreme points of every type of incomplete attribute weights nevertheless it provides us with a flexible method for finding the extreme points including widely used forms of incomplete attribute weights finally incomplete attribute values expressed in various forms are also analyzed to find their characterizing extreme points by applying similar procedures carried out in the incomplete attribute weights

the dimension of chaotic attractors dimension is perhaps the most basic property of an attractor in this paper we discuss a variety of different definitions of dimension compute their values for a typical example and review previous work on the dimension of chaotic attractors the relevant definitions of dimension are of two general types those that depend only on metric properties and those that depend on the frequency with which a typical trajectory visits different regions of the attractor both our example and the previous work that we review support the conclusion that all of the frequency dependent dimensions take on the same value which we call the dimension of the natural measure and all of the metric dimensions take on a common value which we call the fractal dimension furthermore the dimension of the natural measure is typically equal to the lyapunov dimension which is defined in terms of lyapunov numbers and thus is usually far easier to calculate than any other definition because it is computable and more physically relevant we feel that the dimension of the natural measure is more important than the fractal dimension

sensitivity in bayesian statistics the prior and the likelihood abstract one paradigm for sensitivity analyses in bayesian statistics is to specify a reasonable class of priors and to compute the corresponding class of posterior inferences the class is chosen to represent uncertainty about the prior there is often additional uncertainty however about the family of sampling distributions this article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie close to a given parametric family by treating the prior as a probability measure on the space of sampling distributions this article also gives a unified treatment to what are usually considered two separate problems sensitivity to the prior and sensitivity to the sampling model first the notion of close to is made explicit then an algorithm is given for turning ratio linear problems into sequences of linear problems in addition to solving the problem at hand the algorithm simplifies many other robust bayesian computational pro

wave structure similarity of the hllc and roe riemann solvers application to low mach number preconditioning the approximate riemann solver of roe and the solver of harten lax van leer hll and its variants such as the hllc solver are widely used as building blocks of finite volume godunov type methods for the solution of the euler equations of gas dynamics and related hyperbolic flow models the hllc solver has gained increasing popularity over the last two decades since it possesses some of the good properties of the roe solver and in addition satisfies important entropy and positivity conditions with no need of special fixes in this work we rewrite the classical hllc riemann solver in a novel form that highlights the formal mathematical similarity of its wave structure with the one of the roe solver this similarity might be useful to extend to the hllc method some numerical techniques devised specifically for the roe method as an example of application we illustrate the design of a turkel type low mach number preconditioning technique for the hllc scheme by exploiting methodologies proposed in the l

preference programming through approximate ratio comparisons abstract in the context of hierarchical weighting this paper operationalizes interval judgments which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale through such judgments the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates after each new statement the interval judgments are synthesized into dominance relations on the alternatives by solving a series of linear programming problems this leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description moreover the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed

asymptotic error analysis of an imex runge kutta method abstract we consider a system of singularly perturbed differential equations with singular parameter e 1 discretized with an imex runge kutta method the splitting needed for the imex method stems from a linearization of the fluxes around the limit solution we analyze the asymptotic convergence order as e 0 we show that in this setting the stage order of the implicit part of the scheme is of great importance thereby explaining earlier numerical results showing a close correlation of errors of the splitting scheme and the fully implicit one

extended methods for identifying dominance and potential optimality in multi criteria analysis with imprecise information abstract many of the recent prescriptive approaches to multi attribute decision analysis have dealt with situations in which trade off weights are known imprecisely while marginal values are known exactly a way to handle such problems is to utilize a linear programming technique from which non dominated and or potentially optimal score vectors can be obtained in some attributes however it is not easy for decision makers to provide the marginal value functions that are explicit and exact the purpose of this paper is to address problems such that the both attribute weights and marginal values are known imprecisely we then assume without loss of generality that these imprecise information on both weights and values are in the form of inequalities and or equalities such as rankings and bounds the first formulations for checking dominance and potential optimality become non linear programming problems hard to be solved generally we thus present how these non linear problems are reduced to linear programming equivalents

shortest path problems with partial information models and algorithms for detecting dominance abstract in this work we focus on partial information models for the well known shortest path problem where we consider multiple instances of values for the parameters that determine the cost of each arc this allows coping with the uncertainty about the future the imprecision of data the arbitrariness of some options the evolving values of the decision makers dms and or the multiplicity of dms in group decision making this paper proves some results and presents detailed algorithms to identify the set of non dominated paths a concept from decision theory under partial information we first address problems with a finite set of instances then problems with a general eventually not discrete set of instances and finally we study a particular case of the latter which complies with a condition that may hold in some situations to deal with these partial information problems we propose a new use for existing multicriteria algorithms based on the ranking of shortest paths

implementing stochastic multicriteria acceptability analysis abstract stochastic multicriteria acceptability analysis smaa is a family of methods for aiding multicriteria group decision making in problems with inaccurate uncertain or missing information these methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one or that would give a certain rank for a specific alternative the main results of the analysis are rank acceptability indices central weight vectors and confidence factors for different alternatives the rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative the central weight vectors represent the typical preferences favouring each alternative and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision the computations in smaa require the evaluation of multidimensional integrals that must in practice be computed numerically in this paper we present efficient methods for performing the computations through monte carlo simulation analyze the complexity and assess the accuracy of the presented algorithms we also test the efficiency of these methods empirically based on the tests the implementation is fast enough to analyze typical sized discrete problems interactively within seconds due to almost linear time complexity the method is also suitable for analysing very large decision problems for example discrete approximations of continuous decision problems

a data envelopment analysis approach to multicriteria decision problems with incomplete information abstract as a decision aid for discrete multicriteria decision problems this paper proposes a multilevel graph of alternatives to represent the ranking to the extent that this is possible when incomplete information on weights is available under the assumption of the additive value function to construct it the nested decomposition of the set of alternatives is established along the lines of data envelopment analysis dea a numerical example is given to illustrate a multilevel graph based on the nested decomposition and compare it with the hierarchical dominance graph based on dominance relations proposed by park and kim

using fuzzy binary relations for identifying noninterior decision alternatives abstract a fuzzy noninferiority relation is introduced based on this relation fuzzy relations of preference strict preference indifference and incomparability are specified and their properties are investigated a fuzzy noninferior subset is defined and its basic characteristic properties are established an algorithm is presented for identifying a fuzzy set of noninferior alternatives in decision making situations that require the selection of a certain number of noninferior alternatives for more detailed study

a unified method for computing incompressible and compressible flows in boundary fitted coordinates a unified method for computing incompressible and compressible flows with mach uniform accuracy and efficiency is described the method is equally applicable to stationary and nonstationary flows a pressure based discretisation on a staggered grid in general boundary fitted coordinates is used for the euler equations extension to navier stokes is straightforward dimensionless variables that remain finite for all mach numbers are used mach number independent accuracy and efficiency is shown by numerical experiments

a method of multiattribute decision making with incomplete information a precise determination of a multiattribute utility function of a decision maker or a group of decision makers requires considerable information that may not be available in many decision situations in this paper the method hopie which allows one to determine a set of utility functions consistent with the incomplete information received from the decision maker is proposed the method is based on holistic judgments of hypothetical alternatives defined by a certain factorial design it requires that the evaluation of the alternatives be given on an interval scale the method can also accommodate other types of additional information such as pairwise comparisons

ranking and selection for multiple performance measures using incomplete preference information abstract this paper presents two new procedures for ranking and selection r s problems where the best system designs are selected from a set of competing ones based on multiple performance measures evaluated through stochastic simulation in the procedures the performance measures are aggregated with a multi attribute utility function and incomplete preference information regarding the weights that reflect the relative importance of the measures is taken into account a set of feasible weights is determined according to preference statements that are linear constraints on the weights given by a decision maker non dominated designs are selected using two dominance relations referred to as pairwise and absolute dominance based on estimates for the expected utilities of the designs over the feasible weights the procedures allocate a limited number of simulation replications among the designs such that the probabilities of correctly selecting the pairwise and absolutely non dominated designs are maximized the new procedures offer ease of eliciting the weights compared with existing r s procedures that aggregate the performance measures using unique weights moreover computational advantages are provided over existing procedures that identify non dominated designs based on the expected values of the performance measures the new procedures allow to obtain a smaller number of non dominated designs they also identify these designs correctly with a higher probability or require a smaller number of replications for correct selection finally the new procedures allocate a larger number of replications to the non dominated designs that are therefore evaluated with greater accuracy these computational advantages are illustrated through several numerical experiments

ordinal judgments in multiattribute decision analysis abstract the article discusses the contradiction between the ambiguity of human judgment in a multicriterion environment and the exactness of the assessments required in the majority of the decision making methods preferential information from the decision makers in the ordinal form e g more preferable less preferable etc is argued to be more stable and more reliable than cardinal input ways of obtaining and using ordinal judgments for rank ordering of multiattribute alternatives are discussed the effectiveness of the step wise procedure of using ordinal tradeoffs for comparison of alternatives is evaluated we introduce the notion of ordinal tradeoffs presentation of ordinal tradeoffs as a flexible three stage process a paired joint ordinal scale pjos and evaluation of the effectiveness of the three stage process simulation results examine the sensitivity of the number of pairwise comparisons required for given numbers of criteria and categories within criteria as well as the number of alternatives analyzed this simulation shows that ordinal pairwise comparisons provide sufficient power to discriminate between 75 and 80 of the alternatives compared while the proportional number of pairwise comparisons relative to the maximum possible decreases with the number of criteria and categories the method is relatively insensitive to the number of alternatives considered

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

a generalized decomposable multiattribute utility function in this paper a generalized decomposable multiattribute utility function mauf is developed it is demonstrated that this new mauf structure is more general than other well known mauf structures such as additive multiplicative and multilinear therefore it is more flexible and does not require that the decision maker be consistent with restrictive assumptions such as preferential independence conditions about his her preferences we demonstrate that this structure does not require any underlying assumption and hence solves the interdependence among attributes hence there is no need for verification of its structure several useful extensions and properties for this generalized decomposable mauf are developed which simplify its structure or assessment the concept of utility efficiency is developed to identify efficient alternatives when there exists partial information on the scaling constants of an assumed mauf it is assumed that the structure decomposition of the mauf is known and the partial information about the scaling constants of the decision maker is in the form of bounds or constraints for the generalized decomposable structure linear programming is sufficient to solve all ensuing problems some examples are provided

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

establishing strict dominance between alternatives with special type of incomplete information abstract a special model for establishing dominance with decision maker s incomplete information is proposed in multi attribute decision problem under certainty incomplete information is a set of linear inequalities about utilities as well as attribute weights since a general model presented in a prior work uses a linear programming technique a number of linear programs should be solved for checking dominance with the proposed method we can check strict dominance between alternatives by simple matrix operation without solving linear programs thus reducing computational time

sequential incorporation of imprecise information in multiple criteria decision processes abstract in this paper we deal with multicriteria decision processes and develop tools that permit to ease the task of analysing such models we provide a methodology to sequentially incorporate imprecise preference information which is given by means of general linear relations in the weighting coefficients the results presented allow us to evaluate the quality of the information supplied and can be used to reduce the number of irrelevant alternatives to be presented to the decision maker dm several examples based on multiple criteria linear programming illustrate the results of the paper

decision analysis with incomplete utility and probability information an approach to the solution of decision analysis problems under uncertainty with imprecise and incomplete information is presented the methodology is designed for cases in which payoffs conditional on the state of nature are known precisely but only limited or imprecise probability and utility information is available regarding a decision maker s beliefs and tastes a decision maker provides conditional payoffs optionally bounds on state probabilities bounds on the certainty equivalent for a simple lottery any known relationships between probabilities of states of nature and a series of strict preferences between pairs of vectors of conditional payoffs we assume an exponential utility function with unknown parameter the method proceeds by sequentially eliciting preferences new bounds on probabilities and or the certainty equivalent and new relationships among probabilities until the problem is solved the methodology is demonstrated through a two state and a three state example which illust

use of piecewise linear value functions in interactive multicriteria decision support a monte carlo study this paper describes a monte carlo study conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice mcdm problem based on explicit value function models the purpose of the study is to identify those assumptions and parameters which lead to the most efficient use of preference judgements made by the decision maker and to the greatest robustness to judgmental errors it is concluded that nonlinearities in the value function need to be modelled achieved here by use of a piecewise linear form it was also found that search for indifference points rather than using simple preference judgements alone is of great advantage best realized by expressing judgements in terms of pairwise trade offs methods incorporating these features are highly robust to judgmental errors interactive methods of this class are compared with a priori fitting of similar value functions and found to give a very similar quality of solution

preference programming with incomplete ordinal information abstract this paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings these preference statements can be particularly helpful in developing a joint preference representation for a group of decision makers who may find difficulties in agreeing on numerical parameter values because these statements can lead to a non convex set of feasible parameters a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations this makes it possible to complete incomplete ordinal information with other forms of incomplete information

asymptotic single and multiple scale expansions in the low mach number limit an asymptotic analysis of the euler equations in the limit of vanishing mach number is presented which can be employed to extend the validity of numerical methods from the compressible to the low mach number regime r klein j comput phys 121 1995 pp 213 237 l hoffmann and a meister in proceedings of the fourth eccomas computational fluid dynamics conference vol 1 c hirsch et al eds athens 1998 pp 567 572 the work is based on the analysis recently proposed by klein whereby the paper is devoted to a rigorous mathematical justification of this asymptotic investigation in order to give reliable statements concerning the assumptions under which the results hold in contrast to klein a single scale as well as multiple scale expansion is used depending on the spatial domain under consideration

second order implicit explicit total variation diminishing schemes for the euler system in the low mach regime abstract in this work we consider the development of implicit explicit total variation diminishing tvd methods also termed ssp strong stability preserving for the compressible isentropic euler system in the low mach number regime the proposed scheme is asymptotically stable with a cfl condition independent of the mach number in addition it degenerates in the low mach number regime to a consistent discretization of the incompressible system since it has been proved that implicit schemes of order higher than one cannot be tvd ssp 30 we construct a new paradigm of implicit time integrators by coupling first order in time schemes with second order ones in the same spirit as highly accurate shock capturing tvd methods in space for this particular class of schemes the tvd property is first proved on a linear model advection equation and then extended to the isentropic euler case the result is a method which interpolates from the first to the second order both in space and time it preserves the monotonicity of the solution and is highly accurate for all choices of the mach number moreover the time step is only restricted by the non stiff part of the system we finally show thanks to one and two dimensional test cases that the method indeed possesses the claimed properties

a mach sensitive implicit explicit scheme adapted to compressible multi scale flows abstract the method presented below focuses on the numerical approximation of the euler compressible system it pursues a two fold objective being able to accurately follow slow material waves as well as strong shock waves in the context of low mach number flows the resulting implicit explicit imex fractional step approach leans on a dynamic splitting designed to react to the time fluctuations of the maximal flow mach number when the latter rises suddenly the imex scheme so far driven by a material wave courant number turn into a time explicit approximate riemann solver constrained by an acoustic wave courant number it is also possible to enrich the dynamic splitting in order to capture high pressure jumps even when the flow mach number is low one dimensional low mach number test cases involving single or multiple waves confirm that the present approach is as accurate and efficient as an imex lagrange projection method besides numerical results suggest that the stability of the present method holds for any mach number if the courant number related to the convective subsystem arising from the splitting is of order unity

multiple criteria robust interactive decision analysis mcrid for optimizing public policies abstract important public policy decisions are often very complex involving many factors large uncertainties and multiple conflicting objectives decision analysis which is a formal framework for dealing with such issues has been applied to a variety of public sector problems over the last two decades a limitation of using decision analysis is the often onerous assessment burden it places on the decision maker dm we have developed a novel interactive procedure and decision support system dss for performing decision analysis on the personal computer called robust interactive decision analysis rid which avoids the difficult problems of precisely assessing a dm s utility and state probability functions associated with traditional decision treee analysis the rid method permits a dm to voluntarily and interactively express strong viz sure binary preferences for actions partial decision functions and full decision functions and only imprecise probability and utility function assessments the inputs are used with various dominance operators via a mathematical programming framework to prune the state probability utility and decision space until there is convergence on a relatively small subset of efficient strategies or an optimal choice strategy conceptually the operation of the rid method can be regarded as a state pruning system and its computer implementation as a dss in this paper we extended the rid concept and dss to deal with multiple criteria decisions obviating the need to precisely and completely assess attribute weights tradeoffs consequences and or value utility functions the approach which we call multiple criteria robust interactive decision analysis mcrid is developed illustrated and shown to be effective in eliminating many inefficient alternatives however since the aggregate utility of each alternative is interval valued it then becomes difficult to intuitively choose an optimal alternative from among the remaining efficient ones since the intervals are not defined by any specific probability distributions we have tentatively shown that aggregate utility intervals ultimately converge toward a normal density function and can be so approximated with relatively few attributes hence stochastic dominance is employed to further filter out alternatives an interactive goal programming gp technique is then developed to assist the dm in choosing an optimal alternative

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

partial information dominance and potential optimality in multiattribute utility theory when a multiattribute utility function is only partially specified by prior preference statements what can be said about the relative desirability of actual alternatives this question is addressed for the cases of additively separable cardinal utility with unknown scaling constants multiplicatively separable cardinal utility with unknown scaling constants and additively separable ordinal utility we review previous approaches and treat issues of consistency is the prior information consistent dominance does the prior preference information imply that one outcome is preferred to another and potential optimality are there utility functions of the given form consistent with prior preference information under which a particular outcome is preference optimal in the additive cases a key relationship between dominance and potential optimality may be derived the paper concludes by presenting an example application to a well known nuclear siting study

differential characterizations of nonconical dominance in multiple objective decision making suppose a decision maker s preferences are represented by an unknown value function v prior information concerning v in the form of structural assumptions or revealed preferences may serve to restrict v to some class v of value functions an alternative y is dominated by an alternative z if v y v z for almost every v v in which case we write y v z continuous variable problems are considered in which alternatives are sought which are undominated under v for these problems we derive necessary and sufficient differential optimality conditions of the kuhn tucker type an example is presented in which v is a class of measurable value functions of the multiplicative form introduced by dyer and sarin since v may be a nonconical order these results are not subsumed by conventional vector optimization

multi criteria analysis with partial information about the weighting coefficients abstract in this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients we introduce a family of quasiorders that are easily interpretable and manageable which includes among others the natural quasiorder in r n and other well known preference structures in the literature the enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce

maximum entropy utility this paper presents a method to assign utility values when only partial information is available about the decision makers preferences we introduce the notion of a utility density function and a maximum entropy principle for utility assignment the maximum entropy utility solution embeds a large family of utility functions that includes the most commonly used functional forms we discuss the implications of maximum entropy utility on the preference behavior of the decision maker and present an application to competitive bidding situations where only previous decisions are observed by each party we also present minimum cross entropy utility which incorporates additional knowledge about the shape of the utility function into the maximum entropy formulation and work through several examples to illustrate the approach

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

effects of imprecise weighting in hierarchical preference programming abstract preference programming is a general term for multi criteria decision analytical approaches allowing incomplete preference information in the pairs method interval judgments are assigned to weight ratios between attributes to model imprecision in multi attribute value trees this paper studies the effects of a hierarchical model structure on the overall imprecision as the form of the hierarchy also affects the form of imprecision that can be assigned to the model the aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure the study provides simulation results about the ability of various weighting schemes to identify dominated alternatives which are discussed with respect to other issues related to the weighting process according to the results a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model but its cognitive advantages often cancel out this the results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria

pseudofractals and the box counting algorithm we show that for sets with the hausdorff besicovitch dimension equal to zero the box counting bc algorithm commonly used to calculate the renyi exponents dq can exhibit perfect scaling suggesting non zero dq the properties of these pathological sets pseudofractals are investigated numerical as well as analytical estimates for dq are obtained a simple indicator is given to distinguish pseudofractals and fractals in practical applications of the bc method histograms made of pseudofractal sets are shown to have pareto tails