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

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

multiple criteria decision making with interval stochastic variables a method based on interval stochastic dominance abstract a novel method based on interval stochastic dominance to solve the stochastic multiple criteria decision making smcdm problem with interval stochastic variables is proposed by analyzing the uncertainty of interval stochastic variables we propose the method of determining cumulative distribution function of interval stochastic variables then three types of interval stochastic dominance isd rules are investigated the definition of interval stochastic dominance degree isdd is presented and some interesting properties of isd and isdd are proved with respect to the smcdm problem with interval stochastic variables to begin with interval cumulative distribution functions of alternative criterion values are determined then the isd relations matrix associated with pairwise comparison of alternatives on each criterion is obtained based on isd rules and the isdd matrix on each criterion is calculated further based on promethee method the net flows of each alternative are derived so as to obtain the ranking result consequently examples are presented to illustrate the effectiveness of the proposed method

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

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

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

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

heuristics for selecting pair wise elicitation questions in multiple criteria choice problems abstract we present a set of heuristic approaches for selecting pair wise elicitation questions in an interactive process for multiple criteria choice problems our heuristics aim at minimizing the number of question answer iterations leading to the univocal recommendation of the decision maker s dm s most preferred alternative to identify the myopically best question at a given stage of interaction the proposed approaches ask the dm to compare a pair of alternatives that contributes to the greatest reduction of uncertainty with respect to the indication of the best alternative by all compatible value functions this uncertainty is measured either in terms of the number of potentially optimal alternatives or the entropy of first rank acceptabilities while assuming different a priori unknown probabilities of the dm s answers we discuss results from the extensive experiments on artificially generated and real world decision problems depending on the complexity of the considered problem instances we either perform a comprehensive analysis of the question answer interaction trees constructed by the heuristics or traverse their paths randomly by simulating a numerous set of decision policies we demonstrate that the greatest benefits from using our questioning procedures can be observed for problems involving numerous alternatives and few criteria and when the applied piece wise linear value functions consist of a small number of characteristic points the study allows us to identify two approaches that perform well in the average or the least advantageous elicitation scenario

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

quantum scars of classical closed orbits in phase space the way in which quantum eigenstates are influenced by the closed orbits of a chaotic classical system is analysed in phase space x q p through the spectral wigner function w x e this is a sum over wigner functions of eigenstates within a range of energy e in the classical limit w is concentrated on the energy surface and smoothly distributed over it closed orbits provide oscillatory corrections scars for which explicit semiclassical formulae are calculated each scar is a fringe pattern decorating the orbit as x moves off the energy surface the fringes form an airy pattern with spacing of order h as x moves off the closed orbit the fringes form a complex gaussian with spacing h

ordinal criteria in stochastic multicriteria acceptability analysis smaa abstract we suggest a method for providing descriptive information about the acceptability of decision alternatives in discrete co operative group decision making problems the new smaa o method is a variant of the stochastic multicriteria acceptability analysis smaa smaa o is designed for problems where criteria information for some or all criteria is ordinal that is experts or decision makers have ranked the alternatives according to each ordinal criterion considerable savings can be obtained if rank information for some or all the criteria is sufficient for making decisions without significant loss of quality the approach is particularly useful for group decision making when the group can agree on the use of an additive decision model but only partial preference information or none at all is available

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

algebre homologique dans la categorie mod r u g abstract letkbe an algebraically closed field of characteristic zero ga finite dimensional lie algebra overk u g the enveloping algebra ofg ra noetheriank algebra on whichgacts by derivations via a lie algebra morphism andr u g the differential operator rings generated byrandu g this paper is concerned with the homological algebra forr u g modules which areg locally finite especially with injective and projective modules minimal injective resolutions and cohomology soientkun corps algebriquement clos de caracteristique nulle gunek algebre de lie de dimension finie u g l algebre enveloppante deg runek algebre noetherienne sur laquellegopere par derivations via un morphisme d algebres de lie etr u g le produit croise derparu g ce papier traite de l algebre homologique dans la categorie desr u g modulesg localement finis plus particulierement des modules injectifs et projectifs des resolutions injectives minimales et de la cohomologie

reference point approach for multiple decision makers we consider multiple criteria decision making problems where a group of decision makers wants to find the most preferred solution from a discrete set of alternatives we develop a method that uses achievement functions for charting subsets of reference points that would support a certain alternative to be the most preferred one the resulting descriptive information is provided to the decision makers in the form of reference acceptability indices and central reference points for each decision alternative then the decision makers can compare this information with their own preferences we demonstrate the use of the method using a strategic multiple criteria decision model for an electricity retailer

a multiple criteria method for choosing among discrete alternatives abstract an interactive method is presented for solving a discrete alternative multiple criteria problem under certainty the method is based on the approach of zionts and wallenius a computer program embodying the method has been written and the results to date have been favorable extensions to the case in which some of the criteria are not readily quantifiable are also considered

classifying efficient alternatives in smaa using cross confidence factors abstract stochastic multicriteria acceptability analysis smaa is a family of methods for aiding multicriteria group decision making these methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one 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 data are sufficiently accurate for making an informed decision in some cases when the problem involves a large number of efficient alternatives the analysis may fail to discriminate between them this situation is revealed by low confidence factors in this paper we develop cross confidence factors which are based on computing confidence factors for alternatives using each other s central weight vectors the cross confidence factors can be used for classifying efficient alternatives into sets of similar and competing alternatives these sets are related to the concept of reference sets in data envelopment analysis dea but generalized for stochastic models forming these sets is useful when trying to identify one or more most preferred alternatives or suitable compromise alternatives the reference sets can also be used for evaluating whether criteria need to be measured more accurately and at which alternatives the measurements should be focused this may cause considerable savings in measurement costs we demonstrate the use of the cross confidence factors and reference sets using a real life example

an interactive evolutionary metaheuristic for multiobjective combinatorial optimization we propose an evolutionary metaheuristic for multiobjective combinatorial optimization problems that interacts with the decision maker dm to guide the search effort toward his or her preferred solutions solutions are presented to the dm whose pairwise comparisons are then used to estimate the desirability or fitness of newly generated solutions the evolutionary algorithm comprising the skeleton of the metaheuristic makes use of selection strategies specifically designed to address the multiobjective nature of the problem interactions with the dm are triggered by a probabilistic evaluation of estimated fitnesses while memory structures with indifference thresholds restrict the presentation of solutions resembling those that have already been rejected the algorithm has been tested on a number of random instances of the multiobjective knapsack problem mokp and the multiobjective spanning tree problem most simulation results indicate that the algorithm requires only a small number of comparisons to be made for satisfactory solutions to be found

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

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

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

stochastic multicriteria acceptability analysis using the data envelopment model abstract data envelopment analysis dea and stochastic multicriteria acceptability analysis smaa 2 are methods for evaluating alternatives based on multiple criteria while dea is mainly an ex post tool used for classifying alternatives into efficient and inefficient ones smaa 2 is an ex ante tool for supporting multiple criteria decision making both methods use a kind of value function where the importance of criteria is modeled using weights unlike many other methods neither dea nor smaa 2 requires decision makers weights as input instead these so called non parametric methods explore the weight space in order to identify weights favorable for each alternative this paper introduces the smaa d method which is a combination of dea and smaa 2 smaa d can be characterized as an extension of dea to handle uncertain or imprecise data to provide stochastic efficiency measures alternatively the combined method can be seen as a variant of smaa 2 with a dea type value function

quantum classical correspondence in polygonal billiards we show that wave functions in planar rational polygonal billiards all angles rationally related to ensuremath pi can be expanded in a basis of quasistationary and spatially regular states unlike the energy eigenstates these states are directly related to the classical invariant surfaces in the semiclassical limit this is illustrated for the barrier billiard we expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines

localization of wave patterns on classical periodic orbits in a square billiard the connection between wave functions and classical periodic trajectories in a square billiard is analytically constructed by using the representation of su 2 coherent states the analytical function form is modified to show that the wave patterns can be apparently localized on the classical periodic trajectories by superposing a few nearly degenerate eigenfunctions based on the analogy between the schrodinger and helmholtz equations the features of wave functions are experimentally studied from the transverse pattern formation in a laterally confined microcavity laser the experimental transverse pattern in a square shaped microcavity agrees very well with the constructed wave pattern concentrated along classical periodic orbits

robustness analysis in multi objective mathematical programming using monte carlo simulation abstract in most multi objective optimization problems we aim at selecting the most preferred among the generated pareto optimal solutions a subjective selection among objectively determined solutions in this paper we consider the robustness of the selected pareto optimal solution in relation to perturbations within weights of the objective functions for this task we design an integrated approach that can be used in multi objective discrete and continuous problems using a combination of monte carlo simulation and optimization in the proposed method we introduce measures of robustness for pareto optimal solutions in this way we can compare them according to their robustness introducing one more characteristic for the pareto optimal solution quality in addition especially in multi objective discrete problems we can detect the most robust pareto optimal solution among neighboring ones a computational experiment is designed in order to illustrate the method and its advantages it is noteworthy that the augmented weighted tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems due to the existence of unsupported pareto optimal solutions

multivariate gaussian criteria in smaa abstract we consider stochastic multicriteria decision making problems with multiple decision makers in such problems the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions in many real life problems the uncertainties of criteria measurements may be dependent however it is often difficult to quantify these dependencies also most of the existing methods are unable to handle such dependency information in this paper we develop a method for handling dependent uncertainties in stochastic multicriteria group decision making problems we measure the criteria their uncertainties and dependencies using a stochastic simulation model the model is based on decision variables and stochastic parameters with given distributions based on the simulation results we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies we then use the smaa 2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions we demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated european electricity market

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

stochastic multiobjective acceptability analysis for the choquet integral preference model and the scale construction problem abstract the choquet integral preference model is adopted in multiple criteria decision aiding mcda to deal with interactions between criteria while the stochastic multiobjective acceptability analysis smaa is an mcda methodology considered to take into account uncertainty or imprecision on the considered data and preference parameters in this paper we propose to combine the choquet integral preference model with the smaa methodology in order to get robust recommendations taking into account all parameters compatible with the preference information provided by the decision maker dm in case the criteria are on a common scale one has to elicit only a set of non additive weights technically a capacity compatible with the dm s preference information instead if the criteria are on different scales besides the capacity one has to elicit also a common scale compatible with the preferences given by the dm our approach permits to explore the whole space of capacities and common scales compatible with the dm s preference information

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

correspondence between some wave patterns and lissajous figures we study the connections between some specially entangled stationary states and the classical periodic trajectories of two non interacting oscillators the latter are well known lissajous figures which are shown to run precisely over the apogees of their corresponding probability distributions in the above states we propose in this work a very simple criterion enabling us to obtain the best agreement between the quantum and the classical images finally our results are successfully applied to the interpretation of some experimentally observed wave patterns

sigma mu efficiency analysis a methodology for evaluating units through composite indicators abstract we propose a methodology to employ composite indicators for performance analysis of units of interest using and extending the family of stochastic multiattribute acceptability analysis we start evaluating each unit by means of weighted sums of their elementary indicators in the whole set of admissible weights for each unit we compute the mean and the standard deviation of its evaluations clearly the former has to be maximized while the latter has to be minimized as it denotes instability in the evaluations with respect to the variability of weights we consider a unit to be pareto koopmans efficient with respect to and if there is no convex combination of and of the rest of the units with a value of that is not smaller and a value of that is not greater with at least one strict inequality the set of all pareto koopmans efficient units constitutes the first pareto koopmans frontier in the spirit of context dependent data envelopment analysis we assign each unit to one of the sequence of pareto koopmans frontiers we measure the local efficiency of each unit with respect to each frontier but also its global efficiency taking into account all frontiers in the plane thus enhancing the explicative power of the proposed approach to illustrate its potential we present a case study of world happiness based on the data of the homonymous report that is annually produced by the united nations sustainable development solutions network

a method for stochastic multiple attribute decision making based on concepts of ideal and anti ideal points this paper proposes a novel method for solving the stochastic multiple attribute decision making smadm problem where consequences of alternatives with respect to attributes are represented by random variables with cumulative distribution functions first the concepts of ideal and anti ideal cumulative distribution functions are introduced and the related theoretical analysis is given next according to the concept of classical topsis the ideal and anti ideal points of the smadm problem are determined which are in the form of cumulative distribution function vectors then the closeness coefficient of each alternative is obtained by calculating the distances to the ideal and anti ideal points simultaneously based on the obtained closeness coefficients a ranking of alternatives is determined finally two numerical examples are given to illustrate the use of the proposed method

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

robust multi criteria ranking with additive value models and holistic pair wise preference statements we consider a problem of ranking alternatives based on their deterministic performance evaluations on multiple criteria we apply additive value theory and assume the decision maker s dm preferences to be representable with general additive monotone value functions the dm provides indirect preference information in form of pair wise comparisons of reference alternatives and we use this to derive the set of compatible value functions then this set is analyzed to describe 1 the possible and necessary preference relations 2 probabilities of the possible relations 3 ranges of ranks the alternatives may obtain and 4 the distributions of these ranks our work combines previous results from robust ordinal regression extreme ranking analysis and stochastic multicriteria acceptability analysis under a unified decision support framework we show how the four different results complement each other discuss extensions of the main proposal and demonstrate practical use of the approach by considering a problem of ranking 20 european countries in terms of 4 criteria reflecting the quality of their universities

multicriteria estimation of probabilities on basis of expert non numeric non exact and non complete knowledge abstract a new method of alternatives probabilities estimation under deficiency of expert numeric information obtained from different sources is proposed the method is based on the bayesian model of uncertainty randomization additional non numeric non exact and non complete expert knowledge nnn knowledge nnn information is used for final estimation of the alternatives probabilities an illustrative example demonstrates the proposed method application to forecasting of oil shares price with the use of nnn information obtained from different experts investment firms

an interactive weight space reduction procedure for nonlinear multiple objective mathematical programming to make a decision that is defined by multiple conflicting objectives it is necessary to know the relative importance of the different objectives in this paper we present an interactive method and the underlying theory for solving multiple objective mathematical programming problems defined by a convex feasible region and concave continuously differentiable objective functions the relative importance of the different objectives for a decision maker is elicited by using binary comparisons of objective function vectors the method is cognitively easy to use and in test problems has rapidly converged to an optimal solution

a method for stochastic multiple criteria decision making based on dominance degrees this paper proposes a method for solving the stochastic multiple criteria decision making smcdm problem where consequences of alternatives with respect to criteria are represented by random variables with probability distributions firstly definitions and related analysis of dominance degree of one probability distribution over another are given then by calculating the dominance degrees the dominance degree matrix of alternative pairwise comparisons with respect to each criterion is built further using promethee ii method an overall dominance degree matrix of alternative pairwise comparisons is constructed and a net flow of each alternative is calculated based on the obtained net flows a ranking of alternatives is determined finally numerical examples for the three cases are given to illustrate the use of the proposed method

an interactive approach for placing alternatives in preference classes abstract in this paper we consider the multiple criteria decision making problem of partitioning alternatives into preference classes we develop an interactive procedure based on the assumption that the decision maker dm has a linear utility function the approach requires the dm to place an alternative in a preference class from time to time based on the preference information derived from the dm s placement as well as from dominance and linearity we try to place other alternatives we present results on the performance of the algorithm applied to four different sets of alternatives

dual cone approach to convex cone dominance in multiple criteria decision making abstract in a paper published in management science in 1984 korhonen wallenius and zionts presented the idea and method based on convex cone dominance in the discrete multiple criteria decision making framework in our current paper we revisit the old idea from a new standpoint and provide the mathematical theory leading to a dual cone based approach to solving such problems our paper makes the old results computationally more tractable the results provided in the present paper also help extend the theory

pseudo criteria versus linear utility function in stochastic multi criteria acceptability analysis abstract stochastic multi criteria acceptability analysis smaa is a multi criteria decision support method for multiple decision makers dms in discrete problems smaa does not require explicit or implicit preference information from the dms instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one partial preference information can be represented in the weight space analysis through weight distributions in this paper we compare two variants of the smaa method using randomly generated test problems with 2 12 criteria and 4 12 alternatives in the original smaa a utility or value function models the dms preference structure and the inaccuracy or uncertainty of the criteria is represented by probability distributions in smaa 3 electre iii type pseudo criteria are used instead both methods compute for each alternative an acceptability index measuring the variety of different valuations that supports this alternative and a central weight vector representing the typical valuations resulting in this decision we seek answers to three questions 1 how similar are the results provided by the decision models 2 what kind of systematic differences exists between the models and 3 how could one select indifference and preference thresholds of the pseudo criteria model to match a utility model with given probability distributions

eigenmodes and symmetry selection mechanisms in circular large aperture vertical cavity surface emitting lasers the characteristics of the spatial eigenmodes of vertical cavity surface emitting lasers with a large circular aperture are considered close to the lasing threshold experiments yield patterns based on rotational symmetry flowerlike patterns or on cartesian symmetry stripelike patterns for very close operating conditions the former are compatible with the boundary conditions whereas the latter are expected in infinite devices theoretically the problem is considered in the framework of an eigenmode analysis of a linear partial differential equation for the optical field valid at threshold this formulation allows for a simple implementation of asymmetries due to the reflection properties of bragg mirrors as well as of transverse variations of gain and refractive index due to the device structure or due to imperfections in the growth process a sharp transition between flowerlike modes and stripelike modes is shown to occur if the device aperture is increased

smaa 2 stochastic multicriteria acceptability analysis for group decision making stochastic multicriteria acceptability analysis smaa is a multicriteria decision support method for multiple decision makers in discrete problems in smaa the decision makers need not express their preferences explicitly or implicitly instead the method is based on exploring the weight space in order to describe the valuations that would make each alternative the preferred one inaccurate or uncertain criteria values are represented by probability distributions from which the method computes confidence factors describing the reliability of the analysis in this paper we introduce the smaa 2 method which extends the original smaa by considering all ranks in the analysis in situations where the elitistic smaa may assess large acceptability only for extreme alternatives without sufficient majority support the more holistic smaa 2 analysis can be used to identify good compromise candidates the results are presented graphically we consider also situations where partial preference information is available we demonstrate the new method using a real life decision problem

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

a method for stochastic multiple criteria decision making based on pairwise comparisons of alternatives with random evaluations this paper proposes a method for solving stochastic multiple criteria decision making mcdm problems where evaluations of alternatives on considered criteria are random variables with known probability density functions or probability mass functions probabilities on all possible results of pairwise comparisons of alternatives are first calculated using probability theory then all possible results of pairwise comparisons are classified into superior indifferent and inferior ones using a predefined identification rule consequently the probabilities on all possible results of pairwise comparisons are partitioned into superior indifferent and inferior probabilities furthermore based on the derived probabilities an algorithm is developed to rank the alternatives finally a numerical example is used to illustrate the feasibility and validity of the proposed method

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

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

integral analysis method iam this paper presents the theoretical foundations of the new integral analysis method iam and its application to a facility location problem this methodology integrates the cardinal and ordinal criteria of combinatorial stochastic optimization problems in four stages definition of the problem cardinal analysis ordinal analysis and integration analysis the method uses the concepts of stochastic multicriteria acceptability analysis smaa monte carlo simulation optimization techniques and elements of probability the proposed method iam was used to determine optimal locations for the retail stores of a colombian coffee marketing company

on the h finite cohomology abstract let k be a field and h a hopf algebra over k with a bijective antipode suppose that h acts on an associative left noetherian k algebra r such that r is an h module algebra we consider the categories of all h modules the subcategory of those which are h locally finite and the subcategories of each which are also r modules in a compatible way these categories are all abelian with enough injectives and we derive spectral sequences relating ext in them now let h denote taking h invariants and set s r h we define a functor l s r from mod s to mod r h that has good behavior with respect to injective objects we also show that the functor h carries some injectives to injectives when r is commutative h is cocommutative and k is projective in the category of finite dimensional h modules we obtain more precise results comparing for example the picard groups pic r r h and pic s

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

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

smoothed wave functions of chaotic quantum systems abstract it is shown that wave functions of quantum systems as 0 have an extra density near unstable periodic trajectories of the classical problem the averaged wave function square is represented as the sum over a finite number of periodic trajectories the contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory the results are compared with the numerical calculations of the wave functions for the stadium billiard

group decisions with multiple criteria we consider a decision problem where a group of individuals evaluates multiattribute alternatives we explore the minimal required agreements that are sufficient to specify the group utility function a surprising result is that under some conditions a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multiattribute group utility the bilateral agreement between a pair of individuals could be on the weight of an attribute on an attribute evaluation function or on willingness to pay we focus on the case in which each individual s utility function is additive we show that the group utility can be represented as the weighted sum of group attribute weights and more remarkably of attribute evaluation functions these group attribute evaluation functions are in turn weighted sums of individual attribute evaluation functions

smaa stochastic multiobjective acceptability analysis stochastic multiobjective acceptability analysis smaa is a multicriteria decision support technique for multiple decision makers based on exploring the weight space inaccurate or uncertain input data can be represented as probability distributions in smaa the decision makers need not express their preferences explicitly or implicitly instead the technique analyses what kind of valuations would make each alternative the preferred one the method produces for each alternative an acceptability index measuring the variety of different valuations that support that alternative a central weight vector representing the typical valuations resulting in that decision and a confidence factor measuring whether the input data is accurate enough for making an informed decision

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

use of convex cones in interactive multiple objective decision making one approach for solving decision problems involving multiple objectives is interactive optimization methods based on this approach assess the decision maker s preference structure interactively typically based on pairwise comparisons and tradeoffs and guide the search process toward identifying improved solutions a desirable feature of such approaches that is based on minimizing the preference information requirements is fast convergence toward this end the use of convex cones as a preference structure representation has been proposed in the literature in this work new theory is developed that aids in further reducing preference information requirements and improving convergence new cones termed p cones are developed the efficiencies of solution alternatives are evaluated with respect to the p cones and these are termed p cone efficiencies acceleration and early termination procedures that are based on these efficiencies are proposed the procedures are presented within a solution framework for solving multiple objective linear programming molp problems along with computational results

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

the analytic hierarchy process with stochastic judgements the analytic hierarchy process ahp is a widely used method for multicriteria decision support based on the hierarchical decomposition of objectives evaluation of preferences through pairwise comparisons and a subsequent aggregation into global evaluations the current paper integrates the ahp with stochastic multicriteria acceptability analysis smaa an inverse preference method to allow the pairwise comparisons to be uncertain a simulation experiment is used to assess how the consistency of judgements and the ability of the smaa ahp model to discern the best alternative deteriorates as uncertainty increases across a range of simulated problems results indicate that according to conventional benchmarks judgements are likely to remain consistent unless uncertainty is severe but that the presence of uncertainty in almost any degree is sufficient to make the choice of best alternative unclear

a lexicographical compromise method for multiple criteria group decision problems with imprecise information abstract this paper addresses multiple criteria group decision making problems where each group member offers imprecise information on his her preferences about the criteria in particular we study the inclusion of this partial information in the decision problem when the individuals preferences do not provide a vector of common criteria weights and a compromise preference vector of weights has to be determined as part of the decision process in order to evaluate a finite set of alternatives we present a method where the compromise is defined by the lexicographical minimization of the maximum disagreement between the value assigned to the alternatives by the group members and the evaluation induced by the compromise weights

quantum chaos in a ripple billiard we study the quantum chaos of a ripple billiard that has sinusoidal walls we show that this type of ripple billiard has a hamiltonian matrix that can be found exactly in terms of elementary functions this feature greatly improves computation efficiency a complete set of eigenstates from the ground state up to the 10 000th level can be calculated simultaneously nearest neighbor spacing of energy levels of a chaotic ripple billiard shows a brody distribution with a confidence level of 99 by chi 2 test instead of the gaussian orthogonal ensemble prediction for high energy levels we observe scars and interesting patterns that have no resemblance to classical periodic orbits momentum localization of scarred eigenstates is also observed we compare the scar associated localization with quantum dynamical anderson localization by drawing the wave function distribution on basis state coefficients