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

mappac as a compromise between outranking methods and maut abstract this article shows that the bicriteria preference indices of the mappac method may be classified in two categories those of a compensatory type in cases of discordant evaluations methodologically in line with the maut approach and those which underline partial dominance relations in cases of concordant evaluations in analogy with noncompensatory outranking methods and with the electre methods in particular mappac may therefore be considered a mixed or intermediate method a sort of compromise between the approaches mentioned above it will also be shown that the aggregated index of mappac is a function not only of the weight of the criteria and of the entity of the difference in evaluation but also all other conditions remaining unvaried of the number of criteria according to which one action is preferred or indifferent with respect to another it is possible to note a number of similarities and differences between the indices of this method and the concordance indices of the electre methods

the greek banking system reanalysis of performance abstract zopounidis et al used an ordinal regression analysis to assess an additive utility model and to obtain final ranking of a representative sample of commercial greek banks c zopounidis d k despotis e stavropoulou multiattribute evaluation of greek banking performance applied stochastic models and data analysis 11 1995 97 107 in this paper we reanalyze their data by means of a new multivariate analysis method called co plot a two dimensional graphic display technique designed to analyze observations e g 16 banks and attributes e g 7 attributes simultaneously the method produces three results 1 similarity among the banks by the composite of all attributes involved five clusters are obtained 2 the structure of correlations among the attributes three clusters are obtained and 3 the mutual relationships between the banks and the attributes the banks are mapped into a partial order according to their increased performance to obtain their rating the final ranking obtained by the co plot method differed from that obtained by zopounidis et al

comment on adaptive feedback control algorithm we point out a problem in the parametric estimation method based on the adaptive feedback algorithm proposed by d huang phys rev e 73 066204 2006 both illustratively and analytically furthermore under some hypotheses we prove that it is not the so called chaotic dynamical characteristic but the linear independence between the right hand functions and the estimated parameters of the intrinsic system in its attractor that counts in the availability of this algorithm in estimating the unknown parameters

asymptotic limits and zeros of chromatic polynomials and ground state entropy of potts antiferromagnets we study the asymptotic limiting function w g q lim n to infty p g q 1 n where p g q is the chromatic polynomial for a graph g with n vertices we first discuss a subtlety in the definition of w g q resulting from the fact that at certain special points q s the following limits do not commute lim n to infty lim q to q s p g q 1 n ne lim q to q s lim n to infty p g q 1 n we then present exact calculations of w g q and determine the corresponding analytic structure in the complex q plane for a number of families of graphs g including circuits wheels biwheels bipyramids and cyclic and twisted ladders we study the zeros of the corresponding chromatic polynomials and prove a theorem that for certain families of graphs all but a finite number of the zeros lie exactly on a unit circle whose position depends on the family using the connection of p g q with the zero temperature potts antiferromagnet we derive a theorem concerning the maximal finite real point of non analyticity in w g q denoted q c and apply this theorem to deduce that q c sq 3 and q c hc 3 sqrt 5 2 for the square and honeycomb lattices finally numerical calculations of w hc q and w sq q are presented and compared with series expansions and bounds

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

transfer matrices for the partition function of the potts model on cyclic and mobius lattice strips abstract we present a method for calculating transfer matrices for the q state potts model partition functions z g q v for arbitrary q and temperature variable v on cyclic and mobius strip graphs g of the square sq triangular tri and honeycomb hc lattices of width l y vertices and of arbitrarily great length l x vertices for the cyclic case we express the partition function as z l y l x q v d 0 l y c d tr t z l y d m where denotes lattice type c d are specified polynomials of degree d in q t z l y d is the transfer matrix in the degree d subspace and m l x l x 2 for sq tri hc respectively an analogous formula is given for mobius strips we exhibit a method for calculating t z l y d for arbitrary l y explicit results for arbitrary l y are given for t z l y d with d l y and l y 1 in particular we find very simple formulas the determinant det t z l y d and trace tr t z l y corresponding results are given for the equivalent tutte polynomials for these lattice strips and illustrative examples are included we also present formulas for self dual cyclic strips of the square lattice

cardinal ranking of alternative actions extension of the promethee method abstract the method presented in this paper is an extension of the promethee one of the most known multicriteria outranking methods this extension consists in a more detailed investigation of the differences existing among the performances of the actions examined achieved through the notion of ideal and anti ideal alternative hence the state of strict preference relating various pairs of actions can be differentiated with reference to the extreme performances attained by the alternatives under consideration the more accurate description of the reality leads to a relatively more reliable ranking of the available solutions and allows the exploitation of the results for the construction of a cardinal scale assigning to each action a numerical value between 0 and 1 the quantitative differentiation of the alternatives thus achieved gives another dimension of information which is extremely useful for the decision making process a comparative study of the two methods shows the greater sensitivity of exprom and its ability to reflect in the quantitative results any probable deviation in the initial data of a problem this sensitivity is accompanied with a greater stability due to the smoothing of the discontinuities characterizing most preference functions in promethee

sensitivity analysis of efficiency scores how to bootstrap in nonparametric frontier models efficiency scores of production units are generally measured relative to an estimated pro duction frontier nonparametric estimators dea fdh are based on a finite sample of observed production units the bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier the main point in order to validate the bootstrap is to define a reasonable data generating process in this complex framework and to propose a reasonable estimator of it this paper provides a general methodology of bootstrapping in nonparametric frontier models some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants

transfer matrices for the partition function of the potts model on lattice strips with toroidal and klein bottle boundary conditions abstract we present a method for calculating transfer matrices for the q state potts model partition functions z g q v for arbitrary q and temperature variable v on strip graphs g of the square sq triangular tri and honeycomb hc lattices of width l y vertices and of arbitrarily great length l x vertices subject to toroidal and klein bottle boundary conditions for the toroidal case we express the partition function as z l y l x q v d 0 l y j b j d z l y d j m where denotes lattice type b j d are specified polynomials of degree d in q z l y d j are eigenvalues of the transfer matrix t z l y d in the degree d subspace and m l x l x 2 for sq tri hc respectively an analogous formula is given for klein bottle strips we exhibit a method for calculating t z l y d for arbitrary l y in particular we find some very simple formulas for the determinant det t z l y d and trace tr t z l y illustrative examples of our general results are given including new calculations of transfer matrices for potts model partition functions on strips of the square triangular and honeycomb lattices with toroidal or klein bottle boundary conditions

extensions of the prudence principle to exploit a valued outranking relation abstract in many outranking methods the alternatives are first compared pairwise to build a valued outranking relation which is then exploited to derive a recommendation for the decision maker this paper proposes extensions of arrow and raynaud s prudence principle to exploit a valued outranking relation even in cases where the outranking values have an ordinal interpretation the idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons we present a family of exploitation models providing three types of solutions depending on the decision maker s request a linear order a weak order or a partial preorder an algorithm is provided which solves the exploitation models relations between these models and some of their properties are also discussed

novel types of sensitivity analysis for additive mcdm methods three novel types of sensitivity analysis are presented they determine the following 1 the sensitivity of a ranking to specific changes in the evaluations of all alternatives on certain criteria 2 the influence of specific changes in certain criterion scores of an alternative 3 the minimum modification of the weights required to make an alternative ranked first the use of these instruments is demonstrated by the results of a simulation experiment results show that the first and second type of sensitivity analysis enable to apply multiple criteria decision making mcdm methods in dynamic circumstances the third type of sensitivity analysis is demonstrated to be a tool to analyze the total weight space

a promethee based classification method using concordance and discordance relations and its application to bankruptcy prediction outranking relation theory has been widely used to study pattern classification here we propose a classification method with concepts from the flows used in promethee methods which are extensively applied in multi criteria decision aids promethee uses a flow generated on the basis of a preference index and measured by various preference functions for each criterion to represent the preference intensity for one pattern over another pattern however only criteria that are concordant with the preference contribute to a preference index in the present study the opinions from discordant criteria are also taken into account the proposed method newly defines an overall preference index using both concordance and discordance relations for ordinal sorting problems the final classification decision for a new pattern depends on its net flow the criteria weights are determined using a genetic algorithm based approach empirical results obtained for a real world problem regarding bankruptcy prediction demonstrate that the proposed method performs well compared to other well known classification methods

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

flow polynomials and their asymptotic limits for lattice strip graphs we present exact calculations of flow polynomials f g q for lattice strips of various fixed widths l y 4 and arbitrarily great lengths l x with several different boundary conditions square honeycomb and triangular lattice strips are considered we introduce the notion of flows per face fl in the infinite length limit we study the zeros of f g q in the complex q plane and determine exactly the asymptotic accumulation sets of these zeros in the infinite length limit for the various families of strips the function fl is nonanalytic on this locus the loci are found to be noncompact for many strip graphs with periodic or twisted periodic longitudinal boundary conditions and compact for strips with free longitudinal boundary conditions we also find the interesting feature that aside from the trivial case l y 1 the maximal point q cf where crosses the real axis is universal on cyclic and mobius strips of the square lattice for all widths for which we have calculated it and is equal to the asymptotic value q cf 3 for the infinite square lattice

a procedure for ranking efficient units in data envelopment analysis data envelopment analysis dea evaluates the relative efficiency of decision making units dmus but does not allow for a ranking of the efficient units themselves a modified version of dea based upon comparison of efficient dmus relative to a reference technology spanned by all other units is developed the procedure provides a framework for ranking efficient units and facilitates comparison with rankings based on parametric methods

rim reference ideal method in multicriteria decision making abstract multiple criteria decision making methods provide a useful tool to support decision making to date different methods have been developed using different approaches in particular the conception used by the topsis and vikor methods identifies the best alternative based on the positive and the negative ideal solutions in this paper a new method based on the concept of ideal solution is presented as a possible variant of the aforementioned however in our case these values can vary between the maximum value and the minimum value this does not occur in the vikor and topsis methods in which these values are the extreme values moreover our method is characterized to be independent of the type of data moreover rim does not present rank reversal an aspect that is not present in other multiple criteria decision making methods

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

t 0 partition functions for potts antiferromagnets on square lattice strips with twisted periodic boundary conditions we present exact calculations of the zero temperature partition function for the q state potts antiferromagnet or equivalently the chromatic polynomial for two families of arbitrarily long strip graphs of the square lattice with periodic boundary conditions in the transverse direction and i periodic and ii twisted periodic boundary conditions in the longitudinal direction so that the strip graphs are embedded on i a torus and ii a klein bottle in the limit of infinite length we calculate the exponent of the entropy w q show it to be the same for i and ii and determine its analytic structure

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

synchronization based estimation of all parameters of chaotic systems from time series by a simple combination of adaptive scheme and linear feedback with the updated feedback strength for a large class of chaotic systems it is proved rigorously by using the invariance principle of differential equations that all unknown model parameters can be estimated dynamically this approach supplies a systematic and analytical procedure for estimating parameters from time series and it is simple to implement in practice in addition this method is quite robust against the effect of noise and able to respond rapidly to changes in operating parameters of the experimental system lorenz and r ossler hyperchaos systems are used to illustrate the validity of this technique

a multiple criteria ranking procedure based on distance between partial preorders abstract in this paper a multiple criteria ranking procedure based on distance between partial preorders is proposed this method consists of two phases in the first phase the decision maker is asked to rank alternatives with a preorder complete or partial for each criterion and provide complete or partial linear information about the relative importance weights of the criteria in the second phase we introduce a distance procedure to aggregate the above individual rankings into a global ranking a partial preorder an algorithm for the aggregation procedure is proposed followed by a numerical illustration

chromatic polynomials for lattice strips with cyclic boundary conditions abstract the zero temperature q state potts model partition function for a lattice strip of fixed width l y and arbitrary length l x has the form p g q j 1 n g c g j g j l x and is equivalent to the chromatic polynomial for this graph we present exact zero temperature partition functions for strips of several lattices with fbc y pbc x i e cyclic boundary conditions in particular the chromatic polynomial of a family of generalized dodecahedra graphs is calculated the coefficient c g j of degree d in q is c d u 2d q 2 where u n x is the chebyshev polynomial of the second kind we also present the chromatic polynomial for the strip of the square lattice with pbc y pbc x i e toroidal boundary conditions and width l y 4 with the property that each set of four vertical vertices forms a tetrahedron a number of interesting and novel features of the continuous accumulation set of the chromatic zeros b are found

the use of domains in multicriteria decision making abstract this paper describes a domain criterion for a multicriteria problem given decision maker it then outlines possibilities for aggregating individual preference structures in the case of multiple decision makers

project prioritization under policy restrictions a combination of mcda with 0 1 programming abstract multiple criteria decision aid methods are increasingly used in financial decision making in order to capture the multifaceted character of modern enterprises activated in a complex and versatile market environment this paper presents a multiple criteria approach for the selection of firms applying for financial support from public funds besides the budget constraint the specific decision situation imposes the consideration of additional policy constraints that prevent from directly exploiting rankings provided by a multiple criteria method in such a case the problem solution is to find a set of alternatives satisfying the constraints and at the same time maximizing a measure of global performance the proposed procedure relies on the promethee v method which belongs to the well known promethee family of multiple criteria outranking methods and is combined with an integer programming formulation capable to effectively deal with the problem s combinatorial character this method is modified in order to avoid any bias in the selection of the optimal set that may arrive because of the apparent contradiction between the rate of resources consumption and the coefficients of the alternatives in the additive objective function

state estimation for coupled uncertain stochastic networks with missing measurements and time varying delays the discrete time case this paper is concerned with the problem of state estimation for a class of discrete time coupled uncertain stochastic complex networks with missing measurements and time varying delay the parameter uncertainties are assumed to be norm bounded and enter into both the network state and the network output the stochastic brownian motions affect not only the coupling term of the network but also the overall network dynamics the nonlinear terms that satisfy the usual lipschitz conditions exist in both the state and measurement equations through available output measurements described by a binary switching sequence that obeys a conditional probability distribution we aim to design a state estimator to estimate the network states such that for all admissible parameter uncertainties and time varying delays the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square by employing the lyapunov functional method combined with the stochastic analysis approach several delay dependent criteria are established that ensure the existence of the desired estimator gains and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities lmis two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

co plot a graphic display method for geometrical representations of mcdm abstract a relatively new multivariate analysis method called co plot is shown to be highly efficient for the geometrical representation of multicriteria decision problems co plot a two dimensional graphic display technique is designed for multicriteria analysis its main feature is the simultaneous analysis of actions e g observations and criteria e g variables in a simple way the method produces three results 1 similarity among actions by the composite of all criteria involved 2 the structure of correlations among the criteria and 3 the mutual relationships between the actions and the criteria the method is demonstrated on two numerical applications previously analyzed by mareschal and brans b mareschal j p brans european journal of operational research 34 1988 69 77 using the promethee methods and principal component analysis

simple adaptive feedback controller for identical chaos synchronization based on the invariance principle of differential equations a simple adaptive feedback scheme is proposed to strictly synchronize almost all chaotic systems unlike the usual linear feedback the variable feedback strength is automatically adapted to completely synchronize two almost arbitrary identical chaotic systems so this scheme is analytical and simple to implement in practice moreover it is quite robust against the effect of noise the famous lorenz and rossler hyperchaos systems are used as illustrative examples

ground state degeneracy of potts antiferromagnets homeomorphic classes with noncompact w boundaries abstract we present exact calculations of the zero temperature partition function z g q t 0 and ground state degeneracy w g q for the q state potts antiferromagnet on a number of families of graphs g for which generalizing q from z to c the boundary b of regions of analyticity of w in the complex q plane is noncompact passing through z 1 q 0 for these types of graphs since the reduced function w red q 1 w is nonanalytic at z 0 there is no large q taylor series expansion of w red the study of these graphs thus gives insight into the conditions for the validity of the large q expansions it is shown how such families of graphs can be generated from known families by homeomorphic expansion

chromatic polynomials and representations of the symmetric group abstract the chromatic polynomials considered in this paper are associated with graphs constructed in the following way take n copies of a complete graph k b and for i 1 2 n join each vertex in the ith copy to the same vertex in the i 1 th copy taking n 1 1 by convention previous calculations for b 2 and b 3 suggest that the chromatic polynomial contains terms that occur in levels in the present paper the levels are explained by using a version of the sieve principle and it is shown that the terms at level l correspond to the irreducible representations of the symmetric group sym l in the case of the two linear representations the terms can be calculated explicitly by methods based on the theory of distance regular graphs for the nonlinear representations the calculations are more complicated an illustration is given in section 10 where the complete chromatic polynomial for the case b 4 is obtained

a generalized stochastic goal programming model in this paper we show how one can get stochastic solutions of stochastic multi objective problem smop using goal programming models in literature it is well known that one can reduce a smop to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems the first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique in the second part we try to go more in depth on notion of smop solution and we suppose that it has to be a random variable we will present stochastic goal programming model for finding stochastic solutions of smop our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs which depend on the number of experiments to be run needed to be solved on the other hand since in our approach we suppose that a smop solution is a random variable according to the central limit theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a smop solution the developed model will be illustrated through numerical examples

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

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

multicriterion decision making in river basin planning and development five multicriterion decision making mcdm methods namely electre 2 promethee 2 analytic hierarchy process ahp compromise programming cp and exprom 2 are employed to select the best reservoir configuration for the case study of chaliyar river basin kerala india spearman rank correlation coefficient is used to assess the correlation between the ranks obtained by the above mcdm methods although these methods follow different approaches the analysis has shown that the same preference strategy is reached by all the methods comparative evaluation of mcdm methods revealed that compromise programming is best suited for the present case study

objective and subjective rationality in a multiple prior model a decision maker dm is characterized by two binary relations the first reflects choices that are rational in an objective sense the dm can convince others that she is right in making them the second relation models choices that are rational in a subjective sense the dm cannot be convinced that she is wrong in making them in the context of decision under uncertainty we propose axioms that the two notions of rationality might satisfy these axioms allow a joint representation by a single set of prior probabilities and a single utility index it is objectively rational to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set it is subjectively rational to choose f rather than g if and only if the minimal expected utility of f with respect to all priors in the set is at least as high as that of g in other words the objective and subjective rationality relations admit respectively a representation a la bewley 2002 and a la gilboa and schmeidler 1989 our results thus provide a bridge between these two classic models as well as a novel foundation for the latter

multicriteria analysis survey and new directions abstract before the advent of multicriteria analysis decision problems often took the form of the optimization of an objective function or a utility function this approach has the advantage of resulting in well defined mathematical problems but is not always representative of reality in fact the comparison of several possible decisions is rarely made according to a single point of view and the preferences on a point of view are in many cases only modelled with difficulty by a function the aim of this paper is to survey the different directions in which multicriteria analysis has developed multiattribute utility theory outranking relations interactive methods the methodology recently proposed by b roy is also presented

exact chromatic polynomials for toroidal chains of complete graphs abstract we present exact calculations of the partition function of the zero temperature potts antiferromagnet equivalently the chromatic polynomial for graphs of arbitrarily great length composed of repeated complete subgraphs kb with b 5 6 which have periodic or twisted periodic boundary condition in the longitudinal direction in the lx limit the continuous accumulation set of the chromatic zeros b is determined we give some results for arbitrary b including the extrema of the eigenvalues with coefficients of degree b 1 and the explicit forms of some classes of eigenvalues we prove that the maximal point where b crosses the real axis qc satisfies the inequality qc b for 2 b the minimum value of q at which b crosses the real q axis is q 0 and we make a conjecture concerning the structure of the chromatic polynomial for klein bottle strips

approximating promethee ii s net flow scores by piecewise linear value functions abstract p romethee ii is a prominent method for multi criteria decision aid mcda that builds a complete ranking on a set of potential actions by assigning each of them a so called net flow score however to calculate these scores each pair of actions has to be compared causing the computational load to increase quadratically with the number of actions eventually leading to prohibitive execution times for large decision problems for some problems however a trade off between the ranking s accuracy and the required evaluation time may be acceptable therefore we propose a piecewise linear model that approximates p romethee ii s net flow scores and reduces the computational complexity with respect to the number of actions from quadratic to linear at the cost of some wrongly ranked actions simulations on artificial problem instances allow us to quantify this time quality trade off and to provide probabilistic bounds on the problem size above which our model satisfyingly approximates p romethee ii s rankings they show for instance that for decision problems of 10 000 actions evaluated on 7 criteria the pearson correlation coefficient between the original scores and our approximation is of at least 0 97 when put in balance with computation times that are more than 7000 times faster than for the p romethee ii model the proposed approximation model represents an interesting alternative for large problem instances

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

adaptive feedback control algorithm this paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers phys rev lett 93 214101 2004 phys rev e 71 037203 2005 69 067201 2004 where an adaptive feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems this note proves in detail the strictness of this algorithm from the viewpoint of mathematics and gives some interesting remarks for its potential applications to chaos control a synchronization in addition a significant comment on synchronization based parameter estimation is given which shows some techniques proposed in literature less strict and ineffective in some cases

fuzzy outranking for environmental assessment case study iron and steel making industry recent years have seen a world wide change in the environmental policy towards integrated pollution prevention taking into account all environmental media consequently the environmental assessment of production techniques has to consider multiple criteria which cannot be aggregated to one single index the concepts of multi criteria decision making mcdm seem a suitable means in order to implement life cycle assessment lca into integrated decision processes the outranking methods as a special subgroup of mcdm methods are particularly suitable for integral decision making through the notion of weak preference and incomparability which better represent the real decision situation as demonstrated in this paper especially the outranking method promethee brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences scores and weights

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems