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

preference inference with general additive value models and holistic pair wise statements additive multi attribute value models and additive utility models with discrete outcome sets are widely applied in both descriptive and normative decision analysis their non parametric application allows preference inference by analyzing sets of general additive value functions compatible with the observed or elicited holistic pair wise preference statements in this paper we provide necessary and sufficient conditions for the preference inference based on a single preference statement and sufficient conditions for the inference based on multiple preference statements in our computational experiments all inferences could be made with these conditions moreover our analysis suggests that the non parametric analyses of general additive value models are unlikely to be useful by themselves for decision support in contexts where the decision maker preferences are elicited in the form of holistic pair wise statements

electre like clustering from a pairwise fuzzy proximity index abstract in this paper we propose an electre like approach for clustering judges from their l valued pairwise proximities in preference judgements the approach is based on the extraction of l valued null kernels from a pairwise l valued proximity index a practical application will concern the clustering of movie critics

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

formalizing and solving the problem of clustering in mcda the topic of clustering has been widely studied in the field of data analysis where it is defined as an unsupervised process of grouping objects together based on notions of similarity clustering in the field of multi criteria decision aid mcda has seen a few adaptations of methods from data analysis most of them however using concepts native to that field such as the notions of similarity and distance measures as in mcda we model the preferences of a decision maker over a set of decision alternatives we can find more diverse ways of comparing them than in data analysis as a result these alternatives may also be arranged into different potential structures in this paper we wish to formally define the problem of clustering in mcda using notions that are native to this field alone and highlight the different structures which we may try to uncover through this process following this we propose a method for finding these structures as in any clustering problem finding the optimal result in an exact manner is impractical and so we propose a stochastic heuristic approach which we validate through tests on a large set of artificially generated benchmarks

integrated framework for preference modeling and robustness analysis for outranking based multiple criteria sorting with electre and promethee a novel framework for preference modeling and robustness analysis is proposed we apply a sorting rule deriving from the semantic meaning of an outranking relation we ensure input output correspondence with respect to three sorting perspectives the generality of our framework is illustrated with its two specific implementations preference modeling can be simplified when using model instances providing precise assignments we introduce an integrated framework for preference modeling and robustness analysis in outranking based multiple criteria sorting the preference information supplied by the decision maker dm is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy its allowed forms are imprecise assignment examples desired class cardinalities and assignment based pairwise comparisons the exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes these raise robustness concerns in terms of the stability of a suggested assignment for each alternative an observed size of each class and a comparison between recommendation delivered for pairs of alternatives the correspondence between different types of inputs and outputs facilitates the dialogue with the dm and enhances her his confidence in the suggested recommendation while referring only to a semantic meaning of an outranking relation we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results then we implement this general framework in the context of outranking models specific for electre and promethee finally we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives the framework proposed for this case is based on mixed integer linear programming milp being independent of the underlying model and method application of the approaches is demonstrated on the case of classifying polish research units into four quality classes

selection of a representative value function in robust multiple criteria ranking and choice we introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems the proposed method can be seen as a new interactive uta like procedure which extends the utagms and grip methods the preference information supplied by the decision maker dm is composed of a partial preorder and intensities of preference on a subset of reference alternatives robust ordinal regression builds a set of general additive value functions which are compatible with the preference information and returns two binary preference relations necessary and possible they identify recommendations which are compatible with all or at least one compatible value function respectively in this paper we propose a general framework for selection of a representative value function from among the set of compatibles ones there are a few targets which build on results of robust ordinal regression and could be attained by a representative value function in general according to the interactively elicited preferences of the dm the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage the basic procedure is refined by few extensions they enable emphasizing the advantage of alternatives that could be considered as potential best options accounting for intensities of preference or obtaining a desired type of the marginal value functions

jie ke versus alphago a ranking approach using decision making method for large scale data with incomplete information abstract ranking historical players in sports is challenging since some players have never played against each other it is even more complex in go because of alphago a project based on artificial intelligence who became the world s number 1 after it defeated the 528th and the 4th human go players alphago is ranked high in the current go ranking system because it is undefeated the objective of this paper is to propose a new ranking method for large scale go players by means of incomplete fuzzy pair wise comparison matrix whose priority vector is derived using a cosine similarity measure using match results provided by go4go net experiments are designed to rank top go players in the past 45 years and examine the change in ranking after alphago faced off against jie ke furthermore the proposed method was applied to rank all 1544 go players available at go4go net to illustrate its efficiency in handling large scale data

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

robustness analysis for decision under uncertainty with rule based preference model we introduce robust ordinal regression to decision under uncertainty we propose an integrated framework for robustness analysis with the rule based preference model we formulate the procedures for deriving a univocal classification of acts we account for different types of indirect preference information we consider group decision under uncertainty with dominance based rough set approach we consider decision under uncertainty as a multi attribute classification problem where a set of acts is described by outcomes gained with given probabilities the decision maker dm provides desired classification for a small subset of reference acts such preference information is structured using dominance based rough set approach drsa and the resulting lower approximations of the quality class unions are used as an input for construction of an aggregate preference model we induce all minimal cover sets of rules being compatible with the non ambiguous assignment examples and satisfying some additional requirements that may be imposed by the dm applying such compatible instances of the preference model on a set of all acts we draw conclusions about the certainty of recommendation assured by different minimal cover sets of rules in particular we analyze the diversity of class assignments assignment based preference relations and class cardinalities then we solve an optimization problem to get a univocal precise classification for all acts taking into account the robustness concern this optimization problem admits incorporation of additional indirect and imprecise preferences in form of desired class cardinalities and assignment based pairwise comparisons finally we extend the proposed approach to group decision under uncertainty we present a set of indicators and outcomes giving an insight into the spaces of consensus and disagreement between the dms

robust ordinal regression for dominance based rough set approach to multiple criteria sorting we present a new multiple criteria sorting method deriving from dominance based rough set approach drsa the preference information supplied by the decision maker dm is a set of possibly imprecise and inconsistent assignment examples on a subset of reference alternatives relatively well known to the dm to structure the data we use drsa and subsequently represent the assignment examples by all minimal sets of rules covering all alternatives from the lower approximations of class unions such a set of rules is called minimal cover set it is one of the instances of the preference model compatible with dm s preference information in this way we implement the principle of robust ordinal regression ror to decision rule preference model for each alternative we derive the necessary and possible assignments specifying the range of classes to which the alternative is assigned by all or at least one compatible set of rules respectively as well as class acceptability indices we also introduce the notion of a representative compatible minimal cover set of rules whose selection builds on the results of ror addressing the robustness concern application of the approach is demonstrated by classifying 69 land zones in 4 classes representing different risk levels

electregkms robust ordinal regression for outranking methods we present a new method called electregkms which employs robust ordinal regression to construct a set of outranking models compatible with preference information the preference information supplied by the decision maker dm is composed of pairwise comparisons stating the truth or falsity of the outranking relation for some real or fictitious reference alternatives moreover the dm specifies some ranges of variation of comparison thresholds on considered pseudo criteria using robust ordinal regression the method builds a set of values of concordance indices concordance thresholds indifference preference and veto thresholds for which all specified pairwise comparisons can be restored such sets are called compatible outranking models using these models two outranking relations are defined necessary and possible whether for an ordered pair of alternatives there is necessary or possible outranking depends on the truth of outranking relation for all or at least one compatible model respectively distinguishing the most certain recommendation worked out by the necessary outranking and a possible recommendation worked out by the possible outranking electregkms answers questions of robustness concern the method is intended to be used interactively with incremental specification of pairwise comparisons possibly with decreasing confidence levels in this way the necessary and possible outranking relations can be respectively enriched or impoverished with the growth of the number of pairwise comparisons furthermore the method is able to identify troublesome pieces of preference information which are responsible for incompatibility the necessary and possible outranking relations are to be exploited as usual outranking relations to work out recommendation in choice or ranking problems the introduced approach is illustrated by a didactic example showing how electregkms can support real world decision problems

quasi distribution semigroups and integrated semigroups abstract suppose x is a banach space we introduce the concept of quasi distribution semigroups on x as a generalization of the concept of distribution semigroups introduced by lions in 19 in our approach the generator a of a quasi distribution semigroup may not be densely defined also introduced is a functional calculus for a in terms of the fourier transform for fixed r 0 k n 0 define order r k for a quasi distribution semigroup and define an f r k functional calculus we prove that a generates a k 1 times integrated semigroup of exponential type r with local lipschitz continuity if and only if a generates a quasi distribution semigroup of order r k if and only if a has an f r k functional calculus when a is densely defined a quasi distribution semigroup reduces to a distribution semigroup in the sense of lions

asymptotic preserving particle in cell method for the vlasov poisson system near quasineutrality this paper deals with the numerical resolution of the vlasov poisson system in a nearly quasineutral regime by particle in cell pic methods in this regime classical pic methods are subject to stability constraints on the time and space steps related to the small debye length and large plasma frequency here we propose an asymptotic preserving pic scheme which is not subjected to these limitations additionally when the plasma period and debye length are small compared to the time and space steps this method provides a consistent pic discretization of the quasineutral vlasov equation we perform several one dimensional numerical experiments which provide a solid validation of the method and its underlying concepts and compare the method with classical pic and direct implicit methods

modelling of heat transport in magnetised plasmas using non aligned coordinates we present discretisation schemes for the heat diffusion equation in strongly magnetised plasmas in 2 d cartesian and 3 d cylindrical geometry the algorithms described do not use field aligned coordinates but show nevertheless a strong reduction of the pollution of perpendicular heat flux caused by parallel heat conduction compared to standard finite element or other finite difference formulations results for test examples show independence of the numerical error from g for values of g g up to 10 9 in plane and 10 1 2 in periodic cylinder geometry simulating toroidal connection the algorithms appear particularly well suited for dynamic mhd calculations where the effort of using exactly aligned coordinates becomes prohibitive

monotone finite volume schemes for diffusion equations on polygonal meshes we construct a nonlinear finite volume fv scheme for diffusion equation on star shaped polygonal meshes and prove that the scheme is monotone i e it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients our scheme has only cell centered unknowns and it treats material discontinuities rigorously and offers an explicit expression for the normal flux numerical results are presented to show how our scheme works for preserving positivity on various distorted meshes for both smooth and non smooth highly anisotropic solutions and numerical results show that our scheme appears to be approximate second order accuracy for the solution and first order accuracy for the flux

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

approximation of local convoluted semigroups abstract we extend the trotter kato theorem on c 0 semigroups to local convoluted semigroups on dual spaces and apply these results to the general banach space setting compared to known results we obtain weaker convergence assumptions on the resolvent

an asymptotic preserving method for strongly anisotropic diffusion equations based on field line integration in magnetized plasma the magnetic field confines the particles around the field lines the anisotropy intensity in the viscosity and heat conduction may reach the order of 1012 when the boundary conditions are periodic or neumann the strong diffusion leads to an ill posed limiting problem to remove the ill conditionedness in the highly anisotropic diffusion equations we introduce a simple but very efficient asymptotic preserving reformulation in this paper the key idea is that instead of discretizing the neumann boundary conditions locally we replace one of the neumann boundary condition by the integration of the original problem along the field line the singular 1 terms can be replaced by o 1 terms after the integration which yields a well posed problem small modifications to the original code are required and no change of coordinates nor mesh adaptation are needed uniform convergence with respect to the anisotropy strength 1 can be observed numerically and the condition number does not scale with the anisotropy

distribution semigroups and abstract cauchy problems we present a new definition of distribution semigroups covering in particular non densely defined generators we show that for a closed operator a in a banach space e the following assertions are equivalent a a generates a distribution semigroup b the convolution operator i a has a fundamental solution in d l e d where d denotes the domain of a supplied with the graph norm and i denotes the inclusion d e c a generates a local integrated semigroup we also show that every generator of a distribution semigroup generates a regularized semigroup introduction distribution semigroups in banach spaces and their generators were introduced by j l lions in 16 as a generalization of c0 semigroups and their generators like the generators of c0 semigroups the generators of the distribution semigroups in 16 are densely defined it was then shown in 16 that the densely defined closed linear operators a that generate a distribution semigroup are exactly those for which the convolution operator i a where i denotes the inclusion d a e has a fundamental solution treating cauchy problems as convolution equations has turned out to be very useful see 6 12 13 and 14 but in doing so the assumption that d a is dense in e is unnecessary in most of the results on the other hand in the last years there has been an interest in dealing with operators that are not densely defined starting perhaps with 7 reasons for this interest may be that it might not be so easy to decide whether a given operator is densely defined and the difficulties that arise when passing from e to e or l e so the question how the theory of distribution semigroups introduced in 16 can be extended to cover non densely defined generators in such a way that the above characterization via fundamental solutions holds seems natural it turns out that this indeed is possible in a way that even simplifies the original definitions given in 16 moreover the local strongly continuous representations see section 4 of the distribution semigroups thus obtained are exactly the local integrated semigroups for the distribution semigroups in the sense of 16 a relation to local integrated semigroups has been obtained in 23 theorem 5 6 see also 15 theorem 7 6 or 2 theorem 7 2 so the theory presented here received by the editors october 17 1995 and in revised form february 6 1997 1991 mathematics subject classification primary 47d03 34g10 47a10 46f10 c 1999 american mathematical society

finite element and higher order difference formulations for modelling heat transport in magnetised plasmas we present a finite element analogue to the second order finite difference scheme for the solution of the heat diffusion equation in strongly magnetised plasmas given in gunter et al s gunter et al j comp phys 209 2005 354 compared to standard finite element or finite difference formulations it strongly reduces the pollution of perpendicular heat fluxes by parallel ones even without resorting to field aligned coordinates we present both bi linear and bi quadratic versions of this scheme as well as a fourth order extension of the original difference scheme of gunter et al 2005 in the second part of the paper we address the formulation of the boundary conditions at walls with an oblique incidence of field lines and the treatment of the coordinate singularity at r 0 in cylindrical or topologically equivalent coordinates with the reduced pollution finite difference scheme all tests shown indicate that both the finite difference and the finite element versions of the scheme should substantially alleviate the requirement for field alignment of the coordinates over the realistic range of in toroidal magnetic confinement devices

a group decision making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty a new group decision making approach is developed to address a multiple criteria sorting problem with uncertainty the uncertainty in this paper refers to imprecise evaluations of alternatives with respect to the considered criteria the belief structure and the evidential reasoning approach are employed to represent and aggregate the uncertain evaluations in our approach the preference information elicited from a group of decision makers is composed of the assignment examples of some reference alternatives the disaggregation aggregation paradigm is utilized to infer compatible preference models from these assignment examples to help the group reach an agreement on the assignment of alternatives we propose a consensus reaching process in this process a consensus degree is defined to measure the agreement among the decision makers opinions when the decision makers are not satisfied with the consensus degree possible solutions are explored to help them adjust assignment examples in order to improve the consensus level if the consensus degree arrives at a satisfactory level a linear program is built to determine the collective assignment of alternatives the application of the proposed approach to a customer satisfaction analysis is presented at the end of the paper

rank 1 perturbations of cosine functions and semigroups abstract let a be the generator of a cosine function on a banach space x in many cases for example if x is a umd space a b generates a cosine function for each b l d a 1 2 x if a is unbounded and 1 2 1 then we show that there exists a rank 1 operator b l d a x such that a b does not generate a cosine function the proof depends on a modification of a baire argument due to desch and schappacher it also allows us to prove the following if a b generates a distribution semigroup for each operator b l d a x of rank 1 then a generates a holomorphic c 0 semigroup if a b generates a c 0 semigroup for each operator b l d a x of rank 1 where 0 1 then the semigroup t generated by a is differentiable and t t o t as t 0 for any 1 this is an approximate converse of a perturbation theorem for this class of semigroups

enumerating all connected maximal common subgraphs in two graphs we represent a new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem we have developed new algorithms for enumerating all cliques that represent connected maximal common subgraphs these algorithms are based on variants of the bron kerbosch algorithm in this paper we explain the transformation of the maximal common subgraph problem into the clique problem we give a short summary of the variants of the bron kerbosch algorithm in order to explain the modification of that algorithm such that the detected cliques represent connected maximal common subgraphs after introducing and proving several variants of the modified algorithm we discuss the runtimes for all variants by means of random graphs the results show the drastical reduction of the runtimes for the new algorithms

elicitation of multiattribute value functions through high dimensional model representations monotonicity and interactions abstract this work addresses the early phases of the elicitation of multiattribute value functions proposing a practical method for assessing interactions and monotonicity we exploit the link between multiattribute value functions and the theory of high dimensional model representations the resulting elicitation method does not state any a priori assumption on an individual s preference structure we test the approach via an experiment in a riskless context in which subjects are asked to evaluate mobile phone packages that differ on three attributes

acuta a novel method for eliciting additive value functions on the basis of holistic preference statements in multiple criteria decision aiding it is common to use methods that are capable of automatically extracting a decision or evaluation model from partial information provided by the decision maker about a preference structure in general there is more than one possible model leading to an indetermination which is dealt with sometimes arbitrarily in existing methods this paper aims at filling this theoretical gap we present a novel method based on the computation of the analytic center of a polyhedron for the selection of additive value functions that are compatible with holistic assessments of preferences we demonstrate the most important characteristics of this technique with an experimental and comparative study of several existing methods belonging to the uta family

convoluted c cosine functions and semigroups relations with ultradistribution and hyperfunction sines abstract convoluted c cosine functions and semigroups in a banach space setting extending the classes of fractionally integrated c cosine functions and semigroups are systematically analyzed structural properties of such operator families are obtained relations between convoluted c cosine functions and analytic convoluted c semigroups introduced and investigated in this paper are given through the convoluted version of the abstract weierstrass formula which is also proved in the paper ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups several examples of operators generating convoluted cosine functions analytic convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors as an application it is proved that the polyharmonic operator 2 n n n acting on l 2 0 with appropriate boundary conditions generates an exponentially bounded k n convoluted cosine function and consequently an exponentially bounded analytic k n 1 convoluted semigroup of angle 2 for suitable exponentially bounded kernels k n and k n 1

asymptotic preserving scheme for highly anisotropic non linear diffusion equations heat transfer in magnetically confined plasmas is a process characterized by non linear and extremely high anisotropic diffusion phenomena standard numerical methods successfully employed in the numerical treatment of classical diffusion problems are generally inefficient or even prone to break down when such high anisotropies come into play leading thus to the need of new numerical techniques suitable for this kind of problems in the present paper the authors propose a numerical scheme based on an asymptotic preserving ap reformulation of this non linear evolution problem generalizing the ideas introduced in a previous paper for the case of elliptic anisotropic problems p degond a lozinski j narski c negulescu an asymptotic preserving method for highly anisotropic elliptic equations based on a micro macro decomposition j comput phys 231 7 2012 2724 2740 the performances of the here proposed ap scheme are tested numerically in particular it is shown that the scheme is capable to deal with problems characterized by a high degree of anisotropy thus proving to be suitable for the study of anisotropic diffusion in magnetically confined plasmas

an asymptotic preserving method for highly anisotropic elliptic equations based on a micro macro decomposition the concern of the present work is the introduction of a very efficient asymptotic preserving scheme for the resolution of highly anisotropic diffusion equations the characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter 0 e 1 the applicability on cartesian grids to cases of non uniform and non aligned anisotropy fields b and the simple extension to the case of a non constant anisotropy intensity 1 e the mathematical approach and the numerical scheme are different from those presented in the previous work p degond f deluzet a lozinski j narski c negulescu duality based asymptotic preserving method for highly anisotropic diffusion equations communications in mathematical sciences 10 1 2012 1 31 and its considerable advantages are pointed out

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

a new decision making approach for multiple criteria sorting with an imbalanced set of assignment examples abstract we propose a novel approach to address a multiple criteria sorting mcs problem with an imbalanced set of assignment examples the approach employs a piecewise linear additive value function as the preference model and adopts the disaggregation aggregation paradigm to infer a sorting model from provided assignment examples on a set of reference alternatives we utilize a hierarchical clustering algorithm and several linear programming models to identify reference alternatives that are active to develop the sorting model so that inactive ones are eliminated from the whole set of reference alternatives then in order to construct a balanced set of assignment examples a balancing algorithm is proposed to balance active reference alternatives across categories finally the sorting model is obtained by minimizing the sum of violations between values of active reference alternatives and corresponding category thresholds furthermore the performance of the proposed approach is investigated on a hypothetical problem and several real data sets the experimental results show that our approach is efficient to address the mcs problem with an imbalanced set of assignment examples

modeling assignment based pairwise comparisons within integrated framework for value driven multiple criteria sorting abstract we introduce a new preference disaggregation modeling formulations for multiple criteria sorting with a set of additive value functions the preference information supplied by the decision maker dm is composed of 1 possibly imprecise assignment examples 2 desired class cardinalities and 3 assignment based pairwise comparisons the latter have the form of imprecise statements referring to the desired assignments for pairs of alternatives but without specifying any concrete class additionally we account for preferences concerning the shape of the marginal value functions and desired comprehensive values of alternatives assigned to a given class or class range the exploitation of all value functions compatible with these preferences results in three types of results 1 necessary and possible assignments 2 extreme class cardinalities and 3 necessary and possible assignment based preference relations these outputs correspond to different types of admitted preference information by exhibiting different outcomes we encourage the dm in various ways to enrich her his preference information interactively the applicability of the framework is demonstrated on data involving the classification of cities into liveability classes

multiple criteria sorting with a set of additive value functions we present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre defined and ordered classes the preference information supplied by the decision maker dm is a set of assignment examples on a subset of actions relatively well known to the dm these actions are called reference actions each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes the set of assignment examples is used to build a preference model of the dm represented by a set of general additive value functions compatible with the assignment examples for each action a the method computes two kinds of assignments to classes concordant with the dm s preference model the necessary assignment and the possible assignment the necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously the possible assignment specifies in turn the range of classes to which the action can be assigned considering any compatible value function individually the compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs

towards multicriteria clustering an extension of the k means algorithm abstract the research within the multicriteria classification field is mainly focused on the assignment of actions to pre defined classes nevertheless the building of multicriteria categories remains a theoretical question still not studied in detail to tackle this problem we propose an extension of the well known k means algorithm to the multicriteria framework this extension relies on the definition of a multicriteria distance based on the preference structure defined by the decision maker thus two alternatives will be similar if they are preferred indifferent and incomparable to more or less the same actions armed with this multicriteria distance we will be able to partition the set of alternatives into classes that are meaningful from a multicriteria perspective finally the examples of the country risk problem and the diagnosis of firms will be treated to illustrate the applicability of this method

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

on the infinite product ofc0 semigroups given a family etak t 0 k n of commuting contraction semigroups we investigate when the infinite product k 1 etakconverges and defines ac0 semigroup a particular case is the heat semigroup in infinite dimension introduced by cannarsa and da prato j funct anal 118 1993 22 42

using classification as an aggregation tool in mcdm abstract in this paper we propose a method to obtain the set of best alternatives when data involved in mcdm are of different types e g numbers linguistic labels or truth values this method consists of a classification of the alternatives according to criteria and then an ordering of the classes obtained in this way we study each alternative in relation with the other ones the groups formed indicate that their members are equally prefered over the others otherwise we describe some specialized methods to be used in case that all criteria have the same type of values

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

an anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics petroleum engineering and image processing standard numerical methods can produce spurious oscillations when they are used to solve those problems a common approach to avoid this difficulty is to design a proper numerical scheme and or a proper mesh so that the numerical solution validates the discrete counterpart dmp of the maximum principle satisfied by the continuous solution a well known mesh condition for the dmp satisfaction by the linear finite element solution of isotropic diffusion problems is the non obtuse angle condition that requires the dihedral angles of mesh elements to be non obtuse in this paper a generalization of the condition the so called anisotropic non obtuse angle condition is developed for the finite element solution of heterogeneous anisotropic diffusion problems the new condition is essentially the same as the existing one except that the dihedral angles are now measured in a metric depending on the diffusion matrix of the underlying problem several variants of the new condition are obtained based on one of them two metric tensors for use in anisotropic mesh generation are developed to account for dmp satisfaction and the combination of dmp satisfaction and mesh adaptivity numerical examples are given to demonstrate the features of the linear finite element method for anisotropic meshes generated with the metric tensors

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

monotone finite volume schemes of nonequilibrium radiation diffusion equations on distorted meshes we construct a monotone finite volume scheme on distorted meshes for multimaterial nonequilibrium radiation diffusion problems which are described by the coupled radiation diffusion and material conduction equations moreover we prove theoretically that the scheme is monotone numerical results are presented to show that our scheme preserves positivity of solution on various distorted meshes and the contours of numerical solution obtained by our scheme on distorted meshes accord with that on rectangular meshes moreover numerical tests indicate that our monotone scheme is more computationally efficient than the nine point scheme these results show that our nonlinear monotone finite volume scheme is a practical and attractive method for solving nonlinear diffusion equations on distorted meshes

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

handling multicriteria preferences in cluster analysis in the framework of multicriteria decision aid a lot of interest has been devoted to sorting problems in which the set of categories is pre defined besides preference oriented multicriteria clustering has received little attention usual geometric and related metrics are not well suited for this problem here we propose a clustering method based on a valued indifference relation inspired by outranking methods we suggest a method based on comparing cluster centers and an average net flow score of clusters to build a complete ranking of the set of clusters that is a way of defining a set of ordered categories for sorting purposes the new approach performs very well in some examples

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