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

cauchy problems for fractional differential equations with riemann liouville fractional derivatives abstract in this paper we are concerned with cauchy problems of fractional differential equations with riemann liouville fractional derivatives in infinite dimensional banach spaces we introduce the notion of fractional resolvent obtain some its properties and present a generation theorem for exponentially bounded fractional resolvents moreover we prove that a homogeneous order cauchy problem is well posed if and only if its coefficient operator is the generator of an order fractional resolvent and we give sufficient conditions to guarantee the existence and uniqueness of weak solutions and strong solutions of an inhomogeneous order cauchy problem

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

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

recursive projection twin support vector machine via within class variance minimization in this paper a novel binary classifier coined projection twin support vector machine ptsvm is proposed the idea is to seek two projection directions one for each class such that the projected samples of one class are well separated from those of the other class in its respective subspace in order to further boost performance a recursive algorithm for ptsvm is proposed to generate more than one projection axis for each class to overcome the singularity problem principal component analysis pca is utilized to transform the data in the original space into a low dimensional subspace wherein the optimization problem of ptsvm is convex and can be solved efficiently the experimental results on several uci benchmark data sets and usps digit database show the feasibility and effectiveness of the proposed method

relaxation in nonconvex optimal control problems described by fractional differential equations abstract we consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control a relaxation problem is treated along with the original problem it is proved that under general assumptions the relaxation problem has an optimal solution and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory the control and the functional in appropriate topologies simultaneously

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

nonparallel hyperplane support vector machine for binary classification problems in this paper we propose a nonparallel hyperplane support vector machine nhsvm for binary classification problems our proposed nhsvm is formulated by clustering the training points according to the similarity between classes it constructs two nonparallel hyperplanes simultaneously by solving a single quadratic programming problem and is consistent between its predicting and training processes an essential difference that distinguishes it from other nonparallel svms this proposed nhsvm has been analyzed theoretically and implemented experimentally the results of experiments conducted using it on both artificial and publicly available benchmark datasets confirm its feasibility and efficacy especially for cross planes datasets and datasets with heteroscedastic noise

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

a generalized gronwall inequality and its application to a fractional differential equation this paper presents a generalized gronwall inequality with singularity using the inequality we study the dependence of the solution on the order and the initial condition of a fractional differential equation

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

on the relations between electre tri b and electre tri c and on a new variant of electre tri b electre tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories the original method uses limiting profiles a recently introduced method uses central profiles we study the relations between these two methods we do so by investigating if an ordered partition obtained with one method can also be obtained with the other method after a suitable redefinition of the profiles we also investigate a number of situations in which the original method using limiting profiles gives results that do not fit well our intuition this leads us to propose a variant of electre tri that uses limiting profiles we show that this variant may have some advantages over the original method

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

approximate controllability of a system of parabolic equations with delay abstract in this paper we give necessary and sufficient conditions for the approximate controllability of the following system of parabolic equations with delay z t x t d z l z t b u t x t 0 r z 0 x t 0 r z 0 x 0 x x z s x s x s 0 x where is a bounded domain in r n d is an n n nondiagonal matrix whose eigenvalues are semi simple with nonnegative real part the control u l 2 0 r u l 2 0 r l 2 r m and b l u z with u l 2 r m z l 2 r n the standard notation z t x defines a function from 0 to r n with x fixed by z t x s z t s x s 0 here 0 is the maximum delay which is supposed to be finite we assume that the operator l l 2 0 z z is linear and bounded and 0 z l 2 0 z to this end first we reformulate this system into a standard first order delay equation secondly the semigroup associated with the first order delay equation on an appropriate product space is expressed as a series of strongly continuous semigroups and orthogonal projections related with the eigenvalues of the laplacian operator a 2 this representation allows us to reduce the controllability of this partial differential equation with delay to a family of ordinary delay equations finally we use the well known result on the rank condition for the approximate controllability of delay system to derive our main result

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

global maximization of uta functions in multi objective optimization abstract the utas utilite additives type methods for constructing nondecreasing additive utility functions were first proposed by jacquet lagreze and siskos in 1982 for handling decision problems of multicriteria ranking in this article by uta functions we mean functions which are constructed by the uta type methods our purpose is to propose an algorithm for globally maximizing uta functions of a class of linear convex multiple objective programming problems the algorithm is established based on a branch and bound scheme in which the branching procedure is performed by a so called i rectangular bisection in the objective outcome space and the bounding procedure by some convex or linear programs preliminary computational experiments show that this algorithm can work well for the case where the number of objective functions in the multiple objective optimization problem under consideration is much smaller than the number of variables

soft clustering using weighted one class support vector machines this paper describes a new soft clustering algorithm in which each cluster is modelled by a one class support vector machine oc svm the proposed algorithm extends a previously proposed hard clustering algorithm also based on oc svm representation of clusters the key building block of our method is the weighted oc svm woc svm a novel tool introduced in this paper based on which an expectation maximization type soft clustering algorithm is defined a deterministic annealing version of the algorithm is also introduced and shown to improve the robustness with respect to initialization experimental results show that the proposed soft clustering algorithm outperforms its hard clustering counterpart namely in terms of robustness with respect to initialization as well as several other state of the art methods

support function machine for set based classification with application to water quality evaluation in some applications measurement errors and multiple repeated measurements often lead to a set based classification task where objects are represented with a set of samples and the traditional support vector machines svms do not work in these settings to deal with this problem we construct a new classifier called support function machine sfm in this work first sets in d dimensional euclidean space r d are mapped into an infinite dimensional banach space c s whose elements are functions via support functions and then set based classification in r d is converted into function based classification in c s second we define the hyperplane via the riesz representation theorem in banach space and discuss the hausdorff distance of hyperpalnes and maximum margin principle mmp in c s based on mmp we construct an optimal problem and discuss some of its properties thereafter we establish an sfm to solve set based classification experiments about water quality evaluation and set valued data classifications show the superiority of sfm

assessing a set of additive utility functions for multicriteria decision making the uta method abstract the purpose of the method presented in this paper is to assess additive utility functions which aggregate multiple criteria in a composite criterion using the information given by a subjective ranking on a set of stimuli or actions weak order comparison judgments and the multicriteria evaluations of these actions it is an ordinal regression method using linear programming to estimate the parameters of the utility function stability and sensitivity analysis leads to the assessment of a set of utility functions by means of post optimality analysis techniques in linear programming finally a simple illustrative example is presented and some extensions of the method are proposed

a study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning we investigate essential relationships between generalization capabilities and fuzziness of fuzzy classifiers viz the classifiers whose outputs are vectors of membership grades of a pattern to the individual classes the study makes a claim and offers sound evidence behind the observation that higher fuzziness of a fuzzy classifier may imply better generalization aspects of the classifier especially for classification data exhibiting complex boundaries this observation is not intuitive with a commonly accepted position in traditional pattern recognition the relationship that obeys the conditional maximum entropy principle is experimentally confirmed furthermore the relationship can be explained by the fact that samples located close to classification boundaries are more difficult to be correctly classified than the samples positioned far from the boundaries this relationship is expected to provide some guidelines as to the improvement of generalization aspects of fuzzy classifiers

twin support vector machines for pattern classification we propose twin svm a binary svm classifier that determines two nonparallel planes by solving two related svm type problems each of which is smaller than in a conventional svm the twin svm formulation is in the spirit of proximal svms via generalized eigenvalues on several benchmark data sets twin svm is not only fast but shows good generalization twin svm is also useful for automatically discovering two dimensional projections of the data

valued outranking relations in electre providing manageable disaggregation procedures in electre methods the construction of an outranking relation amounts at validating or invalidating for any pair of alternatives a b the assertion a is at least as good as b this comparison is grounded on the evaluation vectors of both alternatives and on additional information concerning the decision makers preferences accounting for two conditions concordance and non discordance in decision processes using these methods the analyst should interact with the decision maker in order to elicit values for preferential parameters this can be done either directly or through a disaggregation procedure that infers the parameters values from holistic judgements provided by the decision maker inference is usually performed through an optimization program that accounts for the aggregation model and minimizes an error function although disaggregation approaches have been largely used in additive models only few advances have been made towards a disaggregation approach for outranking methods indeed outranking methods may lead to computationally difficult inference problems in this paper we are concerned with a slight adaptation of the valued outranking relation used in the electre iii and electre tri such modification is shown to preserve the original discordance concept we show that the modified outranking relation makes it easier to solve inference programs 2003 elsevier b v all rights reserved

approximate controllability of fractional order semilinear systems with bounded delay abstract in this paper sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order the existence and uniqueness of mild solution of the system is also proved the results are obtained by using contraction principle and the schauder fixed point theorem some examples are given to illustrate the theory

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

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

approximate controllability for a class of fractional stochastic wave equations abstract in this paper we consider the approximate controllability for a class of fractional stochastic wave equations in the sense of riemann liouville fractional derivative based on some special functions we transform the fractional stochastic wave equations into fractional evolution equations further we give an appropriate definition of mild solutions for this type of fractional stochastic wave equations moreover with the aid of fixed point theory we discuss the existence results of the mild solutions of the proposed problem finally we establish the approximate controllability when the corresponding linear system is approximately controllable

variable consistency dominance based rough set approach to preference learning in multicriteria ranking abstract we present a methodology for non statistical preference learning in multicriteria ranking based on variable consistency dominance based rough set approach vc drsa a finite set of objects to be ranked is evaluated by a set of criteria which are real valued functions with ordinal or cardinal scales given the statement of a multicriteria ranking problem the only objective information one can get is the dominance relation over the set of objects the dominance relation is however too poor because it leaves many objects incomparable to enrich this relation and make the objects more comparable a decision maker dm must supply some preference information revealing her his value system with respect to multicriteria evaluations we are considering a frequent case when the preference information has the form of pairwise comparisons of some objects relatively well known to the dm called reference objects this information is thus composed of some decision examples on the reference objects it is the input data for a method that learns the preferences of the dm since this information is prone to inconsistencies we propose to structure it using vc drsa then the pairs of objects that are sufficiently consistent serve as a basis for induction of a preference model this model has the form of a set of if then decision rules application of these rules on the whole set of objects to be ranked yields a fuzzy preference structure directed weighted graph this preference structure is then exploited using a ranking method so as to work out a final recommendation we propose a list of properties that helps to choose a proper ranking method the methodology is illustrated by an example

irreducibly inconsistent systems of linear inequalities abstract irreducibly inconsistent systems of linear inequalities are considered from the point of view of applying simplex like methods for investigation we give necessary and sufficient conditions for a system to be irreducibly inconsistent which can be found by applying a simplex algorithm next we consider general inconsistent systems the simplex method can be used to identify irreducibly inconsistent subsystem such subsystems can give structural insight in the inconsistency and are used in trying to make the overall system consistent this can be done in an easy way e g by right hand side manipulations finally the problem of finding a cheapest way of doing this can be formulated and solved as an extended linear program

improvements on twin support vector machines for classification problems the generalized eigenvalue proximal support vector machine gepsvm and twin support vector machine twsvm are regarded as milestones in the development of the powerful svms as they use the nonparallel hyperplane classifiers in this brief we propose an improved version named twin bounded support vector machines tbsvm based on twsvm the significant advantage of our tbsvm over twsvm is that the structural risk minimization principle is implemented by introducing the regularization term this embodies the marrow of statistical learning theory so this modification can improve the performance of classification in addition the successive overrelaxation technique is used to solve the optimization problems to speed up the training procedure experimental results show the effectiveness of our method in both computation time and classification accuracy and therefore confirm the above conclusion further

a twin hypersphere support vector machine classifier and the fast learning algorithm this paper formulates a twin hypersphere support vector machine thsvm classifier for binary recognition similar to the twin support vector machine twsvm classifier this thsvm determines two hyperspheres by solving two related support vector machine svm type problems each one is smaller than the classical svm which makes the thsvm be more efficient than the classical svm in addition the thsvm avoids the matrix inversions in its two dual quadratic programming problems qpps compared with the twsvm by considering the characteristics of the dual qpps of thsvm an efficient gilbert s algorithm for the thsvm based on the reduced convex hull rch instead of directly optimizing its pair of qpps is further presented computational results on several synthetic as well as benchmark datasets indicate the significant advantages of the thsvm classifier in the computational time and test accuracy

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

decision making with interval probabilities handling uncertainty by interval probabilities is recently receiving considerable attention by researchers interval probabilities are used when it is difficult to characterize the uncertainty by point valued probabilities due to partially known information most of researches related to interval probabilities such as combination marginalization condition bayesian inferences and decision assume that interval probabilities are known how to elicit interval probabilities from subjective judgment is a basic and important problem for the applications of interval probability theory and till now a computational challenge in this work the models for estimating and combining interval probabilities are proposed as linear and quadratic programming problems which can be easily solved the concepts including interval probabilities interval entropy interval expectation interval variance interval moment and the decision criteria with interval probabilities are addressed a numerical example of newsvendor problem is employed to illustrate our approach the analysis results show that the proposed methods provide a novel and effective alternative for decision making when point valued subjective probabilities are inapplicable due to partially known information

tpmsvm a novel twin parametric margin support vector machine for pattern recognition a novel twin parametric margin support vector machine tpmsvm for classification is proposed in this paper this tpmsvm in the spirit of the twin support vector machine twsvm determines indirectly the separating hyperplane through a pair of nonparallel parametric margin hyperplanes solved by two smaller sized support vector machine svm type problems similar to the parametric margin email protected support vector machine email protected svm this tpmsvm is suitable for many cases especially when the data has heteroscedastic error structure that is the noise strongly depends on the input value but there is an advantage in the learning speed compared with the email protected svm the experimental results on several artificial and benchmark datasets indicate that the tpmsvm not only obtains fast learning speed but also shows good generalization

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

a twin hyperspheres support vector machine with automatic variable weights for data classification abstract this paper proposes a novel twin hyperspheres support vector machine thsvm classifier for binary classification called the automatic variable weighted thsvm vthsvm classifier by solving a single optimization problem this classifier not only finds a pair of hyperspheres for classification but also automatically constructs a weight vector for each class in order to describe the dissimilarity of different classes this vthsvm is extended to the kernel case by the fact that a kernel can be written as a sum of one s evaluated on each variable separately the main advantage of this method is that it allows the use of adaptive distance which is suitable to find an as compact as possible hypersphere for each class experiments with synthetic and benchmark datasets indicate vthsvm obtains better performance than some other classifiers

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

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

robust ordinal regression for value functions handling interacting criteria we present a new method called utagms int for ranking a finite set of alternatives evaluated on multiple criteria it belongs to the family of robust ordinal regression ror methods which build a set of preference models compatible with preference information elicited by the decision maker dm the preference model used by utagms int is a general additive value function augmented by two types of components corresponding to bonus or penalty values for positively or negatively interacting pairs of criteria respectively when calculating value of a particular alternative a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria similarly a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria the preference information elicited by the dm is composed of pairwise comparisons of some reference alternatives as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference either comprehensively or on a particular criterion in utagms int ror starts with identification of pairs of interacting criteria for given preference information by solving a mixed integer linear program once the interacting pairs are validated by the dm ror continues calculations with the whole set of compatible value functions handling the interacting criteria to get necessary and possible preference relations in the considered set of alternatives a single representative value function can be calculated to attribute specific scores to alternatives it also gives values to bonuses and penalties utagms int handles quite general interactions among criteria and provides an interesting alternative to the choquet integral

approximate controllability for fractional semilinear parabolic equations abstract in this paper we deal with the control systems described by a large class of fractional semilinear parabolic equations firstly we reformulate the fractional parabolic equations into abstract fractional differential equations associated with a semigroup on an appropriate banach space secondly we introduce a suitable concept on a mild solution for this kind of fractional parabolic equations and present the existence and uniqueness of mild solution by utilizing the theory of semigroup of linear operator nonlinear analysis method and fixed point theorem then the approximate controllability of the fractional semilinear parabolic equations is formulated and proved at the end of the paper an example is given to illustrate our main results

eliciting electre tri category limits for a group of decision makers multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories in this paper we consider a well known multiple criteria sorting method electre tri which involves three types of preference parameters 1 category limits defining the frontiers between consecutive categories 2 weights and majority level specifying which coalitions form a majority and 3 veto thresholds characterizing discordance effects we propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers the procedure computes a set of category limits and vetoes common to all decision makers with variable weights for each decision maker hence the method helps reaching a consensus among decision makers on the category limits and veto thresholds whereas finding a consensus on weights is left aside the inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real world decision problems we provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms

uta poly and uta splines additive value functions with polynomial marginals additive utility function models are widely used in multiple criteria decision analysis in such models a numerical value is associated to each alternative involved in the decision problem it is computed by aggregating the scores of the alternative on the different criteria of the decision problem the score of an alternative is determined by a marginal value function that evolves mono tonically as a function of the performance of the alternative on this criterion determining the shape of the marginals is not easy for a decision maker it is easier for him her to make statements such as alternative a is preferred to b in order to help the decision maker uta disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements in this paper we propose to infer polynomials and splines instead of piecewise linear functions for the marginals in this aim we use semidefinite programming instead of linear programming we illustrate this new elicitation method and present some experimental results

building a set of additive value functions representing a reference preorder and intensities of preference grip method we present a method called generalized regression with intensities of preference grip for ranking a finite set of actions evaluated on multiple criteria grip builds a set of additive value functions compatible with preference information composed of a partial preorder and required intensities of preference on a subset of actions called reference actions it constructs not only the preference relation in the considered set of actions but it also gives information about intensities of preference for pairs of actions from this set for a given decision maker dm distinguishing necessary and possible consequences of preference information on the considered set of actions grip answers questions of robustness analysis the proposed methodology can be seen as an extension of the uta method based on ordinal regression grip can also be compared to the ahp method which requires pairwise comparison of all actions and criteria and yields a priority ranking of actions as for the preference information being used grip can be compared moreover to the macbeth method which also takes into account a preference order of actions and intensity of preference for pairs of actions the preference information used in grip does not need however to be complete the dm is asked to provide comparisons of only those pairs of reference actions on particular criteria for which his her judgment is sufficiently certain this is an important advantage comparing to methods which instead require comparison of all possible pairs of actions on all the considered criteria moreover grip works with a set of general additive value functions compatible with the preference information while other methods use a single and less general value function such as the weighted sum

drift diffusion equations with fractional diffusion and the quasi geostrophic equation motivated by the critical dissipative quasi geostrophic equation we prove that drift diffusion equations with l 2 initial data and minimal assumptions on the drift are locally holder continuous as an application we show that solutions of the quasi geostrophic equation with initial l 2 data and critical diffusion 1 2 are locally smooth for any space dimension

electre tri nb a new multiple criteria ordinal classification method abstract this paper presents a new method for multiple criteria ordinal classification sorting problems in an ordinal classification problem the categories also called classes in related literature are pre defined and ordered from the best to the worst or from the worst to the best the actions not necessarily known a priori are assigned to the different ordered categories several electre type methods were designed to deal with this kind of problem however none of them proposes a characterization of the categories through a set of limiting profiles this is the novelty of the current method which may be considered as an extension of electre tri b it fulfills a set of structural requirements uniqueness of the assignments independence monotonicity homogeneity conformity and stability with respect to merging and splitting operations all these features will be presented in the current paper and illustrated through three examples

approximate controllability for a class of semilinear abstract equations in this paper a class of control systems governed by the semilinear abstract equation dot y ay f y bv is considered a sufficient condition for the approximate controllability is obtained which improves j henry s results on a nonlinear parabolic control systems with some more serious restrictions it is suitable not only to the infinite dimensional case but also to the finite dimensional case two examples are given to explain the applications of the theory

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

approximate controllability of a class of semilinear degenerate systems with convection term abstract this paper concerns a class of control systems governed by semilinear degenerate equations with convection term the equations may be weakly degenerate and strongly degenerate on a portion of the lateral boundary and the convection terms can be controlled by the diffusion terms the control systems are shown to be approximately controllable

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

using assignment examples to infer weights for electre tri method some experimental results given a finite set of alternatives a the sorting or assignment problem consists in the assignment of each alternative to one of the pre defined categories in this paper we are interested in multiple criteria sorting problems and more precisely in the existing method electre tri this method requires the elicitation of preferential parameters weights thresholds category limits in order to construct a preference model which the decision maker dm accepts as a working hypothesis in the decision aid study a direct elicitation of these parameters requiring a high cognitive effort from the dm v mosseau r slowinski journal of global optimization 12 2 1998 174 proposed an interactive aggregation disaggregation approach that infers electre tri parameters indirectly from holistic information i e assignment examples in this approach the determination of electre tri parameters that best restore the assignment examples is formulated through a nonlinear optimization program in this paper we consider the subproblem of the determination of the weights only the thresholds and category limits being fixed this subproblem leads to solve a linear program rather than nonlinear in the global inference model numerical experiments were conducted so as to check the behaviour of this disaggregation tool results showed that this tool is able to infer weights that restores in a stable way the assignment examples and that it is able to identify inconsistencies in the assignment examples

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

non additive robust ordinal regression a multiple criteria decision model based on the choquet integral abstract within the multicriteria aggregation disaggregation framework ordinal regression aims at inducing the parameters of a decision model for example those of a utility function which have to represent some holistic preference comparisons of a decision maker dm usually among the many utility functions representing the dm s preference information only one utility function is selected since such a choice is arbitrary to some extent recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the dm s preference information until now robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence in this paper we propose a non additive robust ordinal regression on a set of alternatives a whose utility is evaluated in terms of the choquet integral which permits to represent the interaction among criteria modelled by the fuzzy measures parameterizing our approach in our methodology besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives a a the dm is also requested to express the intensity of preference on pairs of alternatives from a and to supply pairwise comparisons on the importance of criteria and the sign and intensity of interaction among pairs of criteria the output of our approach defines a set of fuzzy measures capacities such that the corresponding choquet integral is compatible with the dm s preference information moreover using linear programming our decision model establishes two preference relations for any a b a the necessary weak preference relation if for all compatible fuzzy measures the utility of a is not smaller than the utility of b and the possible weak preference relation if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b

multisurface proximal support vector machine classification via generalized eigenvalues a new approach to support vector machine svm classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set each of the two nonparallel proximal planes is obtained by a single matlab command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems the effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets these examples show the advantages of the proposed approach in both computation time and test set correctness

approximate controllability of a semilinear heat equation in bbb r n we prove the approximate controllability of the semilinear heat equation in bbb r n we introduce the weighted sobolev spaces of escobedo and kavian and in that functional setting we adapt the technique introduced by fabre puel and zuazua for the problem in bounded domains that is we first prove the approximate controllability of the linear equation and by a fixed point method obtain the main result

resolving inconsistencies among constraints on the parameters of an mcda model we consider a framework where decision makers dms interactively define a multicriteria evaluation model by providing imprecise information i e a linear system of constraints to the model s parameters and by analyzing the consequences of the information provided dms may introduce new constraints explicitly or implicitly results that the model should yield if a new constraint is incompatible with the previous ones then the system becomes inconsistent and the dms must choose between removing the new constraint or removing some of the older ones we address the problem of identifying subsets of constraints which when removed lead to a consistent system identifying such subsets would indicate the reason for the inconsistent information given by dms there may exist several possibilities for the dms to resolve the inconsistency we present two algorithms to identify such possibilities one using 0 1 mixed integer linear programming and the other one using linear programming both approaches are based on the knowledge that the system was consistent prior to introducing the last constraint the output of these algorithms helps the dm to identify the conflicting pieces of information in a set of statements he she asserted the relevance of these algorithms for mcda is illustrated by an application to an aggregation disaggregation procedure for the electre tri method

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

a way to deal with fuzzy preferences in multi criteria decision problems this paper presents a special multiple criteria decision making approach for solving problems in context with fuzzy individual preferences at first we briefly expose the proposed methodology the individual preferences are explicitly given by a complete transitive relation r on a set of reference actions the modelling of the decision maker s preferences is obtained by means of fuzzy outranking relations these fuzzy relations are based on a system of additive utility functions which are estimated by means of ordinal regression methods analysing the preference relation r this is followed by a presentation of two real multicriteria problems which the proposed methodology has been applied to i e a highway plan choice problem and a problem in marketing research dealing with the launching of a new product in each application we tried to specify this method according to the specific structure of the problem considered

approximate controllability for nonlinear evolution hemivariational inequalities in hilbert spaces here we study the approximate controllability for control problems driven by a class of nonlinear evolution hemivariational inequalities in hilbert spaces actually our results cover a broader class of inclusion problems involving time dependent operators first by using a fixed point approach and nonsmooth analysis we show the existence of mild solutions for the inequality problem next we provide a sufficient condition guaranteeing the approximate controllability of our problem in terms of an associated linear control system an example demonstrates the applicability of our results

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

relational systems of preference with one or more pseudo criteria some new concepts and results this paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory sections 1 3 present four fundamental situations of preferences their combinations and the concept of relational system of preferences in 4 a particular case of relational system of preference is studied it is associated with the concept of pseudo criterion derived from the classical concept of criterion by adjunction of two thresholds some results are given generalizing the properties of such well known structures as complete preorders and semiorders sections 5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account

a linear programming approach for learning non monotonic additive value functions in multiple criteria decision aiding abstract a new framework for preference disaggregation in multiple criteria decision aiding is introduced the proposed approach aims to infer non monotonic additive preference models from a set of indirect pairwise comparisons the preference model is presented as a set of marginal value functions and the discriminatory power of the inferred preference model is maximized against its complexity to infer a value function that is compatible with the supplied preference information the proposed methodology leads to a linear programming optimization problem that is easy to solve the applicability and effectiveness of the new methodology is demonstrated in a thorough experimental analysis covering a broad range of decision problems

a constrained least squares regression model abstract least squares regression lsr is a widely used regression technique for multicategory classification conventional lsr model assumes that during the learning phase the labeled samples can be exactly transformed into a discrete label matrix which is too strict to learn a regression matrix for fitting the labels to overcome this drawback lots of lsr s variants utilize the soft target label which contains the continuous values to replace this discrete label to improve the learning performance since the regression matrix can be learnt from these soft target labels it is reasonable to assume that the samples in the same class have similar soft target labels nevertheless most of existing lsr based models don t adequately consider this similarity assumption in this paper we propose a constrained least squares regression clsr model for multicategory classification the main motivation of clsr is to force the samples in the same class to obtain the similar soft target labels to effectively optimize clsr we propose a novel alternating algorithm which can converge to the globally optimal solution extensive experiments results on face and digit data sets confirm the effectiveness of our proposed model

making choices with a binary relation relative choice axioms and transitive closures abstract this article presents an axiomatic analysis of the best choice decision problem from a reflexive crisp binary relation on a finite set a digraph with respect to a transitive digraph optimality and maximality are usually accepted as the best fitted choice axioms to the intuitive notion of best choice however beyond transitivity resp acyclicity optimality and maximality can characterise distinct choice sets resp empty sets accordingly different and rather unsatisfying concepts have appeared such as von neumann morgenstern domination weak transitive closure and kernels here we investigate a new family of eight choice axioms for digraphs relative choice axioms within choice theory these axioms generalise top cycle for tournaments gocha getcha and rational top cycle for complete digraphs we present their main properties such as existence uniqueness idempotence internal structure and cross comparison we then show their strong relationship with optimality and maximality when the latter are not empty otherwise these axioms identify a non empty choice set and underline conflicts between chosen elements in strict preference circuits finally we exploit the close link between this family and transitive closures to compute choice sets in linear time followed by a relevant practical application

functional anova ultramodularity and monotonicity applications in multiattribute utility theory abstract utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision maker s preference structure these properties are usually characterized via partial derivatives however elicitation methods do not necessarily lead to twice differentiable utility functions furthermore while in a single attribute context concavity fully reflects risk aversion in multiattribute problems such correspondence is not one to one we show that tsetlin and winkler s multivariate risk attitudes imply ultramodularity of the utility function we demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion functional anova the necessary and sufficient conditions under which monotonicity and or ultramodularity of single attribute functions imply the monotonicity and or ultramodularity of the corresponding multiattribute function under additive preferential and mutual utility independence are then established without reliance on the utility function differentiability we also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision maker s multivariate risk attitudes

an efficient weighted lagrangian twin support vector machine for imbalanced data classification abstract in this paper we propose an efficient weighted lagrangian twin support vector machine wltsvm for the imbalanced data classification based on using different training points for constructing the two proximal hyperplanes the main contributions of our wltsvm are 1 a graph based under sampling strategy is introduced to keep the proximity information which is robustness to outliers 2 the weight biases are embedded in the lagrangian twsvm formulations which overcomes the bias phenomenon in the original twsvm for the imbalanced data classification 3 the convergence of the training procedure of lagrangian functions is proven and 4 it is tested and compared with some other twsvms on synthetic and real datasets to show its feasibility and efficiency for the imbalanced data classification

approximate controllability of differential inclusions in hilbert spaces abstract in this paper controllability for the system originating from semilinear functional differential equations in hilbert spaces is studied we consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup generated by the linear part of the inclusion is compact and under the assumption that the corresponding linear system is approximately controllable by using resolvent of controllability gramian operator and fixed point theorem sufficient conditions have been formulated and proved an example is presented to illustrate the utility and applicability of the proposed method