group preference aggregation methods employed in ahp an evaluation and an intrinsic process for deriving members weightages abstract the analytic hierarchy process ahp is one of the popular and powerful techniques for decision making a detailed survey of the literature has revealed that there exists no formal evaluation of the group preference aggregation methods currently employed in ahp this paper provides such an evaluation using well established social choice axioms which govern the process of combining individual opinions to obtain a single group opinion the geometric mean method gmm and the weighted arithmetic mean method wamm are the two methods evaluated it is shown using counter examples that the gmm does not always satisfy the pareto optimality axiom which is one of the prominent and widely accepted social choice axioms this finding is significant as the gmm has been the most commonly used method in ahp for combining individual opinions to form a group opinion the other method viz wamm has satisfied all the axioms except the independence of irrelevant alternatives axiom in order to use the wamm one has to find the weightages importance to be assigned to the members of the group this is often a difficult task especially so if the group is large as in the case of public policy decisions and when judgements are elicited through the use of questionnaires these situations need an objective method to derive members weightages but only a few studies are available in the literature to address such a situation we propose a simple and intuitively appealing eigenvector based method to intrinsically determine the weightages for group members using their own subjective opinions the superiority of the proposed method over the previous methods is brought out in the paper

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

treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses finite element approximations of the stokes and navier stokes equations with in homogeneous essential boundary conditions are considered boundary conditions are enforced weakly by introducing lagrange multipliers optimal error estimates including some for the stress vector on the boundary are derived under minimal regularity assumptions on the data particular attention is paid to the analysis of a practical choice of finite element spaces for which the lagrange multiplier calculation uncouples from that for the velocity and pressure the results are also applicable to general second order elliptic systems

control of flow separation over a forward facing step by model reduction abstract design and implementation of reduced order optimal controller for flow separation are investigated the reduced order controller design is based on proper orthogonal decomposition pod and galerkin projection detailed finite element simulations are performed and pod is applied to the resulting data to extract the most energetic eigenmodes these global eigenmodes are then used in conjunction with the galerkin projection to obtain a reduced order low dimensional model reduced order models are not only attractive for real time control computation but also crucial for detailed stability and bifurcation analysis we investigate the design of optimal controller for flow separation in a channel with this model where actuation is performed on a small part of the boundary two different types of surface actuation are considered tangential blowing and suction through a single slot best locations for actuation and adaptive procedure for reduced order model are explored the proposed approaches are evaluated by investigating the control of flow separation over a forward facing step channel our methods are found to be efficient and fast and our methods demonstrate a significant reduction in computational time and feasibility dramatic separation delays are observed on all cases it is found that the tangential blowing is more efficient in mitigating flow separation and reducing wake spread

tools for interactive multiattribute decisionmaking with incompletely identified information abstract the aim of this paper is to present tools or techniques for an interactive multiattribute decisionmaking with the decision maker s incomplete information that is 1 we formally describe mathematical models under certainty and uncertainty for establishing pairwise dominance where the incomplete information becomes the set of constraints in the model 2 we present a description on styles of incomplete parameter value information 3 the characteristic of a weak dominance is described when the decision maker is not willing or able to provide more information on parameters the weak dominance technique is useful for a final choicemaking 4 we propose a dominance graph and also present an algorithm of generating the dominance graph based on the information of pairwise dominance the dominance graph compactly displays the dominance structure of all alternatives thus it can be used for aiding the selection of preferable alternatives

observer based feedback boundary stabilization of the navier stokes equations abstract this paper aims at designing an observer based feedback law which locally stabilizes the solution to the two dimensional navier stokes equations with mixed boundary conditions we consider a finite number of controls acting on a portion of the boundary through robin boundary conditions and construct a linear luenberger observer based on the point observations of the linearized navier stokes equations the sensor location for the point observations is determined by the response of feedback functional gains we prove that the nonlinear system coupled with the observer through the feedback law is locally exponentially stable numerical experiments based on a taylor hood finite element method are presented to illustrate the design for different reynolds numbers

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

linear feedback control and approximation for a system governed by unsteady mhd equations abstract we are concerned with the feedback control of unsteady flow of an electrically conducting fluid confined to a bounded region of space and driven by a combination of distributed body force and externally generated currents the flow is governed by the navier stokes equations and maxwell s equations coupled via ohm s law and the lorentz force the mathematical formulation and numerical resolution of the linear feedback control problem for tracking velocity and magnetic fields of electrically conducting flows in two dimensional domain are presented semi discrete in time and full space time discrete approximations are also studied computational results showing the efficacy of the feedback control are presented and compared with analogous results using optimal control theory

real time computational algorithm for optimal control of an mhd flow system the flow of weakly electrically conducting fluids can be controlled by electromagnetic forces originating from electrodes and permanent magnets we consider the possibility of separation control for an electrically conducting bluff body flow with reduced order modeling the reduced order model is derived using the proper orthogonal decomposition pod and galerkin projection the pod allows one to extract the dominant modes in the observed physical phenomena and to define the smallest possible solution space this can be exploited in a galerkin framework to reduce break the nonlinear infinite dimensional model to a small finite dimensional model we investigate the design of a reduced order nonlinear optimal controller for flow separation in a channel we present numerical experiments with an applied spanwise magnetic field distribution and a boundary electric potential actuation on a part of the boundary our methods are found to be efficient and fast and our methods demonstrate a significant reduction in computational time

ranking with partial information a method and an application a method is presented for ranking multiattributed alternatives using a weighted additive evaluation function with partial information about the weighting scaling constants the method is applied to evaluate materials for use in nuclear waste containment the paper derives conditions to determine whether a pair of alternatives can be ranked given the partial information about weighting constants and presents an algorithm that partially rank orders the complete set of alternatives based on the pairwise ranking information

reduced basis approximation of parametrized optimal flow control problems for the stokes equations this paper extends the reduced basis method for the solution of parametrized optimal control problems presented in negri et al 2013 to the case of noncoercive elliptic equations such as the stokes equations we discuss both the theoretical properties with particular emphasis on the stability of the resulting double nested saddle point problems and on aggregated error estimates and the computational aspects of the method then we apply it to solve a benchmark vorticity minimization problem for a parametrized bluff body immersed in a two or a three dimensional flow through boundary control demonstrating the effectivity of the methodology

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

an energy space finite element approach for elliptic dirichlet boundary control problems in this paper we present a finite element analysis for a dirichlet boundary control problem where the dirichlet control is considered in a convex closed subspace of the energy space h 1 2 gamma h 1 2 as an equivalent norm in h 1 2 gamma h 1 2 we use the energy norm induced by the so called steklov poincare operator which realizes the dirichlet to neumann map and which can be implemented by using standard finite element methods the presented stability and error analysis of the discretization of the resulting variational inequality is based on the mapping properties of the solution operators related to the primal and adjoint boundary value problems and their finite element approximations some numerical results are given which confirm on one hand the theoretical estimates but on the other hand indicate the differences when modelling the control in l 2 gamma l 2

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

domain decomposition methods for advection dominated linear quadratic elliptic optimal control problems abstract we present an optimization level domain decomposition dd preconditioner for the solution of advection dominated elliptic linear quadratic optimal control problems which arise in many science and engineering applications the dd preconditioner is based on a decomposition of the optimality conditions for the elliptic linear quadratic optimal control problem into smaller subdomain optimality conditions with dirichlet boundary conditions for the states and the adjoints on the subdomain interfaces these subdomain optimality conditions are coupled through robin transmission conditions for the states and the adjoints the parameters in the robin transmission condition depend on the advection this decomposition leads to a schur complement system in which the unknowns are the state and adjoint variables on the subdomain interfaces the schur complement operator is the sum of subdomain schur complement operators the application of which is shown to correspond to the solution of subdomain optimal control problems which are essentially smaller copies of the original optimal control problem we show that under suitable conditions the application of the inverse of the subdomain schur complement operators requires the solution of a subdomain elliptic linear quadratic optimal control problem with robin boundary conditions for the state numerical tests for problems with distributed and with boundary control show that the dependence of the preconditioners on mesh size and subdomain size is comparable to its counterpart applied to a single advection dominated equation these tests also show that the preconditioners are insensitive to the size of the control regularization parameter

optimization based additive decomposition of weakly coercive problems with applications we present an abstract mathematical framework for an optimization based additive decomposition of a large class of variational problems into a collection of concurrent subproblems the framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions the significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems consequently assuming that stable numerical methods and efficient solvers are available for every subproblem our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily an application of the framework to the oseen equations illustrates its potential

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

optimal control of navier stokes equations by oseen approximation a non standard sequential quadratic programming type iterational process based on oseen s approximation is proposed and analyzed to solve an optimal control problem for the steady state navier stokes equations further numerical approximation by a finite element method and sample computational experiments are presented too

computations of boundary optimal control problems for an electrically conducting fluid we study four optimal control problems for an electrically conducting fluid the control is the normal electrical current on the boundary of the flow domain the objectives are to match a desired velocity field or to match a desired electrical potential field or to minimize the potential gradient or to minimize the vorticity in the flow domain we develop a systematic way to use the lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed mixed finite element methods are used to find approximate solutions for the optimality systems of equations that characterize the optimal controls a direct method and an iterative method are proposed for solving the discrete nonlinear optimality systems of equations numerical results for several examples are presented

existence of optimal controls for viscous flow problems a class of optimal control problems in viscous flow is studied main result is the existence theorem for optimal control three typical flow control problems are formulated within this general class

adaptive reduced order controllers for a thermal flow system using proper orthogonal decomposition an adaptive reduced order controller design is presented for flow control using proper orthogonal decomposition pod in reduced order controller design the idea is to start with an ensemble of data obtained from numerical simulation of the underlying partial differential equations pdes pod is then used to obtain a reduced set of basis functions which is then used to derive a reduced order model of the pdes via galerkin projection this reduced order model allows us to derive a reduced order controller however it is not clear a priori what is the best way to obtain an ensemble of data that would give basis functions that represent the influence of the control action on the system in this paper we explore an adaptive procedure for reduced order controller design that improves the reduced order model by successively updating the ensemble of data during the optimization iterations we illustrate this method on a control problem in thermal flow system modeled by a thermally coupled navier stokes equations numerical results are presented for a vorticity regulation problem in fluid flows using boundary temperature as control mechanism through our numerical experiments we demonstrate the feasibility and applicability of the adaptive reduced order controllers

group decision making based on acceptable multiplicative consistency of hesitant fuzzy preference relations abstract this paper deals with group decision making gdm with hesitant fuzzy preference relations hfprs based on the acceptable multiplicative consistency and the consensus analysis we first offer a multiplicative consistency index for fuzzy preference relations fprs and then use the monte carlo simulation method to derive the average multiplicative consistency value after that a model based interactive algorithm is offered to test acceptable multiplicative consistency of hfprs by which the concept of acceptable multiplicative consistency for hfprs is obtained meanwhile a model based interactive algorithm for deriving acceptable multiplicative consistent hfprs from unacceptable multiplicative consistent ones is provided where both the total adjustment and the number of adjusted variables are considered as for incomplete hfprs a model based interactive algorithm for getting the values of missing preferences is provided furthermore the weights of the decision makers are determined by the offered model and an algorithm of model based adjustment for the consensus level is provided finally a procedure for gdm with acceptable multiplicative consistent hfprs is given and a case study about selecting the most suitable project management information systems pmiss is provided to show the application of the proposed gdm method and to compare the proposed gdm method with the previous gdm methods

optimal boundary feedback flow stabilization by model reduction abstract in this paper we consider the optimal boundary feedback stabilization of fluid flows governed by navier stokes equations using model reduction the model reduction is carried out using a combination of proper orthogonal decomposition pod and galerkin projection the resulting reduced order model is employed in the optimal linear quadratic regulator lqr design to derive a feedback control the feedback control is then used in the nonlinear navier stokes equation to stabilize the system sufficient conditions are derived for the linear control to stabilize the nonlinear system feasibility of the proposed boundary feedback stabilization design is numerically demonstrated on the problem of stabilizing the flow past an airfoil the control is effected through unsteady blowing on the airfoil surface the computational results show that the closed loop system amplitudes converge to the desired equilibrium state showing the stability predicted by the theory in addition they show that downstream directed blowing on the upper surface of the airfoil near the leading edge is more efficient in stabilizing the state

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

numerical approximation of optimal flow control problems by a penalty method error estimates and numerical results the purpose of this paper is to present numerically convenient approaches to solve optimal dirichlet control problems governed by the steady navier stokes equations we will examine a penalized neumann control approach for solving dirichlet control problems from numerical and computational points of view the control is affected by the suction or injection of fluid through the boundary or by boundary surface movements in the tangential direction the control objective is to minimize the vorticity in the flow or to drive the velocity field to a desired one we develop sequential quadratic programming methods to solve these optimal control problems the effectiveness of the optimal control techniques in flow controls and the feasibility of the proposed penalized neumann control approaches for flow control problems are demonstrated by numerical experiments for a viscous incompressible fluid flow in a two dimensional channel and in a cavity geometry

analysis and finite element approximation of optimal control problems for the stationary navier stokes equations with distributed and neumann controls we examine certain analytic and numerical aspects of optimal control problems for the stationary navier stokes equations the controls considered may be of either the distributed or neumann type the functionals minimized are either the viscous dissipation or the l4 distance of candidate flows to some desired flow we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider the approximation by finite element methods of solutions of the optimality system and derive optimal error estimates

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

monte carlo simulation techniques for group decision making with incomplete information abstract in this paper we deal with group decision making problems where several decision makers elicit their own preferences separately the decision makers preferences are quantified using a decision support system which admits incomplete information concerning the decision makers responses to the questions they are asked consequently each decision maker proposes classes of utility functions and attribute weight intervals for the different attributes we introduce an approach based on monte carlo simulation techniques for aggregating decision maker preferences that could be the starting point for a negotiation process if necessary the negotiation process would basically involve the decision maker tightening the imprecise component utilities and weights to output more meaningful results and achieve a consensus alternative we focus on how attribute weights and the component utilities associated with a consequence are randomly generated in the aggregation process taking into account the decision makers preferences i e their respective attribute weight intervals and classes of utility functions finally an application to the evaluation of intervention strategies for restoring a radionuclide contaminated lake illustrates the usefulness and flexibility of this iterative process

smooth and robust solutions for dirichlet boundary control of fluid solid conjugate heat transfer problems we study a new optimization scheme that generates smooth and robust solutions for dirichlet velocity boundary control dvbc of conjugate heat transfer cht processes the solutions to the dvbc of the incompressible navier stokes equations are typically nonsmooth due to the regularity degradation of the boundary stress in the adjoint navier stokes equations this nonsmoothness is inherited by the solutions to the dvbc of cht processes since the cht process couples the navier stokes equations of fluid motion with the convection diffusion equations of fluid solid thermal interaction our objective in the cht boundary control problem is to select optimally the fluid inflow profile that minimizes an objective function that involves the sum of the mismatch between the temperature distribution in the fluid system and a prescribed temperature profile and the cost of the control our strategy to resolve the nonsmoothness of the boundary control solution is based on two features namely the objective function with a regularization term on the gradient of the control profile on both the continuous and the discrete levels and the optimization scheme with either explicit or implicit smoothing effects such as the smoothed steepest descent and the limited memory broyden fletcher goldfarb shanno l bfgs methods our strategy to achieve the robustness of the solution process is based on combining the smoothed optimization scheme with the numerical continuation technique on the regularization parameters in the objective function in the section of numerical studies we present two suites of experiments in the first one we demonstrate the feasibility and effectiveness of our numerical schemes in recovering the boundary control profile of the standard case of a poiseuille flow in the second one we illustrate the robustness of our optimization schemes via solving more challenging dvbc problems for both the channel flow and the flow past a square cylinder which use initial control profiles far from optimal and require the numerical continuation technique applied on regularization parameters we believe our solution strategy is general and can be applied to other large scale optimal control problems which involve multiphysics processes and require smooth approximations to the optimal control profile

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

a new group ranking approach for ordinal preferences based on group maximum consensus sequences group ranking problems involve aggregating individual rankings to generate group ranking which represents consolidated group preference group ranking problems are commonly applied in real world decision making problems however supporting a group decision making process is difficult due to the existence of multiple decision makers each with his her own opinions hence determining how to best aid the group ranking process is an important consideration this study aims to determine a total ranking list which meets group consensus preferences for group ranking problems a new group consensus mining approach based on the concept of tournament matrices and directed graphs is first developed an optimization model involving maximum consensus sequences is then constructed to achieve a total ranking list compared to previous methods the proposed approach can generate a total ranking list involving group consensus preferences it can also determine maximum consensus sequences without the need for tedious candidate generation processes while also providing flexibility in solving ranking problems using different input preferences that vary in format and completeness in addition consensus levels are adjustable

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

feedback stabilization of a thermal fluid system with mixed boundary control we consider the problem of local exponential stabilization of the nonlinear boussinesq equations with control acting on portion of the boundary in particular given a steady state solution on an bounded and connected domain r 2 we show that a finite number of controls acting on a part of the boundary through neumann robin boundary conditions is sufficient to stabilize the full nonlinear equations in a neighborhood of this steady state solution dirichlet boundary conditions are imposed on the rest of the boundary we prove that a stabilizing feedback control law can be obtained by solving a linear quadratic regulator lqr problem for the linearized boussinesq equations numerical result are provided for a 2d problem to illustrate the ideas

bivariate second order linear partial differential equations and orthogonal polynomial solutions in this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second order linear partial differential equations which are admissible potentially self adjoint and of hypergeometric type general formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation using vector matrix notation moreover rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given as illustration these results are applied to a two parameter monic appell polynomials finally the non monic case is briefly discussed 2011 elsevier inc

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

the ordinal consistency of an incomplete reciprocal preference relation the ordinal consistency is the usual weak transitivity condition that a logical and consistent person should use if he she does not want to express inconsistent opinions and therefore becomes the minimum requirement condition that a consistent reciprocal preference relation should verify in this paper we define and study the ordinal consistency of an incomplete reciprocal preference relation we then develop an algorithm to judge whether an incomplete reciprocal preference relation is ordinally consistent this proposed algorithm can also find all cycles of length 3 to n in the incomplete digraph of the incomplete reciprocal preference relation based on this proposed algorithm and two rules we develop another algorithm to repair an inconsistent incomplete reciprocal preference relation and to convert it to one with ordinal consistency our algorithm eliminates the cycles of length 3 to n in the digraph of an incomplete reciprocal preference relation most effectively our proposed method can preserve the initial preference information as much as possible furthermore the proposed method can be used for an incomplete reciprocal preference relation with strict comparison and non strict comparison information finally the effectiveness and validity of the proposed method are illustrated with examples

optimal control of thermally convected fluid flows we examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view we use thermal convection as control mechanism that is control is effected through the temperature on part of the boundary control problems are formulated as constrained minimization problems existence of optimal control is given and a first order necessary condition of optimality from which optimal solutions can be obtained is established we develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity and channel type flows showing the feasibility of the proposed approach

semidiscretization and error estimates for distributed control of the instationary navier stokes equations optimal control problems governed by the two dimensional instationary navier stokes equations and their spatial discretizations with finite elements are investigated a concept of semi discrete solutions to the control problem is introduced which is utilized to prove existence and uniqueness of discrete controls in neighborhoods of regular continuous solutions furthermore an optimal error estimate in terms of the spatial discretization parameter is given

group decision making based on multiplicative consistent reciprocal preference relations the main aim of this paper is to investigate the consistency and consensus of multiplicative consistent reciprocal preference relations based on the multiplicative consistency property a straightforward method to obtain the priority vector for multiplicative consistent reciprocal preference relation is introduced together with some of its desired properties in addition some interesting properties on consistency and consensus for reciprocal preference relations are further investigated a consensus optimization model for group decision making with reciprocal preference relations is proposed which enables the decision makers to reach consensus with the highest overall consensus level numerical examples are provided to make a discussion and comparison with some existing similar methods

dynamic programming of the navier stokes equations a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation

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