a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

adaptive anisotropic wavelet collocation method on general curvilinear coordinate systems a new general framework for an adaptive anisotropic wavelet collocation method a awcm for the solution of partial differential equations is developed this proposed framework addresses two major shortcomings of existing wavelet based adaptive numerical methodologies namely the reliance on a rectangular domain and the curse of anisotropy i e drastic over resolution of sheet and filament like features arising from the inability of the wavelet refinement mechanism to distinguish highly correlated directional information in the solution the a awcm addresses both of these challenges by incorporating coordinate transforms into the adaptive wavelet collocation method for the solution of pdes the resulting integrated framework leverages the advantages of both the curvilinear anisotropic meshes and wavelet based adaptive refinement in a complimentary fashion resulting in greatly reduced cost of resolution for anisotropic features the proposed adaptive anisotropic wavelet collocation method retains the a priori error control of the solution and fully automated mesh refinement while offering new abilities through the flexible mesh geometry including body fitting the new a awcm is demonstrated for a variety of cases including parabolic diffusion acoustic scattering and unsteady external flow

ranking fuzzy numbers with integral value abstract ranking fuzzy numbers is important in decision making since very often the alternatives are evaluated by fuzzy numbers in a vague environment a comparison between these fuzzy numbers is indeed a comparison between alternatives this paper proposes a method of ranking fuzzy numbers with integral value the method which is independent of the type of membership functions used and the normality of the functions can rank more than two fuzzy numbers simultaneously it is relatively simple in computation especially in ranking triangular and trapezoidal fuzzy numbers further an index of optimism is used to reflect the decision maker s optimistic attitude discussion on comparative advantages is included

a new fuzzy multi objective programming entropy based geometric programming and its application of transportation problems in this paper we introduce a fuzzy mathematical programming with generalized fuzzy number as objective coefficients we also examine a transportation problem with additional restriction there is an additional entropy objective function in the transportation problem besides transportation cost objective function using new fuzzy mathematical programming this multi objective entropy transportation problem with generalized trapezoidal fuzzy number costs has been reduced to a primal geometric programming problem pareto optimal solution of the transportation model is found numerical examples have been provided to illustrate the problem

parallel adaptive wavelet collocation method for pdes a parallel adaptive wavelet collocation method for solving a large class of partial differential equations is presented the parallelization is achieved by developing an asynchronous parallel wavelet transform which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution the data are stored using tree like structure with tree roots starting at a priori defined level of resolution both static and dynamic domain partitioning approaches are developed for the dynamic domain partitioning trees are considered to be the minimum quanta of data to be migrated between the processes this allows fully automated and efficient handling of non simply connected partitioning of a computational domain dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process the parallel efficiency of the approach is discussed based on parallel adaptive wavelet based coherent vortex simulations of homogeneous turbulence with linear forcing at effective non adaptive resolutions up to 20483 using as many as 2048 cpu cores

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

a penalization method to take into account obstacles in incompressible viscous flows from the navier stokes brinkman model a penalization method has been derived by several authors to compute incompressible navier stokes equations around obstacles in this paper convergence theorems and error estimates are derived for two kinds of penalization the first one corresponds to l 2 penalization inducing a darcy equation in the solid body the second one corresponds to a h 1 penalization and induces a brinkman equation in the body numerical tests are performed to confirm the efficiency and accuracy of the method

more on stochastic models in a recent review article g sposito et al 1986 examined the various stochastic theories which are concerned with transport of solutes in porous media in this short note we expand on their discussion to include several topics which had been omitted we begin by looking at two definitions of probability theory and their relation to the concept of an ensemble an rev ensemble of soils is defined and examined the concept of ergodicity is reviewed and it is pointed out that most stochastic models are theoretically unverifiable the relationship between scale of measurement and stochasticity is briefly reviewed and an equation that combines the two concepts is presented

a dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain a dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where sharp transitions occur the scheme handles general boundary conditions the method is applied to the solution of the one dimensional burgers equation with small viscosity a moving shock problem and a nonlinear thermoacoustic wave problem the results indicate that the method is very accurate and efficient

a chance constrained fuzzy goal program abstract a chance constrained goal program in the case of having uncertain aspiration levels is considered however these aspiration levels are random variables with known probability distribution functions the goal constraints considered are probabilistic and fuzzy constraints the equivalent deterministic goal program is developed and an illustrative example is given

application of fuzzy theories to multiple objective decision making in system design abstract much decision making in the real world takes place in an environment in which the goals constraints and consequences of possible actions are not known precisely to deal with such imprecision in a quantitative manner the tools of fuzzy set theory can be advantageously applied the use and effectiveness of fuzzy theories in the formulation and solution of design problems are developed and described via an application in the engineering design of high speed mechanisms an integrated approach to the design of high speed planar mechanisms is formulated as a multiple objective nonlinear programming problem which combines both the kinematic and dynamic synthesis aspects of mechanism design to model the vague and imprecise information in the problem formulation the tools of fuzzy set theory have been used a novel method of solving the resulting fuzzy multiple objective problem using mathematical programming techniques is presented the outlined procedure should be useful in engineering and management design situations where uncertainty or ambiguity arises about the preciseness of permissible parameters degree of credibility and correctness of statements and judgements

equivalence of bicontinuum and second order transport in heterogeneous soils and aquifers the mathematical equivalence of a closed second order transport equation for reactive solutes in saturated heterogeneous porous media e g soils and aquifers and a two region mobile mobile formulation is demonstrated in two ways 1 by averaging the bicontinuum equations and 2 by transforming the second order equation to canonical form the derivation of this equivalence is limited to media with heterogeneities in a plane orthogonal to the flow direction which represents a bidirectional generalization of the stratified case results indicate how the parameters of the bicontinuum formulation can be obtained from statistical descriptions of this heterogeneity and establish a stochastic interpretation for the bicontinuum equations one dimensional analytical solutions of the equivalent transport equations are compared to a three dimensional numerical simulation of transport in a spatially autocorrelated lognormal random conductivity field results indicate that the upscaled equations provide good approximations of the dynamics of the mean resident concentration the flux averaged concentration and their variances

solution of optimal control problems with lumped parameters having single or multiple goal objectives in fuzzy environment abstract in this paper optimal control problems ocp of both linear and nonlinear type with lumped parameters are considered continuous ocp with single or multiple objectives are transformed to finite dimensional optimization problems through discretization the formulation of goal optimal control problem gocp using goal programming methodology first given by levary 1986 for equal time subintervals is extended for unequal subintervals by a generalized formulation the concept of local and global goals proposed here is very useful for multicriteria dynamic optimization problems in several physical situations ocp involve fuzziness in their goals priorities parameters or relative weights and associated linguistic variables etc a new formulation of ocp in fuzzy environment is given as a fuzzy goal optimal control problem fgocp and the solution procedure is illustrated by linear and nonlinear examples

a geometric averaging procedure for constructing supertransitive approximation to binary comparison matrices abstract the usefulness of encoding the fuzzy evaluations of alternatives and the importance weights of criteria in a multiple objective decision problem through binary comparison matrices or pairwise judgment matrices is receiving considerable attention the methodology for identifying the best alternative in a given decision problem involves the computation of the principal eigenvectors of the binary comparison matrices the eigenvectors transform the fuzzy evaluations of the importance of the criteria and the ratings of the alternatives into a ratio scale a difficulty that is often experienced in using this approach in practice is the inconsistency of the binary evaluations this paper proposes a simple averaging procedure to construct a supertransitive approximation to a binary comparison matrix where inconsistency is a problem it is further suggested that such an adjustment might be necessary to more closely reflect the inherent fuzziness of the evaluations contained in a binary comparison matrix the procedure is illustrated by means of examples

convergence of a brinkman type penalization for compressible fluid flows abstract we show convergence of a brinkman type penalization of the compressible navier stokes equation in particular the existence of weak solutions for the system in domains with boundaries varying in time is established

taylor series approach to fuzzy multiobjective linear fractional programming this paper presents the use of a taylor series for fuzzy multiobjective linear fractional programming problems fmolfp the taylor series is a series expansion that a representation of a function in the proposed approach membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a taylor series are unified thus the problem is reduced to a single objective practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach

bector chandra type duality in fuzzy linear programming with exponential membership functions in this paper we study a pair of fuzzy primal dual linear programming problems and calculate duality results using an aspiration level approach we use an exponential membership function which is in contrast to the earlier works that relied on a linear membership function as the fuzzy environment causes a duality gap we investigate how choosing the exponential membership function impacts this gap this issue is particularly important for fuzzy linear programming where in general the primal and dual objective values may not be bounded

fuzzy programming technique to solve multi objective transportation problems with some non linear membership functions abstract the multi objective transportation problem refers to a special class of vector minimum linear programming problems in which the constraints are of equality type and all the objectives are non commensurable and conflict with each other all the methods either generate a set of non dominated solutions or find a compromise solution in this paper we use a special type of non linear hyperbolic and exponential membership functions to solve the multi objective transportation problem it gives an optimal compromise solution the obtained result has been compared with the solution obtained by using a linear membership function to illustrate the methodology a numerical example is presented

fuzzy multi attribute selection among transportation companies using axiomatic design and analytic hierarchy process the basic concept in axiomatic design ad is the existence of design axioms first of these axioms is the independence axiom and the second one is the information axiom information axiom proposes the selection of the best alternative that has minimum information analytic hierarchy process ahp is another multi attribute method which is a decision making method for selecting the best among a set of alternatives given some criteria the method has been extensively applied especially in large scale problems where many criteria must be considered and where the evaluation of alternatives is mostly subjective multi attribute transportation company selection is a very important activity for effective supply chain selection of the best company under determined criteria such as cost time damage loss flexibility and documentation ability using both multi attribute ad and ahp will be realized in this study the fuzzy multiattribute ad approach is also developed and it is compared by one of fuzzy ahp methods in the literature the selection process has been accomplished by aiding a software that includes crisp ad and fuzzy ad

a high order immersed interface method for simulating unsteady incompressible flows on irregular domains immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a cartesian grid while good results both qualitative and quantitative have been obtained most of the methods rely on low order corrections to account for the immersed boundary the objective of the present work is to present as an alternative a high order modified immersed interface method for the 2d unsteady incompressible navier stokes equations in stream function vorticity formulation the method employs an explicit fourth order runge kutta time integration scheme fourth order compact finite differences for computation of spatial derivatives and a nine point fourth order compact discretization of the poisson equation for computation of the stream function corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary as confirmed by analytical tests to validate the method in its application to incompressible flows several physically relevant test cases are computed including uniform flow past a circular cylinder and tollmien schlichting waves in a boundary layer

a fourier penalty method for solving the time dependent maxwell s equations in domains with curved boundaries we present a high order fourier penalty method for the maxwell s equations in the vicinity of perfect electric conductor boundary conditions the approach relies on extending the smooth non periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain the forcing or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter which then allows for higher order numerical methods we present an efficient numerical method for constructing the penalty term and discretize the resulting equations using a fourier spectral method we demonstrate convergence orders of up to 3 5 for the one dimensional maxwell s equations and show that the numerical method does not suffer from dispersion or pollution errors we also illustrate the approach in two dimensions and demonstrate convergence orders of 2 5 for transverse magnetic modes and 1 5 for the transverse electric modes we conclude the paper with numerous test cases in dimensions two and three including waves traveling in a bent waveguide and scattering off of a windmill like geometry

stochastic analysis of nonstationary subsurface solute transport 1 unconditional moments this paper applies stochastic methods to the analysis and prediction of solute transport in heterogeneous saturated porous media partial differential equations for three unconditional ensemble moments the concentration mean concentration covariance and velocity concentration cross covariance are derived by applying perturbation techniques to the governing transport equation for a conservative solute concentration uncertainty is assumed to be the result of unmodeled small scale fluctuations in a steady state velocity field the moment expressions which describe how each moment evolves over time and space resemble the classic deterministic advection dispersion equation and can be solved using similar methods a solution procedure based on a galerkin finite element algorithm is illustrated with a hypothetical two dimensional example for this example the required steady state velocity statistics are obtained from an infinite domain spectral solution of the stochastic groundwater flow equation the perturbation solution is shown to reproduce the statistics obtained from a monte carlo simulation quite well for a natural log conductivity standard deviation of 0 5 and moderately well for a natural log conductivity standard deviation of 1 0 the computational effort required for a perturbation solution is significantly less than that required for a monte carlo solution of acceptable accuracy sensitivity analyses conducted with the perturbation approach provide qualitative confirmation of a number of results obtained by other investigators for more restrictive special cases

satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem this paper proposes a satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem the aim of this presented approach is to make the more important objective achieving the higher desirable satisfying degree for different fuzzy relations and fuzzy importance the reformulated optimization models based on goal programming is proposed not only the satisfying results of all the objectives can be acquired but also the fuzzy importance requirement can be simultaneously actualized the balance between optimization and relative importance is realized we demonstrate the efficiency flexibility and sensitivity of the proposed method by numerical examples

inertial effects in dispersion in porous media 1 in this work we develop the macroscale transport equation for dispersion of a nonreactive chemical species with a particular focus on the influence of inertial contributions at moderate reynolds numbers our starting point is the continuum level description of transport written at the subpore scale volume averaging is used to upscale these equations to develop the macroscale solute balance that applies at the darcy scale we develop a fully transient version of the ancillary closure problem that predicts the total dispersion tensor and we solve the closure using finite fourier transforms the result of this effort is a nonlocal macroscale transport equation where the nonlocal dispersion depends upon the microscale geometry of the pore space and the physical characteristics of the fluid both the longitudinal and transverse components of the total dispersion tensor are computed for a simple three dimensional unit cell the computational results indicate that a simple three dimensional periodic unit cell is able to capture the correct behavior for the longitudinal dispersion in the range 101 pep 2 5 105 although the magnitude of the longitudinal dispersion coefficient is underpredicted by up to a factor of about 4 for the transverse dispersion coefficient the simple unit cell provides much less satisfactory results when compared with experimental data the inertial effects for the longitudinal dispersion coefficient were relatively small but for the transverse dispersion coefficient inertial effects were predicted to increase the transverse dispersion coefficient up to 40 times that which would be predicted for stokes flow

on finding compromise solutions in multicriteria problems using the fuzzy min operator abstract this paper presents an application of fuzzy approaches to the linear vectormaximum problem it shows that using the fuzzy min operator together with linear as well as special nonlinear membership functions the obtained solutions are always compromise solutions of the original multicriteria problem

priority structure in fuzzy goal programming abstract this paper introduces priority structure in fuzzy goal programming fgp this approach utilizes the lexicographic order of goal programming gp and yields an efficient computational algorithm for solving fgp fuzzy priorities are also discussed a numerical example is given to highlight the procedure concluding remarks are also made

a volume penalization method for incompressible flows and scalar advection diffusion with moving obstacles a volume penalization method for imposing homogeneous neumann boundary conditions in advection diffusion equations is presented thus complex geometries which even may vary in time can be treated efficiently using discretizations on a cartesian grid a mathematical analysis of the method is conducted first for the one dimensional heat equation which yields estimates of the penalization error the results are then confirmed numerically in one and two space dimensions simulations of two dimensional incompressible flows with passive scalars using a classical fourier pseudo spectral method validate the approach for moving obstacles the potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no slip and no flux boundary conditions are imposed respectively

a brinkman penalization method for compressible flows in complex geometries to simulate flows around solid obstacles of complex geometries various immersed boundary methods had been developed their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non body conformal cartesian grids the brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations its main idea is to model solid obstacles as porous media with porosity f and viscous permeability approaching zero it has the pronounced advantages of mathematical proof of error bound strong convergence and ease of numerical implementation with the volume penalization technique in this paper it is extended to compressible flows the straightforward extension of penalizing momentum and energy equations using brinkman penalization with respective normalized viscous h and thermal h t permeabilities produces unsatisfactory results mostly due to nonphysical wave transmissions into obstacles resulting in considerable energy and mass losses in reflected waves the objective of this paper is to extend the brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media in addition to penalizing momentum and energy equations the continuity equation for porous media is considered inside obstacles in this model the penalized porous region acts as a high impedance medium resulting in negligible wave transmissions the asymptotic analysis reveals that the proposed brinkman penalization technique results in the amplitude and phase errors of order o email protected 1 2 and o h h t 1 email protected 3 4 when the boundary layer within the porous media is respectively resolved or unresolved the proposed method is tested using 1 and 2 d benchmark problems the results of direct numerical simulation are in excellent agreement with the analytical solutions the numerical simulations verify the accuracy and convergence rates

fuzzy goal programming with nested priorities abstract this paper proposes a new approach to formulating fuzzy priorities in a goal programming problem the proposed methodology remedies certain shortcomings of the composite membership function approach discussed in previous works 7 10 the principal advantage of the proposed method is that it leads to a formulation in which tradeoffs between goals more closely reflect the decision maker s intentions than in other noninteractive approaches 8 9 10 14 in some of which a fixed hierarchy of goals is assumed

a characteristic based volume penalization method for general evolution problems applied to compressible viscous flows in order to introduce solid obstacles into flows several different methods are used including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations one well known method is brinkman penalization which models solid obstacles as porous media while it has been adapted for compressible incompressible viscous and inviscid flows it is limited in the types of boundary conditions that it imposes as are most volume penalization methods typically approaches are limited to dirichlet boundary conditions in this paper brinkman penalization is extended for generalized neumann and robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles this characteristic based volume penalization cbvp method is a comprehensive approach to conditions on immersed boundaries providing for homogeneous and inhomogeneous dirichlet neumann and robin boundary conditions on hyperbolic and parabolic equations this cbvp method can be used to impose boundary conditions for both integrated and non integrated variables in a systematic manner that parallels the prescription of exact boundary conditions furthermore the method does not depend upon a physical model as with porous media approach for brinkman penalization and is therefore flexible for various physical regimes and general evolutionary equations here the method is applied to scalar diffusion and to direct numerical simulation of compressible viscous flows with the navier stokes equations both homogeneous and inhomogeneous neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder theoretical and numerical examination shows that the error from penalized neumann and robin boundary conditions can be rigorously controlled through an a priori penalization parameter h the error on a transient boundary is found to converge as o h which is more favorable than the error convergence of the already established dirichlet boundary condition

fuzzy programming approach to multicriteria decision making transportation problem abstract the linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conflicting in nature all existing methods generate a set of nondominated solutions or construct a single compromise solution this paper presents an application of fuzzy linear programming to the linear multiobjective transportation problem it gives efficient solutions as well as an optimal compromise solution for this method an efficient fortran program has been developed based on the fuzzy linear programming algorithm which is an extended version of the simplex algorithm this method is compared with two existing interactive algorithms using two numerical examples

solving fuzzy transportation problems based on extension principle abstract transportation models play an important role in logistics and supply chain management for reducing cost and improving service this paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem in that the cost coefficients and the supply and demand quantities are fuzzy numbers the idea is based on the extension principle a pair of mathematical programs is formulated to calculate the lower and upper bounds of the fuzzy total transportation cost at possibility level from different values of the membership function of the objective value is constructed two different types of the fuzzy transportation problem are discussed one with inequality constraints and the other with equality constraints it is found that the membership function of the objective value of the equality problem is contained in that of the inequality problem since the objective value is expressed by a membership function rather than by a crisp value more information is provided for making decisions

a fictitious domain approach with spread interface for elliptic problems with general boundary conditions the aim of this article is to solve second order elliptic problems in an original physical domain using a fictitious domain method with a spread interface approach the main idea of the fictitious domain approach consists in immersing the original domain of study into a geometrically bigger and simpler one called fictitious domain as the spatial discretization is being performed in the fictitious domain this method allows the use of structured meshes the discretization is not boundary fitted to the original physical domain this paper describes several ways to impose dirichlet robin or neumann boundary conditions on a spread immersed interface without locally modifying the numerical scheme and without using lagrange multipliers the numerical applications focus on difiusion and convection problems in the unit disk with dirichlet or robin boundary conditions for such problems analytical solutions can be determined for a correctly chosen source term the numerical resolution is performed using a q1 finite element scheme the spread interface approach is then combined with a local adaptive mesh refinement algorithm in order to increase the precision in the vinicity of the immersed boundary the l2 norm of the errors is computed in order to evaluate the capability of the method immersed boundaries are found in many industrial applications like two phase flow simulations fluid structure interaction etc this article represents a first step towards the simulation of these kinds of applications

distribution planning decisions using interactive fuzzy multi objective linear programming this work develops an interactive fuzzy multi objective linear programming i fmolp method for solving the fuzzy multi objective transportation problems with piecewise linear membership function the proposed i fmolp method aims to simultaneously minimize the total distribution costs and the total delivery time with reference to fuzzy available supply and total budget at each source and fuzzy forecast demand and maximum warehouse space at each destination additionally the proposed method provides a systematic framework that facilitates the fuzzy decision making process enabling a decision maker dm to interactively modify the fuzzy data and related parameters until a set of satisfactory solutions is obtained an industrial case is presented to demonstrate the feasibility of applying the proposed method to real transportation problems consequently the proposed method yields an efficient solution and overall degree of dm satisfaction with the determined objective values especially several significant management implications regarding the practical application of the proposed i fmolp method are presented

interactive solutions for the linear multiobjective transportation problem abstract mathematical programming problems that exhibit the mathematical structure of a transportation problem often arise in settings with multiple conflicting objectives existing procedures for analyzing these problems fall into two general categories these methods either generate all nondominated solutions or they construct a single compromise solution this paper presents two interactive algorithms which take advantage of the special form of the multiple objective transportation problem two examples are included to illustrate these algorithms and to demonstrate their viability

stochastic modeling of groundwater flow by unconditional and conditional probabilities 2 the solute transport the problem of solute transport in a heterogeneous formation whose transmissivity or hydraulic conductivity are subject to uncertainty is studied for two and three dimensional flows approximate closed form solutions are derived for the case of a solute pulse in an average uniform flow through a formation of unconditional stationary random transmissivity the solute concentration regarded as a random variable is determined in terms of its expectation and variance and is found to be subject to a high degree of uncertainty the uncertainty is greatly reduced if the solute input zone is large compared to the transmissivity integral scale in any case the concentration expectation does not obey a diffusion type equation in the case of two dimensional flows unless the solute body has traveled a distance larger than a few tens transmissivity integral scales this distance may be exceedingly large in many conceivable applications

a second order approach for the modeling of dispersive transport in porous media 1 theoretical development a new approach for the treatment of dispersive transport in a simplified porous medium is presented use of a volume averaging approach allows the development of a separate point macroscopic balance equation for the dispersion quantity that appears in the averaged transport equation the new equation is a more general representation which avoids the complications and questions that arise concerning the coefficients associated with the fickian approximation for dispersion constitutive relationships are developed for a number of the source terms arising in the averaged dispersion equation the coupled transport and dispersion equations along with darcy s law and the macroscopic continuity equation constitute a closed second order model for dispersion in a porous medium

an additive fuzzy programming model for multiobjective transportation problem abstract all existing methods generate a set of nondominated solutions or construct a single compromise solution for the linear multiobjective transportation problem in which objectives are equally important in this paper an additive fuzzy programming model for the multiobjective transportation problem is presented the method aggregates the membership functions of the objectives to construct the relevant decision function weights and priorities for nonequivalent objectives are also incorporated in the method this model gives a nondominated solution which is nearer to the best compromise solution a fortran program has been developed based on simple and weighted additive algorithms the method is illustrated with a numerical example

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

analysis of flow through heterogeneous random aquifers 2 unsteady flow in confined formations the direct problem of determining the head field in a formation of given stationary isotropic random structure is solved approximately for unsteady flow conditions under restrictive assumptions of sufficiently small conductivity variance and average head gradient slowly varying in time and space closed form expressions are derived for the effective conductivity or storativity and for the head variogram two types of unsteady flow are considered transients and periodic flows in the case of transients it is assumed that initially the head is constant no flow and that ultimately the flow becomes uniform it is found that the effective conductivity and transmissivity are time dependent and drop from the arithmetic mean initially to the steady state value during a relaxation time the latter is much larger for one dimensional flows than for two or three dimensional ones the head variogram also relaxes from the one corresponding to the initial lack of correlation to the steady state variogram during a relaxation time which grows with the lag while in three dimensional structure the relaxation time scales are relatively short and steady state analysis can be used accurately even under transient conditions the tendency to steady state may be very slow in the case of transmissivity because of its large integral scale hence steady state analysis for transients might not be warranted for regional transient flows in the case of periodic flows of seasonal nature the head gradient is assumed to be made up from a steady component and a periodic one if the amplitude of the latter is sufficiently small compared to the steady one steady state value of effective transmissivity and storativity can be adopted the head variogram has also its steady state form for large lags and quasisteady for small lags hence the variogram lies between the steady one steady component of head gradient and the quasisteady one instantaneous head gradient

derivation of vertically averaged equations describing multiphase flow in porous media an extension of the rev averaging technique used to derive balance equations for multiphase or porous media flow problems is presented theorems which allow a one step transformation from three dimensional point equations for a single phase to two dimensional point equations for multiphase systems are derived the theorems are then applied to obtain the vertically averaged balance equations of mass chemical species momentum energy and entropy the relation between these equations and their unaveraged predecessors is clearer than when the standard two step averaging procedure is applied furthermore constitutive relations are more easily hypothesized for the current system of equations than for previously derived forms

linear programming with multiple fuzzy goals abstract this paper describes the use of fuzzy set theory in goal programming gp problems in particular it is demonstrated how fuzzy or imprecise aspirations of the decision maker dm can be quantified through the use of piecewise linear and continuous functions models are then presented for the use of fuzzy goal programming with preemptive priorities with archimedean weights and with the maximization of the membership function corresponding to the minimum goal examples are also provided