optimality conditions for linear programming problems with fuzzy coefficients the optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers the solution concepts proposed in this paper will follow from the similar solution concept called the nondominated solution in the multiobjective programming problem under these settings the optimality conditions will be naturally elicited

analytic derivatives for estimation of linear dynamic models abstract this paper develops two algorithms algorithm 1 computes the exact gaussian log likelihood function its exact gradient vector and an asymptotic approximation of its hessian matrix for discrete time linear dynamic models in state space form algorithm 2 derived from algorithm 1 computes the exact sample information matrix of this likelihood function the computed quantities are analytic not numerical approximations and should therefore be useful for reliably quickly and accurately i checking local identifiability of parameters by checking the rank of the information matrix ii using the gradient vector and hessian matrix to compute maximum likelihood estimates of parameters with newton methods and iii computing asymptotic covariances cramer rao bounds of the parameter estimates with the hessian or the information matrix the principal contribution of the paper is algorithm 2 which extends to multivariate models the univariate results of porat and friedlander 1 by relying on the kalman filter instead of the levinson durbin filter used by porat and friedlander algorithms 1 and 2 can automatically handle any pattern of missing or linearly aggregated data although algorithm 1 is well known it is treated in detail in order to make the paper self contained

weighted coefficients in two phase approach for solving the multiple objective programming problems abstract two phase approach with equal weighted coefficients has been proposed to yield an efficient solution for multiple objective programming problems in this note we will show that the two phase approach as long as the weighted coefficients are positive not necessarily equal will generate an efficient solution a counterexample is given to the case that some weighted coefficients are zero

tensor sylvester matrices and the fisher information matrix of varmax processes the purpose of this paper is to develop compact expressions for the fisher information matrix fim of a gaussian stationary vector autoregressive and moving average process with exogenous or input variables a vector armax or varmax process we develop a representation of the fim based on multiple sylvester matrices an extension of this representation yields another one but in terms of tensor sylvester matrices in order to obtain the results presented in this paper the approach used in a klein g melard p spreij on the resultant property of the fisher information matrix of a vector arma process linear algebra appl 403 2005 291 313 is extended

pareto optimality of compromise decisions the questions of the existence of pareto optimal decisions and the existence of compromise decisions for decision problems in finite dimensional spaces are investigated several conditions for a compromise decision to be pareto optimal are derived the concept of the compromise decision and some of the results are then generalized by allowing in the definition of the compromise solution arbitrary triangular norms instead of the triangular norm defined by the minimum operation only

pictorial representations of fuzzy connectives part ii cases of compensatory operators and self dual operators abstract as the continuation of part i in which pictorial representations of t norms t conorms and averaging operators were made with the aid of a computer this paper discusses compensatory operators and proposes generalized compensatory operators which can be obtained from averaging operators self dual operators are discussed which can be defined by using t norms t conorms and averaging operators finally symmetric sums are reviewed which are also self dual operators the pictorial representations of these operators are also made

some properties of weakly convex fuzzy mappings in this paper we introduce the concepts of weakly convex fuzzy sets weakly convex fuzzy mappings and weakly quasi convex fuzzy mappings and then give characterization theorems for these fuzzy sets and fuzzy mappings

multi objective optimization with a max t norm fuzzy relational equation constraint in this paper we consider minimizing multiple linear objective functions under a max t norm fuzzy relational equation constraint since the feasible domain of a max archimedean t norm relational equation constraint is generally nonconvex traditional mathematical programming techniques may have difficulty in yielding efficient solutions for such problems in this paper we apply the two phase approach utilizing the min operator and the average operator to aggregate those objectives to yield an efficient solution a numerical example is provided to illustrate the procedure

φ 1 concavity and fuzzy multiple objective decision making concave properties play a dominate role in solving both classic and fuzzy optimization problems however since fuzzy problems are generally represented by sets not crisp numbers various aggregation schemes are needed to manipulate and to combine the different elements in a fuzzy optimization problem based on these different aggregations various concavity properties can be formulated and explored in this paper the intersection aggregation and the convex combination aggregation are explored based on the email protected 1 concave fuzzy sets first the concept of f 1 convexity which covers a wider class of sets and functions is extended to fuzzy sets email protected 1 concave and email protected 1 quasiconcave fuzzy sets are then introduced and some useful aggregation and composition rules are developed based on these aggregation and composition rules and the generalized concave properties fuzzy multiple objective decision making problems are formulated and the conditions to ensure local global maximum property are discussed

hybrid fem floquet modes po technique for multi incidence rcs prediction of array antennas an original method is proposed which associates rigorous 3d finite element methods fem with floquet modes through factopo multidomain formalism for computing the radar cross section rcs of large array antennas the most original aspect of the method is the fact that the source unit cell is characterized by a generalized scattering matrix gsm which does not depend on the plane wave incidence impinging the structure consequently the factorization step of the fem matrix which is the main computational effort is performed only once the assembling procedure consists then in expressing the fem gsm matrix in the floquet mode basis for each incidence and to solve a linear system giving the complex amplitude of the floquet modes on the array cell interface associated with this formalism lateral and back structure effects can be treated using physical optics po combined with the equivalent current method ecm to improve the accuracy for far broadside incidence

closed and convex fuzzy sets in this paper we establish a characterization theorem for closed fuzzy sets and give two weak conditions that a closed fuzzy set is a convex fuzzy set we also present some results for convex fuzzy sets strictly convex fuzzy sets and closed fuzzy sets

fuzzy multiple objective programming and compromise programming with pareto optimum abstract a fuzzy multiple objective decision making approach is proposed based on the desirable features of compromise programming and the fuzzy set theory the proposed two phase approach guarantees both nondominated and balanced solutions for solving both the crisp and the fuzzy multiple objective decision making problems furthermore it is shown that the original compromise programming does not guarantee nondominated solutions if the distance parameter is assumed to be infinite and the resulting programming problem s solution is not unique

a domain decomposition method for the vector wave equation a nonoverlapping domain decomposition method ddm is presented for the finite element fe solution of electromagnetic scattering problems by inhomogeneous three dimensional 3 d bodies the computational domain is partitioned into concentric subdomains on the interfaces of which conformal vector transmission conditions are prescribed and that can be implemented in the inhomogeneous part the ddm is numerically implemented when a conformal vector absorbing boundary condition abc is utilized on the outer boundary terminating the fe mesh while employing the standard edge based fe formulation then numerical experiments are performed on a sphere and a cone sphere that emphasize the advantages of this technique in terms of memory storage and computing times especially when the total number of unknowns is very large also these numerical experiments serve as a severe test for the performances of the abc

an integrated approach for deriving priorities in analytic network process a multiple objective programming approach for the analytic network process anp is proposed to obtain all local priorities for crisp or interval judgments at one time even in an inconsistent situation the weakness of the anp and fuzzy anp fanp is that the complexity of generating priorities is equal to the number of comparison matrices in the proposed approach all sets of crisp priorities for each pairwise comparison matrix can be obtained directly moreover from the outcomes of three examples the power to reach a limiting supermatrix is less than or equal to the power of the fanp thus the proposed approach can be regarded as an efficient alternative of the fuzzy anp

on convex and concave fuzzy mappings abstract in this paper we introduce the concepts of convex subsets of f 0 the set of all fuzzy numbers and monotonic fuzzy mappings on r2 and show that a monotonic fuzzy mapping f on a convex set c r1 or r2 is quasi convex and quasi concave we establish two characterizations for convex fuzzy mappings and two characterizations for concave fuzzy mappings we also prove the least upper bound property

an explicit expression for the fisher information matrix of a multiple time series process the principal result in this paper is concerned with the derivative of a vector with respect to a block vector or matrix this is applied to the asymptotic fisher information matrix fim of a stationary vector autoregressive and moving average time series process varma representations which can be used for computing the components of the fim are then obtained in a related paper a klein a generalization of whittle s formula for the information matrix of vector mixed time series linear algebra appl 321 2000 197 208 the derivative is taken with respect to a vector this is obtained by vectorizing the appropriate matrix products whereas in this paper the corresponding matrix products are left unchanged

poset valued convexities we analyze cut properties of lattice and poset valued functions fuzzy sets of n dimensional real variable with respect to convexity in the lattice valued case convexity of a fuzzy set is equivalent with the convexity of its standard cuts dealing with non standard cuts we show that unless the space of the values is a chain such statement in general does not hold we present analogue results in the more general setting of poset valued functions we also prove that there exist lattice and poset valued functions whose cuts are precisely the convex sets of particular families our work is motivated by possible applications of convex functions e g in image processing

matrix differential calculus applied to multiple stationary time series and an extended whittle formula for information matrices abstract the purpose of this paper is to set forth easily implementable expressions for the fisher information matrix fim of a gaussian stationary vector autoregressive and moving average process with exogenous or input variables a vector armax or varmax process the entries of the fim are represented as circular integral expressions and can be computed by applying cauchy s residue theorem an extension of the whittle formula for the fim of multiple time series processes is developed for varmax processes it will be shown that the extended whittle formula yields the fim when a bivariate structure consisting of the varmax process and the exogenous input process is considered consequently the equivalence between a frequency and time domain representation of the fim of varmax processes is established in order to obtain the results presented in this paper the differentiation techniques developed and used in a klein p spreij an explicit expression for the fisher information matrix of a multiple time series process linear algebra appl 417 2006 140 149 are applied

hybrid fe bi modeling of 3 d doubly periodic structures utilizing triangular prismatic elements and an mpie formulation accelerated by the ewald transformation we present the formulation of a finite element boundary integral method for the analysis of three dimensional doubly periodic structures based on arbitrary nonorthogonal lattice configurations the method starts from a functional description of the field problem where only a single unit cell of the array is considered this unit cell is meshed with triangular prismatic volume elements and the electric field intensity is discretized with edge based expansion functions on the sidewalls of the unit cell phase boundary conditions are employed to relate the fields on opposing walls of the unit cell on the top and or bottom unit cell planar surfaces the mesh is terminated using a mixed potential integral equation the required space domain periodic green s function is calculated after applying the ewald 1921 transformation to convert the slowly converging series representation into two rapidly converging series the method is validated for simple slot and strip frequency selective surfaces as well as microstrip dipole arrays more complex geometries investigated are slot coupled microstrip patches photonic bandgap materials and the so called artificial puck plate frequency selective surface bandpass structure

construction of the exact fisher information matrix of gaussian time series models by means of matrix differential rules the fisher information matrix is of fundamental importance for the analysis of parameter estimation of time series models in this paper the exact information matrix of a multivariate gaussian time series model expressed in state space form is derived a computationally efficient procedure is used by applying matrix differential rules for the derivatives of a matrix function j j with respect to its vector argument an algorithm is given it is sketched for the general state space structure without specifying a parametrization it is then detailed for the vector autoregressive moving average varma model with a given parametrization where explicit recurrent relations are developed

an interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters abstract a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed in general two types of fuzziness of human judgements should be incorporated in multiobjective programming problems one is the experts ambiguous understanding of the nature of the parameters in the problem formulation process and the other is the fuzzy goals of the decision maker for each of the objective functions in order to cope with both types of fuzziness multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem formulation are formulated and the concept of generalized multiobjective linear programming and m pareto optimality is introduced in our interactive fuzzy satisficing method the satisficing solution of the decision maker is derived efficiently from among m pareto optimal solutions on the basis of the proposed method an interactive computer program is written to implement man machine interactive procedures finally an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs

a two phase possibilistic linear programming methodology for multi objective supplier evaluation and order allocation problems in this study an integration of the analytic hierarchy process ahp and a multi objective possibilistic linear programming moplp technique is developed to account for all tangible intangible quantitative and qualitative factors which are used to evaluate and select suppliers and to define the optimum order quantities assigned to each a multi objective linear programming technique is first employed to solve the problem to model the uncertainties encountered in the integrated supplier evaluation and order allocation methodology fuzzy theory is adopted hence possibilistic linear programming plp is proposed for solving the problem as it is believed to be the best approach for absorbing the imprecise nature of the real world in the supplier evaluation phase environmental criteria are also considered

domain decomposition method based on generalized scattering matrix for installed performance of antennas on aircraft we describe the factorization factopo domain decomposition method based on the boundary element method bem and the finite element method fem applied to the analysis of antenna performance on aircraft the benefits of the subdomain method are mainly the ability to deal with collaborative studies involving several companies and the reduction of the computation costs by one or more orders of magnitude especially in the context of parametric studies furthermore this paper proposes global functions defined on fictitious surfaces surrounding radiating elements to deal with the computation of antenna far field patterns in a multidomain mode by masking the complexity of the antenna wires thin surfaces materials feeding network the external domain of the aircraft can be closed so that the combined field integral equation can be used which is better conditioned than the electric field integral equation and converges much faster the accuracy and efficiency of this technique is assessed by directivity computations of vhf monopole antennas mounted on fokker 100 and atr42 scaled mock up domain decomposition results obtained by combining two sets of subdomains are compared with measurements and the feko commercial method of moments code

evaluate fuzzy optimization problems based on biobjective programming problems abstract the embedding theorem shows that the set of fuzzy numbers can be embedded into a banach space inspired by this embedding theorem we propose a solution concept of the fuzzy optimization problem by solving a biobjective optimization problem which is transformed from the original fuzzy optimization problem using the embedding theorem we then also consider the fuzzy optimization problem with fuzzy coefficients i e the coefficients are assumed to be fuzzy numbers under a setting of core values of fuzzy numbers we show that the optimal solution of its corresponding crisp optimization problem the usual optimization problem is also an optimal solution of the original fuzzy optimization problem

triangular norm based graded convex fuzzy sets in this paper we develop the theory of graded convex fuzzy set graded strongly convex fuzzy set graded strictly convex fuzzy set based on triangular norms in which the degree of fuzzy convexity is described by one real number we also investigate some graded properties of these graded convex fuzzy sets and present the relations between these graded convex fuzzy sets and their topological properties and give several conditions for a fuzzy set to be a graded convex fuzzy set finally we generalize the notion of global maximizer and prove an important property of graded convex fuzzy sets

fuzzy multiple level programming the use of fuzzy set concept to overcome the computational difficulties of multi level optimization for large systems appears to be a powerful approach and can solve practical large problems in a very simplified manner furthermore unlike the duo ploy or multi ploy approaches the proposed interactive concept provides flexibility which is essential due to the different styles of management in different organizations the approach is formulated based on exploring the fuzziness or indefiniteness which is almost always present in a decentralized large hierarchy organization the advantage of this approach is that not only the problem is much more simplified for solution purposes the original problem is also much more realistically represented

a fuzzy control model fcm for dynamic portfolio management abstract in the present study we continue previous work by recasting the portfolio management problem into a control theoretic form still retaining a recursive programming structure through time the uncertainty of future prices and risk levels is recognized by fuzzy numbers our system has interesting directions for future research improving performance through expert systems support for forecasting using the experience from the model in efforts to theory design solving the fuzzy control model fcm when the state objectives return predictions and the level of economic friction are fuzzy

a novel fdtd time stepping scheme to calculate rcs of curved conducting objects using adaptively adjusted time steps the chief shortcoming of the conventional conformal finite difference time domain cfdtd method is a global time step reduction to ensure stability due to the small irregular cells truncated by the curved conducting geometry introducing the local time stepping into the cfdtd method is an efficient way and has been numerically proven in our previous work in this paper we further employ the concept of the equivalent material constants into the integral form of faraday s law to analyze the curved configuration with or without the coating hence we can theoretically derive the stability criterion of each irregular cell based on the same procedure for the courant friedrichs lewy cfl stability criterion therefore the local time step size of each small irregular cell can be chosen adaptively an adaptively adjusted time stepping procedure is presented and is theoretically proven to ensure numerical stability the radar cross section rcs results of various curved conducting objects with the coating are computed comparisons of accuracy and efficiency of our method with other established methods are performed

the definition of convex fuzzy subset following the seminal work of zadeh on the definition of a convex fuzzy subset three new kinds of definitions of convex fuzzy subsets are proposed first by the use of the relations between fuzzy points and fuzzy sets the definition of a convex fuzzy subset is introduced the acceptable nontrivial concepts obtained in this manner are the q convex fuzzy subset and q convex fuzzy subset second by the use of the implication operators of fuzzy logic an r convex fuzzy subset is proposed relations between the convex fuzzy subset and r convex fuzzy subset are discussed finally based on the concept of falling shadow a theoretical approach of convex fuzzy subset is established and the convex fuzzy subset based on t norm is proposed

fuzzy approaches to multicriteria de novo programs abstract multicriteria de novo programming is a promising tool for optimal system design however there exist no algorithms for solving a general multicriteria de novo program only special cases have been discussed this paper proposes a two step fuzzy approach based on the ideal and negative ideal solutions it is shown that this approach is very efficient and is applicable to the general multicriteria de novo programming the fuzzy version of this problem is also formulated and analyzed numerical examples are given to illustrate the approaches

fuzzy convexity and multiobjective convex optimization problems in this paper based on the more restrictive definition of fuzzy convexity due to ammar and metz 1 several useful composition rules are developed the advantages in using the more restrictive definition of fuzzy convexity are that local optimality implies global optimality and that any convex combination of such convex fuzzy sets is also a convex fuzzy set as shown in this paper these properties are laking in the usual convex fuzzy sets in addition to illustrate the applications in fuzzy convex optimization two examples in multiple objective programming are considered

brief paper accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation in this paper we study the accuracy of linear multiple input multiple output mimo models obtained by maximum likelihood estimation we present a frequency domain representation for the information matrix for general linear mimo models we show that the variance of estimated parametric models for linear mimo systems satisfies a fundamental integral trade off this trade off is expressed as a multivariable water bed effect an extension to spectral estimation is also discussed

simulation of a supply chain game with multiple fuzzy goals supply chain management scm issues have been popularly discussed in recent years however few papers in past literature have been dedicated to the use of fuzzy multi objective game framework for analyzing how the strategic partnership influences individual and global performance in a supply chain this study formulates a game framework for the investigation of strategic behavior of supply chain partners based on fuzzy multi objective programming the alliance matrix and achievement level aspiration degree this work assumes the partners as having multiple objectives and the supply chain is multi product and multi material to validate our model we simulate the micro and macro performance of a supply chain by the achievement level under various partner alliances in addition a sensitivity analysis is conducted finally some useful lessons are summarized

some properties of m fuzzifying convexities induced by m orders abstract in this paper the notions of geometric interval spaces convex geometries and base point orders in the theory of convexity spaces are generalized to m fuzzifying convexity spaces using m fuzzifying restricted hull operators the m fuzzifying convexity spaces induced by m orders are defined conveniently then it is shown that m fuzzifying convexity spaces induced by m orders are m fuzzifying jhc and arity 2 and if the m order is strongly anti symmetric then the m fuzzifying convexity space is an m fuzzifying convex geometry and its segment operator is an m fuzzifying geometric interval operator

scattering from 3 d cavities with a plug and play numerical scheme combining ie pde and modal techniques in this paper we present a multidomain and multi method coupling scheme called factopo based on generalized scattering matrix computations on three dimensional 3 d subdomains the global target spl omega is split in n sub v subdomains v sub i i 1 n sub v separated by n sub i fictitious surfaces spl gamma sub j j 1 n sub i we use a modal representation of the tangent fields on the interfaces in each domain the generalized scattering matrix s sub i is computed with different methods such as the 3 d finite element method fem or the electric field integral equation efie this coupling scheme leads to an important reduction in computational resources especially for cavities with one dimension much larger than the other two the advantages of this formulation for parametric studies is illustrated by two cases computing the rcs of an air intake terminated with a flat pec or a fan channel and of an antenna structure coupled to an electronic feed with a varying parameter deneb numerical as well as experimental results are presented

fuzzy φ convexity and fuzzy decision making the notion of convexity and its various generalization is important for quantitative and qualitative studies in operations research or applied mathematics it has also been considered by many authors in fuzzy set theory in this paper we study the concept of f convex and f quasiconvex fuzzy sets which was proposed bychen et al 1 and develop some useful extrema properties of these fuzzy sets we prove that any local maximizer of a f convex fuzzy set is also a global maximizer and that any strict local maximizer of a f quasiconvex fuzzy set is also a global maximizer we also study the class of strictly f convex respectively strictly f quasiconvex fuzzy sets that is more restricted than the class of f convex respectively f quasiconvex fuzzy sets we prove for both families of strictly f convex and strictly f quasiconvex fuzzy sets that every local maximizer is also the unique global maximizer in addition some applications to fuzzy decision making are discussed

interactive compensatory fuzzy programming for decentralized multi level linear programming dmllp problems abstract this paper presents interactive compensatory fuzzy programming for decentralized multi level linear programming dmllp problems by adjusting the cooperative decision making process between the different levels and also between the decision makers of the same level our aim is to obtain a preferred compensatory compromise pareto optimal solution for dmllp for this the weights of objectives at each level are assigned by the next upper level decision maker dm by using analytic hierarchy process ahp or any other weighting methods the weight of any objective for whole system is equal to the product of the weights on the path tying it to the top decision maker dm 0 using these weights equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights werners compensatory fuzzy and operator is offered to solve dmllp problem the most important idea to be emphasized is that equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights thanks to this equivalence dmllp problem has been transformed to the multi objective linear programming molp problem at level 0 the equivalence is reflected to the compensatory model within the constraints and the equivalence also enables all dms to obtain proportional satisfactions with their weights as much as possible so in our compensatory model a reduction on equivalent satisfactory level of one dm can be compensated for by an increase in the equivalent satisfactory level of another dm furthermore being developed a finite interactive iterative procedure with maximum interaction step a set of compensatory solutions which are also pareto optimal is obtained depending on compensation parameter giving a theorem we will show that the solutions generated by werners compensatory fuzzy and operator do guarantee pareto optimality for our dmllp problem and comparing it with some other computational efficient compensatory fuzzy aggregation operators we will conclude that this operator is more appropriate for dmllp illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed interactive fuzzy compensatory method for dmllp

phased array antenna analysis with the hybrid finite element method a new analysis technique for infinite phased array antennas was developed and demonstrated it consists of the finite element method fem in combination with integral equation radiation conditions and a novel periodic boundary condition for 3 d fem grids accurate modeling of rectangular circular and circular coaxial feeds is accomplished by enforcing continuity between the fem solution and several waveguide modes across an aperture in the array s ground plane the radiation condition above the array is enforced by a periodic integral equation in the form of a floquet mode summation thus reducing the solution to that of a single array unit cell the periodic boundary condition at unit cell side walls is enforced through a matrix transformation that mathematically folds opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle the unit cell electric field is expanded in vector finite elements galerkin s method is used to cast the problem as a matrix equation which is solved by the conjugate gradient method a general purpose computer code was developed and validated for cases of open ended waveguides microstrip patches clad monopoles and printed flared notches showing that the analysis method is accurate and versatile

fuzzy multi level minimum cost flow problems both multiple objectives and multiple hierarchies minimum cost flow problems with fuzzy costs and fuzzy capacities in the arcs are investigated to reduce the complexity a possibility programming is used to handle the vagueness in the parameters fuzzy approach can considerably simplify the problem and thus a fairly general multi level problem can be solved reasonably easily in spite of the fact that the multi level problem is np hard and very difficult to solve several numerical examples are considered to illustrate the approach

a parametric approach to fuzzy linear programming in this paper we discuss how to deal with decision problems that are described with lp models and formulated with elements of imprecision and uncertainty more precisely we will study lp models in which the parameters are not fully known but only with some degree of precision even with incomplete information the model builder or model user is normally able to give a realistic interval for the parameters of an lp model for the constraint vector this is combined with some wishes or some leeway on the constraints even with ambiquity in the objective function there is normally some preference ordering to be found among alternative ways of action we will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets after an overview of some central contributions to fuzzy linear programming we will develop an lp model in which the parameters are not fully known only with some degree of precision and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision the fuzzy lp model derived in this way appears to be fairly easy to handle computationally which is demonstrated with a numerical example

interdependence in fuzzy multiple objective programming abstract in multiple objective programs mop application functions are establised to measure the degree of fulfillment of the decision maker s requirements achievement of goals nearness to an ideal point satisfaction etc about the objective functions see e g delgado et al 1990 zimmermann 1978 and are extensively used in the process of finding good compromise solutions we have earlier demonstrated that the use of interdependences among objectives of a mop in the definition of the application functions provides for more correct solutions and faster convergence in this paper generalizing the principle of application functions to fuzzy multiple objective programs fmop with interdependent objectives we define a large family of application functions for fmop and illustrate our ideas by a simple three objective program

tabu search for fuzzy optimization and applications in this paper we present a tabu search technique to approximately solve fuzzy optimization problems we demonstrate the performance of the proposed method by applying it to an elementary fuzzy optimization problem other applications of the method to fuzzy linear programming fuzzy regression and the training of fuzzy neural networks are also presented

concepts of generalized concavity based on aggregation functions in the present paper the quasiconcavity of membership functions is generalized based on conjunctive aggregation functions and the properties of the generalized quasiconcavity are investigated fuzzy multicriteria and scalar programming problems are then considered and the properties of pareto optimal solutions and compromise solutions as well as their relationships are derived finally we discuss the application of the obtained results to facility location problems

using analytic hierarchy process and fuzzy set theory to rate and rank the disability abstract any discrimination against qualified disabled people in all employment practices is violating the americans with disabilities act ada and it must be prohibited assigning qualified disabled people to a proper job or making reasonable accommodations for disabled employees is not only ethical but also necessary for reducing the social economic burden therefore in order to place qualified disabled people in appropriate job positions a multidimensional assessment method should be developed for measuring and interpreting the disabled people s residual capabilities with respect to their strengths weaknesses and their compatibility to job requirements and work environments thus the primary purpose of this study is to discuss how to structure a hierarchy related to the problem of deriving an overall disability index odi for measuring the individual s disability the analytic hierarchy process along with the entropy theory and fuzzy set theory is applied for eliciting the weights among the attributes and aggregating the multiple attributes into a single measurement we believe that the resultant odi is meaningful and useful for both the evaluator who supervises a rehabilitation program and the human resource director who engages in a hiring process

on fuzzy convexity and parametric fuzzy optimization abstract in this paper some different types of convexity and generalized convexity of fuzzy sets are defined and their properties are studied a general fuzzy nonlinear programming problem is formulated with application of the concept of convexity

two phase approach for solving the fuzzy linear programming problems we propose a two phase approach to solve the fuzzy linear programming problem although several methods in the literature have been proposed to treat this problem the two phase approach has the merit stated as if the decision maker is seeking an efficient solution which can improve the max min operators solution so that each membership degree should be improved then the two phase method automatically attains this desire if there is room to improve an interpretation of this result is that the two phase method not just pursue the highest membership degree in the objective but also pursue a better utilization of each constrained resource

neural net solutions to fuzzy linear programming we show how a neural net with sign restrictions on its weights can be trained to produce approximate solutions to fuzzy linear programming problems the neural net approximates the joint solution buckley 1995 to the fuzzy linear program

compensatory operators in fuzzy linear programming with multiple objectives previously h j zimmermann 11 presented a fuzzy approach to solve the linear vectormaximum problem in the mentioned approach the author uses the minimum or the product operators to translate the semantic meaning of the and the aim of this paper is to reconsider this approach by using operators which allow some degree of compensation between aggregated membership functions firstly the c operator already defined in 12 is used to combine our fuzzy objectives it is shown that solutions obtained by this way are always efficient unfortunately the substitute problem is not generally computationally feasible we suggest then the min bounded sum operator which is a compensatory one has some desired properties and is supported by empirical arguments it allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand point of efficiency

an interactive satisfying method based on alternative tolerance for multiple objective optimization with fuzzy parameters an interactive satisfying method based on alternative tolerance is presented for the multiple objective optimization problem with fuzzy parameters using the alpha level sets of the fuzzy numbers all the objectives are modeled as the fuzzy goals and the tolerances of the objectives are iteratively changed according to a decision maker for a satisfying solution via a specific attainable point programming model the membership functions can be modified and then a lexicographic two phase programming procedure is constructed correspondingly to find the final solution in a special case the objective constraint is added instead of changing the membership functions therefore the dissatisfying objectives for the decision maker can be improved step by step the presented method not only acquires the alpha pareto optimal or weak alpha pareto optimal solution of the fuzzy multiple objective optimization but also satisfies the progressive preference of the decision maker a numerical example shows its power

a fem domain decomposition method for photonic and electromagnetic band gap structures this paper introduces an efficient domain decomposition algorithm for the solution of time harmonic electromagnetic fields arising in three dimensional finite size photonic band gap and electromagnetic band gap structures the method is based on the finite element approximation and a nonoverlapping domain decomposition method a set of cement unknowns on the inter domain interfaces has been explicitly introduced to enforce the appropriate field continuities the introduction of these extra unknowns allows for nonconforming nonmatching triangulations across domain eliminating the need for periodic mesh to ensure and improve the convergence of the outer iteration loop robin transmission condition is used to communicate information across interfaces the resulting system of equations is solved with a fast algorithm that loosely resembles the well known finite element tearing and interconnecting algorithm in this algorithm the method solves in the preprocessing step for the robin primal subdomain problems multiple times by exciting one dual unknown at a time this step generates an iteration matrix that is then used to update the dual unknowns in the outer loop iteration the present method becomes extremely efficient for problems with geometric repetitions such as photonic and electromagnetic band gap structures

a generalization of whittle s formula for the information matrix of vector mixed time series abstract in a pioneering paper whittle developed a formula for expressing fisher s information matrix of multivariate time series models cf p whittle j royal statist soc b 15 1953 125 139 it is described as a function of the spectral density of the time series process the existing relationship is extended to the whole matrix instead of one element and is related with a time domain alternative expression the latter derives fisher s information matrix from the log gaussian likelihood function the equivalence of both approaches frequency and time domain which is summarized in a theorem shows that a considerable reduction in matrix integrals is taking place when moving from the former to the latter the hermitian property of the matrices under study contributes to construct the link between the two approaches and the theorem is further illustrated by an example

convexity and upper semicontinuity of fuzzy sets since almost all practical problems are fuzzy and approximate fuzzy decision making becomes one of the most important practical approaches one off the important aspects for formulating and for solving fuzzy decision problems is the concept of convexity in this paper we investigate the interrelationships of several concepts of generalized convex fuzzy sets we also prove that in the upper semicontinuous case the class of semistrictly quasi convex fuzzy sets lies between the convex and quasi convex classes aggregation or composition is an essential part for optimization or modeling and some important composition rules for upper semicontinuous fuzzy sets are developed we prove that a convex combination of upper semicontinuous fuzzy sets is an upper semicontinuous fuzzy set and the intersection of finitely many upper semicontinuous fuzzy sets is an upper semicontinuous fuzzy set finally the criteria for the existence of fuzzy decision under upper semicontinuity conditions are derived and two examples in multiple objective programming are used to illustrate the approach

solving the multiobjective possibilistic linear programming problem in conventional multiobjective decision making problems the estimation of the parameters of the model is often a problematic task normally they are either given by the decision maker dm who has imprecise information and or expresses his considerations subjectively or by statistical inference from past data and their stability is doubtful therefore it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed in this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters fp molp whose possibility distributions are given by fuzzy numbers estimated from the information provided by the dm as the parameters intervening in the model are fuzzy the solutions will be also fuzzy we propose a new pareto optimal solution concept for fuzzy multiobjective programming problems it is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem the method relies on cuts of the fuzzy solution to generate its possibility distributions these ideas are illustrated with a numerical example

on the resultant property of the fisher information matrix of a vector arma process a matrix is called a multiple resultant matrix associated to two matrix polynomials when it becomes singular if and only if the two matrix polynomials have at least one common eigenvalue in this paper a new multiple resultant matrix is introduced it concerns the fisher information matrix fim of a stationary vector autoregressive and moving average time series process varma the two matrix polynomials are the autoregressive and the moving average matrix polynomials of the varma process in order to show that the fim is a multiple resultant matrix two new representations of the fim are derived to construct such representations appropriate matrix differential rules are applied the newly obtained representations are expressed in terms of the multiple sylvester matrix and the tensor sylvester matrix the representation of the fim expressed by the tensor sylvester matrix is used to prove that the fim becomes singular if and only if the autoregressive and moving average matrix polynomials have at least one common eigenvalue it then follows that the fim and the tensor sylvester matrix have equivalent singularity conditions in a simple numerical example it is shown however that the fim fails to detect common eigenvalues due to some kind of numerical instability whereas the tensor sylvester matrix reveals it clearly proving the usefulness of the results derived in this paper

brief paper on the accuracy in errors in variables identification compared to prediction error identification errors in variables estimation problems for single input single output systems with gaussian signals are considered in this contribution it is shown that the fisher information matrix is monotonically increasing as a function of the input noise variance when the noise spectrum at the input is known and the corresponding noise variance is estimated furthermore it is shown that whittle s formula for the fisher information matrix can be represented as a gramian and this is used to provide a geometric representation of the asymptotic covariance matrix for asymptotically efficient estimators finally the asymptotic covariance of the parameter estimates for the system dynamics is compared for the two cases i when the model includes white measurement noise on the input and the variance of the noise is estimated and ii when the model includes only measurement noise on the output in both cases asymptotically efficient estimators are assumed an explicit expression for the difference is derived when the underlying system is subject only to measurement noise on the output

preincavity and fuzzy decision making since almost all practical problems are fuzzy and approximate fuzzy decision making becomes one of the most important practical approaches however the resulting problems are frequently complicated and difficult to solve one effective way to overcome these difficulties is to explore the concavity or generalized concavity properties of the resulting problems in this paper we introduce and study the concept of supp preincave and supp prequasiincave fuzzy sets we give characterizations for a supp preincave fuzzy set in terms of its fuzzy hypograph and a supp prequasiincave fuzzy set in terms of its level sets furthermore we also prove that any local maximizer of a supp preincave fuzzy set is also a global maximizer and that any strictly local maximizer of a supp prequasiincave fuzzy set is also a global maximizer finally some aggregation rules for supp preincave and supp prequasiincave fuzzy sets are given and some applications to fuzzy decision making are discussed

concavoconvex fuzzy set abstract the concept of a concavoconvex fuzzy set in euclidean space is reported the idea is conceived by combining the concepts of convex and concave fuzzy sets together useful properties of the concavoconvex fuzzy set are established the union intersection of two concavoconvex fuzzy sets is either concavoconvex or concave convex depending on the type of their characteristic function