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

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

a note on the spectra and pseudospectra of waveform relaxation operators for linear differential algebraic equations in this note we derived the expressions of the spectra and pseudospectra of waveform relaxation operators for general linear differential algebraic equations of index one the expressions are generalizations of those of lumsdaine and wu siam j sci comput 18 1997 pp 286 304 and the derivation here is nontrivial numerical experiments are given to verify the theoretical results

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

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

controllability of semilinear impulsive nonautonomous systems in this paper we apply rothe s type fixed point theorem to prove the controllability of the following semilinear impulsive nonautonomous systems of differential equations where a t b t are continuous matrices of dimension n n and n m respectively the control function u belongs to and k 1 2 3 p under additional conditions we prove the following statement if the linear is controllable on 0 then the semilinear impulsive system is also controllable on 0 moreover we could exhibit a control steering the nonlinear system from an initial state z0 to a final state z1 at time 0

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

spectra and pseudospectra of waveform relaxation operators we describe the spectra and pseudospectra of continuous time and discrete time waveform relaxation operators since the spectrum of the finite interval waveform relaxation operator is only a singleton the spectrum of the infinite interval operator is typically used to describe the behavior of waveform relaxation algorithms here we show that the pseudospectrum is a more useful tool for analyzing convergence of waveform iterations on finite intervals and prove that the pseudospectrum of the infinite interval operator is in fact the limit of the pseudospectra of the finite interval operators

discrete time accelerated block successive overrelaxation methods for time dependent stokes equations to further study the application of waveform relaxation methods in fluid dynamics in actual computation this paper provides a general theoretical analysis of discrete time waveform relaxation methods for solving linear daes a class of discrete time waveform relaxation methods named discrete time accelerated block successive overrelaxation dabsor methods is proposed for solving linear daes derived from discretizing time dependent stokes equations in space by using method of lines the analysis of convergence property and optimality of the dabsor method are presented in detail the theoretical results and the efficiency of the dabsor method are verified by numerical experiments

on characterizations of preinvex fuzzy mappings several characterizations about preinvex fuzzy mapping are obtained in this paper firstly an equivalent condition of preinvex fuzzy mapping is established under certain conditions furthermore the necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided by using the given equivalent condition of preinvex fuzzy mapping finally a new proof of some known important conclusions is offered these results generalize and improve some known results

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

controllability of the impulsive functional bbm equation with nonlinear term involving spatial derivative abstract for a broad class of control systems modeling real life problems delays and impulses are natural properties that do not modify their behavior so we conjecture that under certain conditions delays and abrupt changes as perturbations of a system do not modify properties such as controllability in this regard we prove the approximate controllability of the impulsive functional benjamin bona mahony bbm equation with nonlinear term involving spatial derivative this can be achieved using the technique avoiding fixed point theorems employed by a e bashirov et al in this case the delay helps us to prove the approximate controllability by pulling back the control solution to a fixed curve in a short time interval

convergence of waveform relaxation methods for differential algebraic systems this paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of picard iterations and more general waveform relaxation methods for differential algebraic systems of neutral type the results are obtained by the contraction mapping principle on banach spaces with weighted norms and by the use of the perron frobenius theory of nonnegative and nonreducible matrices it is demonstrated that waveform relaxation methods are convergent faster than the classical picard iterations

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

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

preinvex fuzzy mappings abstract in this paper we introduce the concepts of preinvex fuzzy mappings quasi preinvex fuzzy mappings and invex sets by modifying the concepts proposed by noor we also give two characterization theorems for preinvex fuzzy mappings and present some new results for preinvex fuzzy mappings strictly preinvex fuzzy mappings and quasi preinvex fuzzy mappings

some properties of convex fuzzy sets and convex fuzzy cones abstract convexity is an important concept for the quantitative and qualitative study in operation research which helps to optimize the solution of its problems therefore many authors were interested in this branch and studied this property on sets cones hulls and functions in this paper we study a modified concept called fuzzy convexity by introducing the notion of convex m convex and quasiconvex fuzzy sets cones and hulls some of their relations and topological properties are presented

pseudospectra of linear operators if a matrix or linear operator a is far from normal its eigenvalues or more generally its spectrum may have little to do with its behavior as measured by quantities such as an or exp ta more may be learned by examining the sets in the complex plane known as the pseudospectra of a defined by level curves of the norm of the resolvent zi a 1 five years ago the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications since that time analogous computations have been carried out for differential and integral operators this paper a companion to the earlier one presents ten examples each chosen to illustrate one or more mathematical or physical principles

on convergence of the wr hss iteration method for a system of linear differential equations abstract we consider a waveform relaxation wr method based on the hermitian skew hermitian splitting hss of the system matrices which is a continuous time iteration method in actual implementation the continuous time wr hss method cwr hss is replaced by the discrete time wr hss method dwr hss defined on a time level sequence if the time step size tends to zero the approximate solution obtained by the dwr hss method on each time level is proved to converge to the limit of the approximate solution obtained by the cwr hss method i e the exact solution of a corresponding system of linear differential equations finally the above relationship between the cwr hss method and the dwr hss method is verified by the numerical tests based on the unsteady discrete elliptic problem therefore the dwr hss method is a reliable option for solving the unsteady discrete elliptic problem in both theoretical and practical aspects

partial controllability concepts the main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form i e given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract hilbert or banach space and disturbed by a deterministic function or by a white noise process at the same time some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged respectively the ordinary controllability conditions for them are too strong since they assume extended state space it is reasonable to introduce partial controllability concepts which assume original state space in this paper we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases

dynamic iteration methods applied to linear dae systems abstract we continue the study of the convergence of dynamic iteration methods by applying them to linear dae systems we show that convergence rate can be studied by similar means as for ode s and that it is critical for convergence to preserve the structure of the dae system when it is split for the iteration

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

computing periodic solutions of linear differential algebraic equations by waveform relaxation we propose an algorithm which is based on the waveform relaxation wr approach to compute the periodic solutions of a linear system described by differential algebraic equations for this kind of two point boundary problems we derive an analytic expression of the spectral set for the periodic wr operator we show that the periodic wr algorithm is convergent if the supremum value of the spectral radii for a series of matrices derived from the system is less than 1 numerical examples where discrete waveforms are computed with a backward difference formula further illustrate the correctness of the theoretical work in this paper

eigenvalues and pseudo eigenvalues of toeplitz matrices the eigenvalues of a nonhermitian toeplitz matrix a are usually highly sensitive to perturbations having condition numbers that increase exponentially with the dimension n an equivalent statement is that the resolvent zz a of a toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest exponentially large as a function of n even when z is far from the spectrum because of these facts the meaningfulness of the eigenvalues of nonhermitian toeplitz matrices for any but the most theoretical purposes should be considered suspect in many applications it is more meaningful to investigate the e pseudo eigenvalues the complex numbers z with ll zz a 11 l this paper analyzes the pseudospectra of toeplitz matrices and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated toeplitz and laurent operators our results are reasonably complete in the triangular case and preliminary in the cases of nontriangular toeplitz matrices block toeplitz matrices and toeplitz like matrices with smoothly varying coefficients computed examples of pseudospectra are presented throughout and applications in numerical analysis are mentioned

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

on convergence conditions of waveform relaxation methods for linear differential algebraic equations for linear constant coefficient differential algebraic equations we study the waveform relaxation methods without demanding the boundedness of the solutions based on infinite time interval in particular we derive explicit expression and obtain asymptotic convergence rate of this class of iteration schemes under weaker assumptions which may have wider and more useful application extent numerical simulations demonstrate the validity of the theory

computation of pseudospectra by continuation the concept of pseudospectrum was introduced by trefethen to explain the behavior of nonnormal operators many phenomena for example hydrodynamic instability and convergence of iterative methods for linear systems cannot be accounted for by eigenvalue analysis but are more understandable by examining the pseudospectra the straightforward way to compute pseudospectra involves many applications of the singular value decomposition svd this paper presents several fast continuation methods to calculate pseudospectra of different types of matrices

convexity and semicontinuity of fuzzy sets in this paper we study a modified concept called fuzzy convexity which was proposed by ammar and metz fuzzy sets and systems 49 1992 135 a criteria for convex fuzzy sets under lower semicontinuity is given we prove in the upper semicontinuous case that the class of semistrictly quasiconvex fuzzy sets lies between the quasiconvex and strictly quasiconvex classes we also prove for both families of semistrictly quasiconvex and strictly quasiconvex fuzzy sets that every local maximizer is also a global one in addition a characterization of quasimonotonic fuzzy sets in terms of level sets is given

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

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

convergence analysis of an arnoldi order reduced runge kutta method for integro differential equations of pantograph type in this paper we consider a numerical method for linear functional integro differential equations with pantograph delays to deal with the pantograph delays we introduce a geometrically increasing mesh and propose a new kind of runge kutta methods based on the arnoldi order reduced technique the convergence analysis of the new method is presented and the method is proved to be at least first order the numerical experiments attached show that the new method can achieve almost the same accuracy as the corresponding runge kutta method for some properly chosen krylov subspaces

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

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

on controllability conception for stochastic systems the controllability notions for partially observed stochastic systems are defined their relation with complete and approximate controllabilities is shown in particular it is proven that the approximate controllability condition is necessary and the complete controllability condition is sufficient for the partially observed linear gaussian control system to attain the arbitrarily small neighborhood of each point in the state space with probability arbitrarily closely to one

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

nonnegative solutions of fractional functional differential equations in this paper we discuss the existence and monotone iterative method of nonnegative solutions for fractional functional differential equations the main conclusion is that the nonnegative solutions can be derived from the monotone iterative method which starts off with a nonnegative upper solution or the zero function under different conditions our approach of obtaining nonnegative solutions is feasible for computational purposes

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