some quadrature formulae with nonstandard weights in this paper the authors study truncated quadrature rules based on the zeros of generalized laguerre polynomials then they prove the stability and the convergence of the introduced integration rules some numerical tests confirm the theoretical results

fuzzy linear programming and applications abstract this paper presents a survey on methods for solving fuzzy linear programs first lp models with soft constraints are discussed then lp problems in which coefficients of constraints and or of the objective function may be fuzzy are outlined pivotal questions are the interpretation of the inequality relation in fuzzy constraints and the meaning of fuzzy objectives in addition to the commonly applied extended addition based on the min operator and used for the aggregation of the left hand sides of fuzzy constraints and fuzzy objectives a more flexible procedure based on yager s parametrized t norm t p is presented finally practical applications of fuzzy linear programs are listed

numerical computation of hypersingular integrals on the real semiaxis abstract in this paper we propose some different strategies to approximate hypersingular integrals 0 g x x t p 1 d x where p is a positive integer t 0 and the integral is understood in the hadamard finite part sense hadamard finite part integrals shortly fp integrals regarded as p th derivative of cauchy principal value integrals are of interest in the solution of hypersingular bie which model many different kind of physical and engineering problems see 1 and the references therein 2 3 4 the procedure we employ here is based on a simple tool like the truncated gaussian rule see 5 conveniently modified to remove numerical cancellation we will consider functions g having different decays at infinity the method is shown to be numerically stable and convergent and some error estimates in suitable zygmund type spaces are proved finally some numerical tests which confirm the efficiency of the proposed procedures are presented

a method to evaluate the hilbert transform on 0 the author proposes a method to approximate the hilbert transform on the real positive semiaxis by a suitable lagrange interpolating polynomial the method employs truncated gaussian rules and uses the interlacing properties of the zeros of generalized laguerre polynomials the error estimate in a weighted uniform norm is proved and some numerical tests show the efficacy of the proposed procedure

numerical treatment of a class of systems of fredholm integral equations on the real line in this paper the authors propose a nystrom method based on a truncated gaussian rule to solve systems of fredholm integral equations on the real line they prove that it is stable and convergent and that the matrices of the solved linear systems are well conditioned moreover they give error estimates in weighted uniform norm and show some numerical tests fredholm integral equations nystrom method truncated gaussian rule

linear programming with fuzzy variables in practice there are many problems in which all decision parameters are fuzzy numbers and such problems are usually solved by either possibilistic programming or multiobjective programming methods unfortunately all these methods have shortcomings in this note using the concept of comparison of fuzzy numbers we introduce a very effective method for solving these problems then we propose a new method for solving linear programming problems with fuzzy variables

on the numerical solution of fredholm integral equations on unbounded intervals the authors propose some numerical methods to solve fredholm integral equations of the second kind on unbounded intervals the proposed procedure includes projection methods and their discretized versions special attention is turned to the conditioning of the linear system corresponding to the finite dimensional equation

multiple objective linear programming models with interval coefficients an illustrated overview in most real world situations the coefficients of decision support models are not exactly known in this context it is convenient to consider an extension of traditional mathematical programming models incorporating their intrinsic uncertainty without assuming the exactness of the model coefficients interval programming is one of the tools to tackle uncertainty in mathematical programming models moreover most real world problems inherently impose the need to consider multiple conflicting and incommensurate objective functions this paper provides an illustrated overview of the state of the art of interval programming in the context of multiple objective linear programming models

a lagrange type projector on the real line we introduce an interpolation process based on some of the zeros of the mth generalized freud polynomial convergence results and error estimates are given in particular we show that in some important function spaces the interpolating polynomial behaves like the best approximation moreover the stability and the convergence of some quadrature rules are proved

fuzzy least absolutes regression using shape preserving operations the purpose of this study is to introduce a new fuzzy regression model based on the least absolutes method the fuzzy simple and fuzzy multivariate regression models with fuzzy input fuzzy output are considered in which the coefficients of the models are themselves fuzzy the proposed method is based on a new metric on the space of lr fuzzy numbers fuzzy arithmetic operations are based on the weakest triangular norm t w which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication the results of comparative studies and numerical examples indicate that using the similarity measure criterion as well as a predictive ability index the proposed method has a better performance than the least squares method especially when the data set includes some outlier data point s

solving fuzzy stochastic linear programming problems using superiority and inferiority measures in this paper the author presents a model to measure the superiority and inferiority of fuzzy numbers fuzzy stochastic variables then the new measures are used to convert the fuzzy stochastic linear program into the corresponding deterministic linear program numerical examples are provided to illustrate the effectiveness of the proposed method

violation analysis on two step method for interval linear programming in many real world problems system parameters or model coefficients may be bounded between lower and upper bounds due to a variety of uncertainties over the past decades intensive research efforts have focused on interval linear programming ilp to tackle such uncertainties as one of the most popular methods for solving ilp problems two step method tsm proposed by huang et al in 1995 allows uncertain information to be directly communicated into the optimization process and resulting solutions such that decision alternatives could be generated through the interpretation of interval solutions however part of optimum solution points obtained through tsm may go beyond the decision space in some cases this phenomenon referred to as solution violation may mislead decision makers to unreasonable policies plans or strategies which play important roles in the social and economic development therefore this study first investigates and identifies the essential cause for the solution violation of tsm following that an improved solution method namely itsm is proposed to avoid resulting violation by introducing extra constraints in the solving process a numeric example is then presented to demonstrate the effectiveness of itsm in handling solution violation

gaussian quadrature rules with exponential weights on 1 1 we study the behavior of some truncated gaussian rules based on the zeros of pollaczek type polynomials these formulas are stable and converge with the order of the best polynomial approximation in suitable function spaces moreover we apply these results to the related lagrange interpolation process and to prove the stability and the convergence of a nystrom method for fredholm integral equations of the second kind finally some numerical examples are shown

approximation of the hilbert transform on the real line using hermite zeros the authors study the hilbert transform on the real line they introduce some polynomial approximations and some algorithms for its numerical evaluation error estimates in uniform norm are given

numerical quadratures for singular and hypersingular integrals abstract we present a procedure for the design of high order quadrature rules for the numerical evaluation of singular and hypersingular integrals such integrals are frequently encountered in solution of integral equations of potential theory in two dimensions unlike integrals of both smooth and weakly singular functions hypersingular integrals are pseudo differential operators being limits of certain integrals as a result standard quadrature formulae fail for hypersingular integrals on the other hand such expressions are often encountered in mathematical physics see for example 1 and it is desirable to have simple and efficient quadrature formulae for them the algorithm we present constructs high order quadratures for the evaluation of hypersingular integrals the additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals hilbert transforms and integrals involving both smooth and logarithmically singular functions this results in significantly simplified implementations the performance of the procedure is illustrated with several numerical examples

on uniform approximations to hypersingular finite part integrals abstract in this paper new uniform approximation schemes for computation of hypersingular finite part integrals are studied the methods are verified to be supremely qualified for oscillatory integrands in addition based on the results on chebyshev approximations the uniform convergence and computational error bounds are considered preliminary numerical results show the stability and efficiency of the schemes

generalized fuzzy linear programming for decision making under uncertainty feasibility of fuzzy solutions and solving approach in this study a generalized fuzzy linear programming gflp method is developed for dealing with uncertainties expressed as fuzzy sets the feasibility of fuzzy solutions of the gflp problem is investigated a stepwise interactive algorithm sia based on the idea of design of experiment is then advanced to solve the gflp problem this sia method was implemented through i discretizing membership grade of fuzzy parameters into a finite number of a cut levels ii converting the gflp model into an interval linear programming ilp submodel under every a cut level iii solving the ilp submodels through an interactive algorithm and obtaining the associated interval solutions iv acquiring the membership functions of fuzzy solutions through statistical regression methods a simple numerical example is then proposed to illustrate the solution process of the gflp model through sia a comparison between the solutions obtained though sia and monte carlo method is finally conducted to demonstrate the robustness of the sia method the results indicate that the membership functions for decision variables and objective function are reasonable and robust

solving a class of fuzzy linear programs by using semi infinite programming techniques this paper deals with a class of fuzzy linear programming problems characterized by the fact that the coefficients in the constraints are modeled as lr fuzzy numbers with different shapes solving such problems is usually more complicated than finding a solution when all the fuzzy coefficients have the same shape we propose a primal semi infinite algorithm as a valuable tool for solving this class of fuzzy linear programs and we illustrate it by means of several examples

duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables linear programming problems with trapezoidal fuzzy variables fvlp have recently attracted some interest some methods have been developed for solving these problems by introducing and solving certain auxiliary problems here we apply a linear ranking function to order trapezoidal fuzzy numbers then we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results in particular we prove that the auxiliary problem is indeed the dual of the fvlp problem having established the dual problem the results will then follow as natural extensions of duality results for linear programming problems with crisp data finally using the results we develop a new dual algorithm for solving the fvlp problem directly making use of the primal simplex tableau this algorithm will be useful for sensitivity or post optimality analysis when using primal simplex tableaus

interactive multiobjective fuzzy random programming through the level set based probability model this paper considers a multiobjective linear programming problem involving fuzzy random variable coefficients a new fuzzy random programming model is proposed by extending the ideas of level set based optimality and a stochastic programming model the original problem involving fuzzy random variables is transformed into a deterministic equivalent problem through the proposed model an interactive algorithm is provided to obtain a satisficing solution for a decision maker from among a set of newly defined pareto optimal solutions it is shown that an optimal solution of the problem to be solved iteratively in the interactive algorithm is analytically obtained by a combination of the bisection method and the simplex method

post optimality analysis on the membership functions of a fuzzy linear programming problem models of linear programming problems with fuzzy constraints are very well known in the current literature in almost all cases to solve these problems linear membership functions are used because they have very good properties and are very easy to manipulate in some cases however because of the knowledge that the decision maker has such membership functions could be modeled as nonlinear although the complexity of the problem could increase this paper considers the use of nonlinear membership functions in fuzzy linear programming problems to show that the corresponding solution to be obtained can be derived from a parallel linear model moreover it is easier to solve than the nonlinear model making use of a similar procedure to that of post optimal analysis in classical linear programming the case in which these membership functions are defined by means of piecewise linear approximations is also considered and analyzed

hypersingular integrals how smooth must the density be hypersingular integrals are guaranteed to exist at a point x only if the density function f in the integrand satises certain conditions in a neighbourhood of x it is well known that a su cient condition is that f has a holder continuous rst derivative this is a stringent condition especially when it is incorporated into boundary element methods for solving hypersingular in tegral equations this paper is concerned with nding weaker conditions for the existence of one dimensional hadamard nite part integrals it is shown that it is sucien t for the even part of f with respect to x to have a holder continuous rst derivative the odd part is al lowed to be discontinuous a similar condition is obtained for cauchy principal value integrals these simple results have non trivial consequences they are applied to the calculation of the tangential derivative of a single layer potential and to the normal derivative of a double layer potential particular attention is paid to discontinuous densities and to discontinuous boundary conditions also despite the weaker sucien t conditions it is rearmed that for hypersingular integral equations collocation at a point x at the junction between two standard conforming boundary elements is not permissible theoretically various modications to the denition of nite part integral are explored

numerical methods for some special fredholm integral equations on the real line the authors propose a simple numerical method to approximate the solution of csie the convergence and the stability of the procedure are proved and some numerical examples are shown

solving linear programming problems under fuzziness and randomness environment using attainment values in this paper the author presents a model to measure attainment values of fuzzy numbers fuzzy stochastic variables these new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem numerical comparisons are provided to illustrate the effectiveness of the proposed method

interactive decision making in fuzzy linear optimization problems abstract this paper presents an interactive method for solving a multi criteria linear program where coefficients of the objective functions and or of the constraints are known exactly but imprecisely assuming fuzzy aspiration levels for each of the goals and basing on a comparison of flat fuzzy numbers the original fuzzy problem is transformed into a crisp satisfactory model to determine a suitable compromise solution we will maximize the minimum of the surpluses over the aspiration levels this induces a problem with a nonlinear objective function which is equivalent to a linear program

the euler maclaurin expansion and finite part integrals in this paper we compare g p the mellin transform together with its analytic continuation and overline overline g p the related hadamard finite part integral of a function g x which decays exponentially at infinity and has specified singular behavior at the origin except when p is a nonpositive integer these coincide when p is a nonpositive integer overline overline g p is well defined but g p has a pole we show that the terms in the laurent expansion about this pole can be simply expressed in terms of the hadamard finite part integral of a related function this circumstance is exploited to provide a conceptually uniform proof of the various generalizations of the euler maclaurin expansion for the quadrature error functional

a computational algorithm for solving periodic penta diagonal linear systems in this paper we present a new efficient computational algorithm for solving periodic penta digonal linear systems the implementation of the algorithm using computer algebra systems cas such as maple macsyma mathematica and matlab is straightforward an example is given in order to illustrate the algorithm

on solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem in this paper a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered first we show that the efficient solutions fuzzy quadratic multiobjective programming problems series optimal solutions of relative scalar fuzzy quadratic programming some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients having decision vectors as fuzzy variables an application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given at the end numerical examples are illustrated in the support of the obtained results

a new recursive algorithm for inverting general periodic pentadiagonal and anti pentadiagonal matrices in the current article the authors present a new recursive symbolic computational algorithm that will never break down for inverting general periodic pentadiagonal and anti pentadiagonal matrices it is a natural generalization of the work presented in m e a el mikkawy e d rahmo a new recursive algorithm for inverting general tridiagonal and anti tridiagonal matrices appl math comput 204 2008 368 372 the algorithm is suited for implementation using computer algebra systems cas such as mathematica macsyma and maple an illustrative example is given

fuzzy goal programming a parametric approach narasimhan incorporated fuzzy set theory within goal formulation in 1980 since then much research has been performed in this field and various models for solving fuzzy goal programming have been proposed one of the well known models was proposed by tiwari et al in 1987 19 where an additive model was proposed this paper is an extension to the tiwari et al model that deals with the sum of weighted negative deviations between the desirable achievement degree and the common target here properties of the model are proposed a numerical example is also given to illustrate the approach

on the uniform convergence of gaussian quadrature rules for cauchy principal value integrals and their derivatives the convergence of the aforementioned quadrature rules for integrands possessing h6lder continuous derivatives of an appropriate order is proved to be uniform and not only pointwise the rate of convergence is also established and an application to the numerical solution of singular integral equations is made

projection methods and condition numbers in uniform norm for fredholm and cauchy singular integral equations in this paper the authors propose a numerical method for the approximate solution of some classes of fredholm and cauchy integral equations including the discrete collocation and collocation methods

numerical evaluation of hypersingular integrals abstract boundary integral equations which employ integrals which exist only if defined in the cauchy principal value sense or as the hadamard finite part are currently used with success to solve many two and three dimensional problems of applied mechanics we will recall definitions and main properties of these integrals examine some numerical approaches for their evaluation and present several new results

quadrature rules with multiple nodes for evaluating integrals with strong singularities we present a method based on the chakalov popoviciu quadrature formula of lobatto type a rather general case of quadrature with multiple nodes for approximating integrals defined by cauchy principal values or by hadamard finite parts as a starting point we use the results obtained by l gori and e santi cf on the evaluation of hilbert transforms by means of a particular class of turan quadrature rules numer algorithms 10 1995 27 39 quadrature rules based on s orthogonal polynomials for evaluating integrals with strong singularities oberwolfach proceedings applications and computation of orthogonal polynomials isnm 131 birkhauser basel 1999 pp 109 119 we generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae numerical examples illustrations and comparisons are also shown

possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems abstract in this paper several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems interval and triangular possibility distributions are used to express the non interactive cases between the fuzzy decision variables and exponential possibility distributions are used to represent the interrelated cases possibilistic linear programming problems based on exponential possibility distributions become non linear optimization problems in order to solve optimization problems easily algorithms for obtaining center vectors and distribution matrices in sequence are proposed by the proposed algorithms the possibility distribution of fuzzy decision variables can be obtained

definitions properties and applications of finite part integrals by using standard calculus we discuss some definitions and properties of finite part integrals point out the essence of this concept and show how these integrals naturally arise in some integral equation applications a couple of new examples are also described

a general model for fuzzy linear programming abstract in the current literature there are several models of fuzzy linear programming problems the aim of this paper is first to describe the more important problems in fuzzy linear programming and second to give a general model of fuzzy linear programming problems involving all of the above ones finally a resolution method for that general model is proposed

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

decomposition methods in stochastic programming stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition we review basic ideas of cutting plane methods augmented lagrangian and splitting methods and stochastic decomposition methods for convex polyhedral multi stage stochastic programming problems

numerical integration of functions with a very small significant support in some applications one has to deal with the problem of integrating over a bounded interval a smooth function taking significant values with respect to the machine precision or to the accuracy one wants to achieve only in a very small part of the domain of integration in this paper we propose a simple and efficient numerical approach to compute or discretize integrals of this type we also consider a class of second kind integral equations whose integral operator has the above behavior some numerical testing is presented

a note on generalized fuzzy linear programming for decision making under uncertainty feasibility of fuzzy solutions and solving approach in this short note we point out that the paper entitled above suffers from certain mistakes

numerical approximation of weakly singular integrals on the half line this paper deals with the numerical approximation of a weakly singular integral transform by means of laguerre nodes error estimates in a weighted uniform norm and some numerical tests are given

approximate solution of dual fuzzy matrix equations in this paper we propose a simple and practical method to solve the dual fuzzy matrix equation ax b cx d in which a c are mxn matrices and b d are mxp lr fuzzy numbers matrices by means of the arithmetic operations on lr fuzzy numbers space the dual fuzzy matrix equation could be converted into two classical matrix equations and the lr minimal fuzzy solution and the strong weak lr minimal fuzzy solutions of the dual fuzzy matrix equation are derived by solving two classical matrix equations based on the generalized inverses of matrices meanwhile as a special case of the dual fuzzy matrix equation the fuzzy solutions of the dual fuzzy linear systems are investigated finally some numerical examples are given to illustrate the effectiveness of the proposed method

on the inverse of a general pentadiagonal matrix in this paper employing the general doolittle factorization an efficient algorithm is developed to find the inverse of a general pentadiagonal matrix which is suitable for implementation using computer algebra systems software such as matlab and maple examples are given to illustrate the efficiency of the algorithm

grey integer programming an application to waste management planning under uncertainty abstract this paper introduces a grey integer programming gip method for facility expansion planning under uncertainty by incorporating the concepts of grey number and grey mathematical programming into a mixed integer linear programming optimization framework the approach is an improvement upon previous integer programming methods in terms of its technical characteristics and applicability it allows uncertain information to be effectively communicated into the optimization process and the resulting solutions it also has low computational requirements and is thus applicable to practical problems the modelling approach is applied to a hypothetical planning problem of waste flow allocation and treatment disposal facility expansion within a regional solid waste management system the binary variable solutions provide the ranges of different development alternatives within a multi period multi facility and multi scale context and the continuous variable solutions provide optimal schemes for waste flow allocation corresponding to the upper and lower bounds of the objective function value the results indicate that reasonable and useful solutions can be achieved through the developed approach

numerical methods for fredholm integral equations on the square abstract in this paper we shall investigate the numerical solution of two dimensional fredholm integral equations by nystrom and collocation methods based on the zeros of jacobi orthogonal polynomials the convergence stability and well conditioning of the method are proved in suitable weighted spaces of functions some numerical examples illustrate the efficiency of the methods

interlacing properties of the zeros of the orthogonal polynomials and approximation of the hilbert transform abstract in this paper starting from interlacing properties of the zeros of the orthogonal polynomials the authors propose a new method to approximate the finite hilbert transform for this method they give error estimates in uniform norm

extended procedure for computing the values of the membership function of a fuzzy solution to a class of fuzzy linear optimization problems in 1994 chanas and kuchta suggested one approach to determine the membership function of a fuzzy solution to the fuzzy linear optimization problem with fuzzy coefficients in the objective function based on computing the sum of lengths of certain intervals in 2012 dempe and ruziyeva introduced a methodology for realizing chanas and kuchta s idea and derived explicit formulas for computing the endpoints of the suggested intervals in the particular case of triangular fuzzy numbers the purpose of this paper is to extend dempe and ruziyeva s approach by handling the possible degeneracy of basic feasible solutions and derive new formulas for computing the values of the membership function the special example considered by dempe and ruziyeva is again used to illustrate the relevance of the extended solving procedure and new formulas

nystrom methods for bivariate fredholm integral equations on unbounded domains abstract in this paper we propose a numerical procedure in order to approximate the solution of two dimensional fredholm integral equations on unbounded domains like strips half planes or the whole real plane we consider global methods of nystrom types which are based on the zeros of suitable orthogonal polynomials one of the main interesting aspects of our procedures regards the quality of the involved functions since we can successfully manage functions which are singular on the finite boundaries and can have an exponential growth on the infinite boundaries of the domains moreover the errors of the methods are comparable with the error of best polynomial approximation in the weighted spaces of functions that we go to treat the convergence and the stability of the methods and the well conditioning of the final linear systems are proved and some numerical tests which confirm the theoretical estimates are given

computational methods for solving fully fuzzy linear systems abstract since many real world engineering systems are too complex to be defined in precise terms imprecision is often involved in any engineering design process fuzzy systems have an essential role in this fuzzy modelling which can formulate uncertainty in actual environment in addition this is an important sub process in determining inverse eigenvalue and some other useful matrix computations too one of the most practicable subjects in recent studies is based on lr fuzzy numbers which are defined and used by dubois and prade with some useful and easy approximation arithmetic operators on them recently dehghan et al m dehghan m ghatee b hashemi some computations on fuzzy matrices submitted for publication extended some matrix computations on fuzzy matrices where a fuzzy matrix appears as a rectangular array of fuzzy numbers in continuation to our previous work we focus on fuzzy systems in this paper it is proved that finding all of the real solutions which satisfy in a system with interval coefficients is np hard the same result can similarly be derived for fuzzy systems so we employ some heuristics based methods on dubois and prade s approach finding some positive fuzzy vector x which satisfies a x b where a and b are a fuzzy matrix and a fuzzy vector respectively we propose some new methods to solve this system that are comparable to the well known methods such as the cramer s rule gaussian elimination lu decomposition method doolittle algorithm and its simplification finally we extend a new method employing linear programming lp for solving square and non square over determined fuzzy systems some numerical examples clarify the ability of our heuristics

gauss quadrature rules for finite part integrals we construct a set of polynomials n x which are orthogonal with respect to w x x 2 where wx is a weight function these polynomials can be used for the definition of a gauss quadrature formula for the finite part integral the process is exactly the same as the one used for the extraction of the classical gauss formula for the riemann integrals three different methods are derived the first and most accurate quadrature formula is successfully tested in some numerical examples the proposed quadrature formulas have many applications in problems of mathematical physics mechanics etc

a new approach to some possibilistic linear programming problems abstract in practice the unit costs profits of new products or new projects the lending and borrowing interest rates and cash flows are always imprecise we provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and or constraint coefficients our strategy is to maximize the most possible value of the imprecise profit at the same time we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit this strategy is equivalent to the practical considerations of financial problems in this paper a numeric investment problem is solved for illustrating the new approach

fuzzy stochastic based violation analysis method for planning water resources management systems with uncertain information in this study a fuzzy stochastic based violation analysis fsva approach is developed for the planning of water resources management systems with uncertain information based on a multistage fuzzy stochastic integer programming fsip model in fsva a number of violation variables for the objective and constraints are allowed such that in depth analyses of tradeoffs among economic objective satisfaction degree and constraint violation risk can be facilitated besides the developed method can deal with uncertainties expressed as probability distributions and fuzzy sets it can also reflect the dynamics in terms of decisions for water allocation and surplus flow diversion through transactions at discrete points of a complete scenario set over a multistage context the developed fsva method is applied to a case study of water resources management within a multi stream multi reservoir and multi period context the results indicate that the satisfaction degrees and system benefits would be different under varied violation levels moreover different violation levels can also lead to changed water allocation and surplus flow diversion plans violation analyses are also conducted to demonstrate that violating different constraints have different effects on system benefit and satisfaction degree

new method for solving fuzzy transportation problems with lr flat fuzzy numbers transportation problems have various applications in logistics and supply chains for reducing costs in real life situations the parameters of transportation problems may not be known precisely because of uncontrollable factors herein we propose a new method for solving fuzzy transportation problems ftps in which the transportation costs and supply and demand are represented by non negative lr flat fuzzy numbers the ftp is converted into four transportation problems which are solved using standard transportation simplex algorithms the advantages of the proposed method over existing methods are discussed in the context of two application examples the results show that the proposed method is simpler and computationally more efficient than existing methods in the literature

the use of parametric programming in fuzzy linear programming in this paper the possibility of the identification of a complete fuzzy decision not only the maximizing alternative in fuzzy linear programming by use of the parametric programming technique is presented also it is shown that this fact can be useful in the zimmermann approach to multiple objective linear programming the presented remarks are illustrated by some numerical examples

a direct approach for boundary integral equations with high order singularities summary boundary integral equations with extremely singular i e more than hypersingular kernels would be useful in several elds of applied mechanics particularly when second and third order derivatives of the primary variable are required however their denition and numerical treatment pose several problems in this paper it is shown how to obtain these boundary integral equations with still unnamed singularities and moreover how to eciently and reliably compute all the singular integrals this is done by extending in full generality the so called direct approach only for deniteness the method is presented for the analysis of the deection of thin elastic plates numerical results concerning integrals with singularities up to order r 4 are presented to validate the proposed algorithm copyright 2000 john wiley sons ltd

hilbert and hadamard transforms by generalized chebyshev expansion abstract an automatic quadrature is presented for approximating hadamard finite part fp integrals of a smooth function with a double pole singularity within the range of integration the quadrature rule is derived from the differentiation of an approximation to a cauchy principal value integral or the hilbert transform the approximation to the fp integral is represented as a function of the value of pole by using chebyshev polynomials of the second kind since the error can be estimated independently of the value of pole a set of integrals for a set of values of pole can be efficiently approximated to a required tolerance with the same number of function evaluations numerical examples are also included to illustrate the performance of the methods

a new recursive algorithm for inverting general tridiagonal and anti tridiagonal matrices in the current article the authors present a new recursive symbolic computational algorithm for inverting general tridiagonal and anti tridiagonal matrices an illustrative example is given

markov sonin gaussian rule for singular functions the paper deals with the approximation of integrals r fw where w is a markov sonin weight and f can be singular at the origin gaussian type quadrature roles having a better behaviour w r t the ordinary gaussian rule are introduced error estimates in weighted l1 norm and some numerical tests are given

truncated quadrature rules over 0 infty and nystrom type methods we propose replacing the classical gauss laguerre quadrature formula by a truncated version of it obtained by ignoring the last part of its nodes this has the effect of obtaining optimal orders of convergence corresponding quadrature rules with kernels are then considered and optimal error estimates are derived also for them these rules are finally used to define stable nystrom type interpolants for a second kind of integral equation on the real semiaxis whose solutions decay exponentially at infty

nystrom method for fredholm integral equations of the second kind in two variables on a triangle the paper deals with the approximation of the solution of the following bivariate fredholm integral equationf y email protected dk x y f x w x dx g y email protected d where the domain d is a triangle the proposed procedure by a suitable transformation is essentially the nystrom method based on the zeros of univariate jacobi orthogonal polynomials convergence stability and well conditioning of the method are proved in order to illustrate the efficiency of the proposed method some numerical tests are given

a fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix in the current paper we present a computationally efficient algorithm for obtaining the inverse of a tridiagonal matrix and a pentadiogonal matrix few conditions are required and the algorithm is suited for implementation using computer algebra systems

a structure preserving matrix factorization for solving general periodic pentadiagonal toeplitz linear systems abstract in the current article a new algorithm for solving linear systems with the periodic pentadiagonal toeplitz ppt coefficient matrix is presented this algorithm is based on a structure preserving matrix factorization and sherman morrison woodbury formula some numerical examples are given in order to illustrate the effectiveness of the proposed algorithms all of the experiments are performed on a computer with the aid of programs written in matlab

linear programming with fuzzy parameters an interactive method resolution this paper proposes a method for solving linear programming problems where all the coefficients are in general fuzzy numbers we use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints it allows us to work with the concept of feasibility degree the bigger the feasibility degree is the worst the objective value will be we offer the decision maker dm the optimal solution for several different degrees of feasibility with this information the dm is able to establish a fuzzy goal we build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal a reasonable solution is the one that has the biggest membership degree to this fuzzy subset finally to illustrate our method we solve a numerical example

evolutionary algorithm solution to fuzzy problems fuzzy linear programming in this paper we wish to find solutions to the fully fuzzified linear program where all the parameters and variables are fuzzy numbers we first change the problem of maximizing a fuzzy number the value of the objective function into a multi objective fuzzy linear programming problem we prove that fuzzy flexible programming can be used to explore the whole undominated set to the multi objective fuzzy linear program an evolutionary algorithm is designed to solve the fuzzy flexible program and we apply this program to two applications to generate good solutions

extended lagrange interpolation in weighted uniform norm the author studies the uniform convergence of extended lagrange interpolation processes based on the zeros of generalized laguerre polynomials

a modified pso algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints fri fc in this paper optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t norm is considered as fuzzy composition and fuzzy inequality replaces ordinary inequality in the constraints unlike most optimization algorithms in fuzzy relational inequalities with fuzzy constraints fri fc we find a near feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp ordinary inequality constraints such solutions are called super optima in this paper subsequently an algorithm is proposed to find a super optimum with pre specified desirable infeasibility for this purpose we firstly study some structural properties of the fri fc problem and present a new formulization that is independent of t norms used in the constraints of the problem this new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters however it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super optimum under a certain sufficient condition finally a modified pso is presented in which the ability of pso to solve unconstrained problems with continuous domain the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized fri fc problems the modified pso algorithm has been applied to the generalized fri fc problem defined with ten well known continuous t norms additionally an idea of the fri fc problems as outer approximators for fri problems with ordinary inequalities is also investigated

an information axiom based decision making approach under hybrid uncertain environments this paper aims to develop a decision making approach based on the information axiom under hybrid uncertain environments in these environments fuzziness and randomness co exist to model the hybrid uncertainties the design range and system range of an evaluation criterion are expressed as a fuzzy variable and a random variable respectively calculating the information contents for these criteria would involve integrals whose bounds are fuzzy variables to calculate these integrals an expected information content model eicm is proposed based upon the credibility theory to reflect the designer s risk appetite accurately the confidence levels are introduced and a credibility information content model cicm based on the chance constrains programming model is constructed two algorithms based on fuzzy simulation methods and genetic algorithm are developed for these two models finally a case study is illustrated to highlight the effectiveness and accuracy of the proposed approach

some numerical algorithms to evaluate hadamard finite part integrals abstract some algorithms are described for the numerical evaluation of hadamard finite part integrals of type 1 1 f x x t 2 v dx t where v is a jacobi weight convergence results and some numerical examples are given

approximation of the hilbert transform on the real semiaxis using laguerre zeros the authors propose two new algorithms for the computation of cauchy principal value integrals on the real semiaxis the proposed quadrature rules use zeros of laguerre polynomials theoretical error estimates are proved and some numerical examples are showed