fuzzy goal programming complementary slackness conditions and computational schemes abstract goal programming gp is an important category in linear programming and multiobjective versions which minimize the deviation among value of each objective function and its goal with satisfying other constraints of problem in this paper we deal with fuzzy goal programming fgp which is a generalized problem in vague nature where parameters relations and goals are given as fuzzy quantities with respect to imprecise data recently inuiguchi et al m inuiguchi j ramik t tanio m vlach satisficing solutions and duality in interval and fuzzy linear programming fuzzy sets and systems 135 2003 151 177 have proved some important dual theorems on fgp which are very close to the same crisp versions in continuation to their works based on fuzzy extensions of relations we get complementary slackness conditions for fgp which have an essential role in many optimization techniques moreover we obtain the most optimistic and pessimistic satisficing solutions employing these conditions and present a convex combination of them which covers the satisficing solutions for a fixed level of certainty our practical schemes implement an efficient interior point algorithm as sub procedure so they are polynomial time algorithms

the approximation method for two stage fuzzy random programming with recourse in this paper a new class of fuzzy random optimization problem called two stage fuzzy random programming or fuzzy random programming with recourse frpr problem is first presented then its deterministic equivalent programming problem is characterized because the frpr problems include fuzzy random variable parameters with an infinite support they are inherently infinite dimensional optimization problems that can rarely be solved directly therefore an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed which results in finite dimensional frpr problems after that this paper is devoted to establishing the conditions under which the objective value optimal objective value and minimizers of such finite dimensional frpr problem can be shown to converge to the objective value respectively optimal objective value and minimizers of the original infinite dimensional frpr problem

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

second order oscillation of forced functional differential equations with oscillatory potentials new oscillation criteria are established for second order differential equations containing both delay and advanced arguments of the form k t x t p t x t t a 1x t t q t x s t b 1x s t e t t 0 where a 1 and b 1 k p q e t s are continuous real valued functions k t 0 is nondecreasing t and o are nondecreasing t t t s t t and lim t t t the potentials p q and e are allowed to change sign and the information on the whole half line is not required as opposed to the usual case in most articles among others as an application of the results we are able to deduce that every solution of x t m 1sintx t p12 m 2costx t p6 cos2t m 1 m 2 0 is oscillatory provided that either m 1 orm 2 is sufficiently large

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

convergence of optimal solutions about approximation scheme for fuzzy programming with minimum risk criteria this paper presents a class of two stage fuzzy programming with minimum risk criteria in the sense of value at risk var since the proposed two stage fuzzy minimum risk problem fmrp often includes fuzzy variable coefficients defined through possibility distributions with infinite supports it is inherently an infinite dimensional optimization problem that can rarely be solved directly thus algorithm procedures for solving such an optimization problem must rely on soft computing and approximation schemes which result in a finite dimensional optimization problem in this paper we develop an approximation method to compute the objective function of the two stage fmrp and discuss the convergent results about the use of the approximation method in fmrp including the convergence of the objective value optimal value and the optimal solutions to apply the convergent results about the approximation method we consider a two stage fuzzy facility location allocation fla problem with var objective and solve the problem indirectly by solving its approximating problem since the approximating fuzzy fla problem is neither linear nor convex conventional optimization algorithms cannot be used to solve it in this paper we design a hybrid particle swarm optimization pso algorithm to solve the approximating fuzzy fla problem one numerical example with five facilities and ten customers is also presented to demonstrate the effectiveness of the designed algorithm

oscillation of second order differential equations with mixed argument abstract our aim in this paper is to present a sufficient condition for the oscillation of the second order differential equation with mixed argument formula we compare with the first order advanced equation of the form z t q 2 t z t 0

linear programming with fuzzy coefficients in constraints abstract this paper presents a new method for solving linear programming problems with fuzzy coefficients in constraints it is shown that such problems can be reduced to a linear semi infinite programming problem the relations between optimal solutions and extreme points of the linear semi infinite program are established a cutting plane algorithm is introduced with a convergence proof and a numerical example is included to illustrate the solution procedure

duality in fuzzy number linear programming by use of a certain linear ranking function we explore some duality properties in fuzzy number linear programming problems by use of a linear ranking function we introduce the dual of fuzzy number linear programming primal problems we then present several duality results

controllability of multiplex multi time scale networks the paradigm of layered networks is used to describe many real world systems from biological networks to social organizations and transportation systems while recently there has been much progress in understanding the general properties of multilayer networks our understanding of how to control such systems remains limited one fundamental aspect that makes this endeavor challenging is that each layer can operate at a different time scale thus we cannot directly apply standard ideas from structural control theory of individual networks here we address the problem of controlling multilayer and multi time scale networks focusing on two layer multiplex networks with one to one interlayer coupling we investigate the practically relevant case when the control signal is applied to the nodes of one layer we develop a theory based on disjoint path covers to determine the minimum number of inputs n i necessary for full control we show that if both layers operate on the same time scale then the network structure of both layers equally affect controllability in the presence of time scale separation controllability is enhanced if the controller interacts with the faster layer n i decreases as the time scale difference increases up to a critical time scale difference above which n i remains constant and is completely determined by the faster layer we show that the critical time scale difference is large if layer i is easy and layer ii is hard to control in isolation in contrast control becomes increasingly difficult if the controller interacts with the layer operating on the slower time scale and increasing time scale separation leads to increased n i again up to a critical value above which n i still depends on the structure of both layers this critical value is largely determined by the longest path in the faster layer that does not involve cycles by identifying the underlying mechanisms that connect time scale difference and controllability for a simplified model we provide crucial insight into disentangling how our ability to control real interacting complex systems is affected by a variety of sources of complexity

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

portfolios with fuzzy returns selection strategies based on semi infinite programming this paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables the investor s problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset the corresponding optimal portfolio is derived using semi infinite programming in a soft framework the return on each asset and their membership functions are described using historical data the investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio this approach is illustrated with a numerical example

new nonoscillation criteria for delay differential equations abstract this paper is concerned with the nonoscillation of first order delay differential equations of the form x t p t x t 0 t t 0 where p c t 0 r r 0 t is nondecreasing t t for t t 0 and lim t t new nonoscillation conditions are obtained these conditions concern the case when the well known nonoscillation condition t t p s ds 1 e is not satisfied

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

inequality relation between fuzzy numbers and its use in fuzzy optimization the inequality relation between two fuzzy numbers is investigated a certain type of such a relation motivated by practical interpretation is proposed and its correspondence with the usual lattice type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed the concept of r l fuzzy number is introduced the class of all r l fuzzy numbers covering practically the whole set of normal convex fuzzy numbers comparing two r l fuzzy numbers of the same type the relation introduced in the paper may be replaced by four ordinary inequalities this fact may be taken advantage of in optimization problems with linear fuzzy constraints

linear semi infinite programming theory an updated survey abstract this paper presents an state of the art survey on linear semi infinite programming theory and its extensions in particular convex semi infinite programming this review updates a previous survey semi infinite programming non convex optim appl 25 1998 of the same authors on the same topic which was published in 1998

measuring the satisfaction of constraints in fuzzy linear programming the paper proposes a new kind of method for solving fuzzy linear programming problems based on the satisfaction or fulfillment degree of the constraints using a new ranking method of fuzzy numbers the fulfillment of the constraints can be measured then the properties of the ranking index are discussed with this ranking index the decision maker can make the constraints tight or loose based on his optimistic or pessimistic attitude and get the optimal solution from the fuzzy constraint space the corresponding value of objective distribution function can be obtained a numerical example illustrates the merits of the approach

on nonoscillation of mixed advanced delay differential equations with positive and negative coefficients for a mixed advanced delay differential equation with variable delays and coefficients email protected t a t x g t b t x h t 0 t t 0 where a t 0 b t 0 g t t h t t explicit nonoscillation conditions are obtained

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

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

a review of duality theory for linear programming over topological vector spaces abstract in this paper duality theory for infinite dimensional linear programs is discussed in a topological vector space setting infinite dimensional linear programs occur in many different areas and the duality theory of such problems has been discussed by a number of authors however the results are scattered in the literature and are proved in a variety of different settings the purpose of this paper is to bring together the main results on this subject and to present them in a unified setting and notation with some new simpler proofs