two level linear programming decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which often exist in practice multilevel programming models partition control over decision variables among ordered levels within a hierarchical planning structure a planner at one level of the hierarchy may have his objective function and set of feasible decisions determined in part by other levels however his control instruments may allow him to influence the policies at other levels and thereby improve his own objective function this paper examines the special case of the two level linear programming problem geometric characterizations and algorithms are presented with some examples the goal is to demonstrate the tractability of such problems and motivate a wider interest in their study

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

interactive fuzzy stochastic two level linear programming with simple recourse abstract in this paper assuming cooperative behavior of the decision makers two level linear programming problems involving random variables in constraints are considered using the concept of simple recourse the formulated stochastic two level simple recourse problems are transformed into deterministic two level programming ones taking into account vagueness of judgments of the decision makers interactive fuzzy programming is presented in the proposed interactive method after determining the fuzzy goals of the decision makers at both levels a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

hierarchical optimization a satisfactory solution abstract hierarchical optimization or multi level programming techniques are extensions of stackelberg games for solving decentralized planning problems with multiple decision makers in a hierarchical organization they become more important for contemporary decentralized organizations where each unit or department seeks its own interests traditional approaches include vertex enumeration algorithms and approaches based on kuhn tucker conditions or penalty functions these are not only technically inefficient but also lead to a paradox that the follower s decision power dominates the leader s in this study concepts of memberships of optimalities and degrees of decision powers are proposed to solve the above problems efficiently in the proposed hierarchy decision process the leader first sets memberships of optimalities of his her possible objective values and decisions as well as his her decision power and then asks the follower for his her optima calculated in isolation under given constraints the follower s decision with the corresponding levels of optimalities and decision powers are submitted to and modified by the leader with considerations of overall benefit for the organization and distribution of decision power until a best preferred solution is reached

on decomposability of multilinear sets we consider the multilinear set mathcal s defined as the set of binary points x y satisfying a collection of multilinear equations of the form y i prod i in i x i i in mathcal i where mathcal i denotes a family of subsets of 1 ldots n of cardinality at least two such sets appear in factorable reformulations of many types of nonconvex optimization problems including binary polynomial optimization a great simplification in studying the facial structure of the convex hull of the multilinear set is possible when mathcal s is decomposable into simpler multilinear sets mathcal s j j in j namely the convex hull of mathcal s can be obtained by convexifying each mathcal s j separately in this paper we study the decomposability properties of multilinear sets utilizing an equivalent hypergraph representation for multilinear sets we derive necessary and sufficient conditions under which mathcal s is decomposable into mathcal s j j in j based on the structure of pair wise intersection hypergraphs our characterizations unify and extend the existing decomposability results for the boolean quadric polytope finally we propose a polynomial time algorithm to optimally decompose a multilinear set into simpler subsets our proposed algorithm can be easily incorporated in branch and cut based global solvers as a preprocessing step for cut generation

modified fgp approach for multi level multi objective linear fractional programming problems in this paper we present a new modified method for solving multi level multi objective linear fractional programming problems ml molfpps based on fuzzy goal programming fgp approach with some modifications in the algorithm suggested by baky 2010 18 which dealt with multi level multi objective linear programming problem ml molpp in proposed modified approach numerator and denominator function of each objective at each level are individually transformed into fuzzy goals and their aspiration levels are determined using individual best solutions different linear membership functions are defined for numerator and denominator function of each objective function then highest degree of each of these membership goals is achieved by minimising the sum of negative deviational variables the proposed algorithm simplifies the ml molfpp by eliminating solution preferences by the decision makers at each level thereby avoiding difficulties associate with multi level programming problems and decision deadlock situations the aim of this paper is to present simple and efficient technique to obtain compromise optimal solution of ml molfp problems numerical examples are illustrated in order to support the proposed modified fgp technique

a stable neural network based observer with application to flexible joint manipulators a stable neural network nn based observer for general multivariable nonlinear systems is presented in this paper unlike most previous neural network observers the proposed observer uses a nonlinear in parameters neural network nlpnn therefore it can be applied to systems with higher degrees of nonlinearity without any a priori knowledge about system dynamics the learning rule for the neural network is a novel approach based on the modified backpropagation bp algorithm an e modification term is added to guarantee robustness of the observer no strictly positive real spr or any other strong assumption is imposed on the proposed approach the stability of the recurrent neural network observer is shown by lyapunov s direct method simulation results for a flexible joint manipulator are presented to demonstrate the enhanced performance achieved by utilizing the proposed neural network observer

interactive fuzzy programming for multi level linear programming problems with fuzzy parameters this paper presents interactive fuzzy programming for multi level linear programming problems with fuzzy parameters in fuzzy programming for multi level linear programming problems recently developed by lai et al since the fuzzy goals are determined for both an objective function and decision variables at the upper level undesirable solutions are produced when these fuzzy goals are inconsistent in order to overcome such problems after eliminating the fuzzy goals for decision variables interactive fuzzy programming for multi level linear programming problems with fuzzy parameters is presented in our interactive method after determining the fuzzy goals of the decision makers at all levels a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers with considerations of overall satisfactory balance among all levels illustrative numerical examples for two level and three level linear programming problems are provided to demonstrate the feasibility of the proposed method

fuzzy goal programming approach to multilevel programming problems the purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach here the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers since the objectives are potentially conflicting in nature a possible relaxation of the higher level decision is considered for avoiding decision deadlock then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values the efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches

a penalty function method for solving weak price control problem abstract the price control problem is an important linear bilevel programming problem in this paper we are concerned with a class of weak price control problems with non unique lower level solutions for such problems we study the existence of solution via a penalty method then we propose a simple algorithm for this problem and present the convergence of the algorithm the example illustrates that the method is feasible and efficient

fuzzy programming approach to multi objective stochastic programming problems when b i s follow joint normal distribution abstract in this paper a multi objective chance constrained programming problem has been considered when bi s are normal random variables and the constraints have a joint probability distribution the probabilistic problem is converted into an equivalent deterministic non linear programming problem then the fuzzy programming technique has been applied to obtain a compromise solution a numerical example is also presented to illustrate the methodology

an efficient point algorithm for a linear two stage optimization problem this paper presents an algorithm using sensitivity analysis to solve a linear two stage optimization problem the underlying theory rests on a set of first order optimality conditions that parallel the kuhn tucker conditions associated with a one dimensional parametric linear program the solution to the original problem is uncovered by systematically varying the parameter over the unit interval and solving the corresponding linear program finite convergence is established under nondegenerate assumptions the paper also discusses other solution techniques including branch and bound and vertex enumeration and gives an example highlighting their computational and storage requirements by these measures the algorithm presented here has an overall advantage finally a comparison is drawn between bicriteria and bilevel programming and underscored by way of an example

on stability analysis of multicriteria lp problems with fuzzy parameters abstract in this paper we investigate the stability of solution in fuzzy multiobjective linear programming with symmetrical triangular fuzzy numbers with respect to change of fuzzy parameters

on a new class of bilevel programming problems and its use for reformulating mixed integer problems abstract we extend some known results about the bilevel linear problem blp a hierarchical two stage optimization problem showing how it can be used to reformulate any mixed integer linear problem then we introduce some new concepts which might be useful to fasten almost all the known algorithms devised for blp as this kind of reformulation appears to be somewhat artificial we define a natural generalization of blp the bilevel linear quadratic problem bl qp and show that most of the exact and or approximate algorithms originally devised for the blp such as gsa or k th best can be extended to this new class of bilevel programming problems for bl qp more natural reformulations of mips are available leading to the use of known nonexact algorithms for blp as heuristic approaches to mips we report some contrasting results obtained in the network design problem case showing that although the direct application of our dual gsa algorithm is not of any practical use we obtain as a by product a good theoretical characterization of the optimal solutions set of the ndp along with a powerful scheme for constructing fast algorithms for the minimum cost flow problem with piecewise convex linear cost functions

the relationship between goal programming and fuzzy programming abstract goal programming gp and fuzzy programming fp are two approaches for solving the vector optimization problem by reducing it to a single or sequential objective one these two approaches have some similarities and both of them have more than one form to handle the multiobjective problem this paper highlights the similarities between gp and fp and answers the question how each one can lead to the other however we will consider in this paper the min operator to transform the linear fp to a crisp program since this approach is more popular and applied than the others in addition some new forms of fuzzy programs are presented in this paper these new forms use the concept of deviational variables of gp and not the min operator to transform the fp to a crisp one finally a numerical example to illustrate the relationship between the two approaches is given

interactive fuzzy programming for multi level 0 1 programming problems through genetic algorithms abstract in this paper we propose interactive fuzzy programming for multi level 0 1 programming problems through genetic algorithms our method is supposed to apply to hierarchical decision problems in which decision making at each level is sequential from upper to lower level and decision makers are essentially cooperative after determining the fuzzy goals of the decision makers at all levels a satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers at the upper level with considerations of overall satisfactory balance among all levels an illustrative numerical example for three level 0 1 programming problems is provided to demonstrate the feasibility 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

computational difficulties of bilevel linear programming we show using small examples that two algorithms previously published for the bilevel linear programming problem blp may fail to find the optimal solution and thus must be considered to be heuristics a proof is given that solving blp problems is np hard which makes it unlikely that there is a good exact algorithm

fuzzy programming approach to multi level programming problems multi level programming is characterized as mathematical programming to solve decentralized planning problems we have considered a multi level linear programming problem and applied fuzzy mathematical programming fmp approach to obtain the solution of the system we have suggested fmp method for the minimization of the objectives using linear membership functions fmp is a supervised search procedure supervised by the higher level decision maker dm the higher level dm provides the preferred values of decision variables under his control to enable the lower level dm to search for his optimum in a wider feasible space and the bounds of his objective function to direct the lower level dm to search for his solutions in the right direction

the projected faces property and polyhedral relations margot 1994 in his doctoral dissertation studied extended formulations of combinatorial polytopes that arise from smaller polytopes via some composition rule he introduced the projected faces property of a polytope and showed that this property suffices to iteratively build extended formulations of composed polytopes for the composed polytopes we show that an extended formulation of the type defined by margot is always possible only if the smaller polytopes have the projected faces property therefore this produces a characterization of the projected faces property affinely generated polyhedral relations were introduced by kaibel and pashkovich optima 85 2 7 2011 to construct extended formulations for the convex hull of the images of a point under the action of some finite group of reflections in this paper we prove that the projected faces property and affinely generated polyhedral relation are equivalent conditions

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

linear bilevel programming with interval coefficients in this paper we address linear bilevel programs when the coefficients of both objective functions are interval numbers the focus is on the optimal value range problem which consists of computing the best and worst optimal objective function values and determining the settings of the interval coefficients which provide these values we prove by examples that in general there is no precise way of systematizing the specific values of the interval coefficients that can be used to compute the best and worst possible optimal solutions taking into account the properties of linear bilevel problems we prove that these two optimal solutions occur at extreme points of the polyhedron defined by the common constraints moreover we develop two algorithms based on ranking extreme points that allow us to compute them as well as determining settings of the interval coefficients which provide the optimal value range

three models of fuzzy integer linear programming abstract in this paper we study some models for dealing with fuzzy integer linear programming problems which have a certain lack of precision of a vague nature in their formulation we present methods to solve them with either fuzzy constraints or fuzzy numbers in the objective function or fuzzy numbers defining the set of constraints these methods are based on the representation theorem and on fuzzy number ranking methods

a neural network approach for solving nonlinear bilevel programming problem a neural network model is presented for solving nonlinear bilevel programming problem which is a np hard problem the proposed neural network is proved to be lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem the asymptotic properties of the neural network are analyzed and the condition for asymptotic stability solution feasibility and solution optimality are derived the transient behavior of the neural network is simulated and the validity of the network is verified with numerical examples

application of particle swarm optimization algorithm for solving bi level linear programming problem bi level linear programming is a technique for modeling decentralized decision it consists of the upper level and lower level objectives this paper attempts to develop an efficient method based on particle swarm optimization pso algorithm with swarm intelligence the performance of the proposed method is ascertained by comparing the results with genetic algorithm ga using four problems in the literature and an example of supply chain model the results illustrate that the pso algorithm outperforms ga in accuracy

a fuzzy approach for bi level integer non linear programming problem abstract bi level programming a tool for modeling decentralized decisions consists of the objective of the leader at its first level and that is of the follower at the second level integer programming deals with the mathematical programming problems in which some or all the variables are to be integer this paper studies a bi level integer non linear programming problem with linear or non linear constraints and in which the non linear objective function at each level are to maximized the bi level integer non linear programming bli nlp problem can be thought as a static version of the stackelberg strategy which is used leader follower game in which a stackelberg strategy is used by the leader or the higher level decision maker hldm given the rational reaction of the follower or the lower level decision maker lldm this paper proposes a two planner integer model and a solution method for solving this problem this method uses the concept of tolerance membership function and the branch and bound technique to develop a fuzzy max min decision model for generating pareto optimal solution for this problem an illustrative numerical example is given to demonstrate the obtained results

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

the polynomial hierarchy and a simple model for competitive analysis the multi level linear programs of candler norton and townsley are a simple class of sequenced move games in which players are restricted in their moves only by common linear constraints and each seeks to optimize a fixed linear criterion function in his her own continuous variables and those of other players all data of the game and earlier moves are known to a player when he she is to move the one player case is just linear programming

a three level optimization method for fuzzy large scale multiobjective nonlinear programming problems abstract in general mathematical models to reflect real world complicated decision situations are often formulated as largescale programming problems which include a large number of variables and or constraints furthermore considering the fuzziness of human s subjective judgement in real world decision making it is necessary to deal with the large scale programming problems in the fuzzy environment from such a point of view in this paper under the assumption that the decision maker dm has fuzzy goal for each of the objective functions and the corresponding membership function may be nonlinear a 3 level optimization method is proposed for large scale multiobjective nonlinear programming problems ls monlps with the block angular structure to obtain the compromise solution of the dm based on the proposed algorithm the computer program is developed in fortran language and applied to the numerical example to clarify the efficiency of the proposed algorithm

a fuzzy satisficing method for large scale linear programming problems with block angular structure abstract in this paper we focus on large scale linear programming problems with block angular structure for which the dantzig wolfe decomposition method has been successfully applied by considering the vague nature of human judgements we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constraints for the coupling constraints having elicited the corresponding linear membership functions through the interaction with the decision maker if we adopt the convex fuzzy decision for combining them it is shown that under some appropriate conditions the formulated problem can be reduced to a number of independent linear subproblems and the overall satisficing solution for the decision maker is directly obtained just only solving the subproblems

comment to interactive fuzzy goal programming approach for bilevel programming problem by s r arora and r gupta the fuzzy bilevel programming problem is solved in the paper 1 using an approach of fuzzy goal programming using a simple example we show that this will not lead to a satisfactory solution especially the fuzzy constraint that the upper level variable is near some desired one has no influence on the computed solution in the example this constraint is used to model the hierarchy in the approach in 1 at the end of the paper we suggest one straightforward possibility for modeling the fuzzy bilevel programming problem and converting it into a crisp substitute

efficient solutions for the linear bilevel programming problem abstract one of the interesting features of the bilevel programming problem is that its optimal solution may not be pareto optimal this behavior may be economically inadmissible this paper will present a post optimality analysis it is intended to provide some rational efficient solutions for decision makers after a non pareto optimal solution is obtained for a linear bilevel programming problem an efficient solution which obeys some properties will be adopted by decision makers according to their decision preferences

a fuzzy dual decomposition method for large scale multiobjective nonlinear programming problems abstract in this paper we propose a fuzzy dual decomposition method for large scale multiobjective nonlinear programming problems ls monlps with the block angular structure by considering the vague nature of human judgements we assume that the decision maker dm may have a fuzzy goal for each of the objective functions in the ls monlp after eliciting the corresponding membership function for each of the objective functions through the interaction with the dm an extended primal problem and the corresponding extended dual problem are formulated then a two level optimization algorithm for the extended dual problem is proposed for deriving the compromise solution for the dm to the ls monlp based on the proposed algorithm fortran programs are developed and an illustrative numerical example is demonstrated

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

a simple tabu search method to solve the mixed integer linear bilevel programming problem abstract multilevel programming is characterized as mathematical programming to solve decentralized planning problems the models partition control over decision variables among ordered levels within a hierarchical planning structure of which the linear bilevel form is a special case of a multilevel programming problem in a system with such a hierarchical structure the high level decision making situations generally require inclusion of zero one variables representing yes no decisions we provide a mixed integer linear bilevel programming formulation in which zero one decision variables are controlled by a high level decision maker and real value decision variables are controlled by a low level decision maker an algorithm based on the short term memory component of tabu search called simple tabu search is developed to solve the problem and two supplementary procedures are proposed that provide variations of the algorithm computational results disclose that our approach is effective in terms of both solution quality and efficiency

interactive fuzzy random two level linear programming based on level sets and fractile criterion optimization in this paper assuming cooperative behavior of the decision makers two level linear programming problems under fuzzy random environments are considered by introducing a level sets of fuzzy random variables and defining an a stochastic two level linear programming problem for guaranteeing the degree of realization of the problem through a new decision making model proposed based on the fractile criterion optimization model considering fuzzy goals the a stochastic two level programming problem can be equivalently transformed into a deterministic problem interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented an illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method

numerical solutions for systems of qualitative nonlinear algebraic equations by fuzzy logic abstract this paper presents a fuzzy logic approach for determining a numerical solution to a consistent system of algebraic equations f x 0 in which the function f is not explicitly defined and may be underdetermined such systems arise frequently in many engineering design problems where design parameters must be chosen using qualitative information by the designer to meet a set of desired performance constraints the proposed method also can be used for a consistent system of nonlinear equations in which f is explicitly defined and may have fewer independent equations than the number of unknowns however this method is very computationally demanding hence it is not advisable to apply it to problems involving explicit functions that can be solved using other existing numerical methods it is seen that this method works quite well and numerical solutions for such problems can be obtained although it is much slower than newton s method when employed to consistent explicit nonlinear equations

a parametric study of multiobjective nlp problems with fuzzy parameters in the objective functions abstract this paper deals with the stability of multiobjective nonlinear programming problems with ordinary and fuzzy parameters in the objective functions these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the qualitative analysis of the notions solvability set stability sets of the first kind and of the second kind in parametric nonlinear programming problems are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality an algorithm for obtaining any subset of the parametric space which has the same corresponding pareto optimal solution is also presented an illustrative example is given to clarify the obtained results

compensatory fuzzy multiple level decision making abstract fuzzy set theory has been shown to be an effective tool to overcome the computational difficulties encountered in solving large multiple level programming problems shih et al 1996 in this paper compensatory operators are introduced for adjusting the decision making process between the different levels and also between the decision makers of the same level after a brief consideration of the bi level and three level systems the large decentralized organizations with both equal and unequal goals are investigated various numerical examples are given to compare the influences of compensation and to illustrate the approaches

on two level optimization decentralized planning has long been recognized as an important decision making problem many approaches based on the concepts of large scale system decomposition have generally lacked the ability to model the type of truly independent subsystems which have often existed in practice similarly tractable game theoretic approaches have not allowed for a continuous solution space in which one player s decision restricts the feasible choices of another this correspondence offers a formulation to help model this type of decision making hierarchy characterizations and algorithmic approaches for a class of two level problems are discussed

interactive random fuzzy two level programming through possibility based probability model this paper considers interactive decision making methods for random fuzzy two level linear programming problems assuming that the decision makers concern about the probabilities that their own objective function values are smaller than or equal to certain target values fuzzy goals of the decision makers for the probabilities are introduced then the possibility based probability model to maximize the degrees of possibility with respect to the attained probability is considered interactive fuzzy nonlinear programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented an illustrative numerical example demonstrates the feasibility and efficiency of the proposed method

weak linear bilevel programming problems existence of solutions via a penalty method we are concerned with a class of weak linear bilevel programs with nonunique lower level solutions for such problems we give via an exact penalty method an existence theorem of solutions then we propose an algorithm

the traveling salesman problem in graphs with 3 edge cutsets this paper analyzes decomposition properties of a graph that when they occur permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities the central notion is that of a 3 edge cutset namely a set of 3 edges that when removed disconnects the graph conversely our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem the approach is illustrated on two examples halin graphs and prismatic graphs

fuzzy boolean programming problems with fuzzy costs a general study abstract this paper deals with boolean linear programming problems involving coefficients in the objective function as fuzzy numbers in the study of these problems different approaches can be proposed to use ranking fuzzy numbers methods and fuzzy preference relations obtaining auxiliary classical boolean programming problems and to use the representation theorem obtaining a convex set with extreme points defined by the lower or upper bound of the a level sets of the fuzzy coefficients and consequently an auxiliary interval boolean programming problem in this paper we develop and link the different approaches

task space adaptive control of robotic manipulators with uncertainties in gravity regressor matrix and kinematics thus far most research in adaptive control of robotic manipulators has assumed that models of regressor matrix and kinematics are known exactly to overcome these drawbacks we propose in this paper a task space adaptive law for setpoint control of robots with uncertainties in gravity regressor matrix and kinematics in addition we investigate the stability problem when an estimated task space velocity is used in the feedback loop sufficient conditions for choosing the feedback gains gravity regressor and jacobian matrix are presented to guarantee the stability

efficient relighting of rbf based illumination adjustable images an illumination adjustable image iai contains a large number of prerecorded images under various light directions relighting a scene under complicated lighting conditions can be achieved from the iai using the radial basis function rbf approach to represent an iai is proven to be more efficient than using the spherical harmonic approach however to represent high frequency lighting effects we need to use many rbfs hence the relighting speed could be very slow this brief investigates a partial reconstruction scheme for relighting an iai based on the locality of rbfs compared with the conventional rbf and spherical harmonics sh approaches the proposed scheme has a much faster relighting speed under the similar distortion performance

reference direction interactive method for solving multiobjective fuzzy programming problems abstract a reference direction interactive method called rdim is proposed in this paper for solving multiobjective fuzzy programming problems the method combines the reference direction approach for multiobjective linear programming of korhonen and laakso 1986 a visual interactive method for solving multiple criteria problems european journal of operational research 24 277 287 with the interactive satisficing method of sakawa and yano 1989 an interactive fuzzy satisficing method for multiobjective nonlinear programming problem with fuzzy parameters fuzzy sets and systems 30 221 238 the proposed method is applicable to nonsymmetric linear as well as nonlinear mathematical models wherein the objectives are modeled as fuzzy goals and the satisfaction of fuzzy constraints is considered at different level sets of the fuzzy parameters involved at each interactive phase the decision maker dm specifies a reference direction in the membership function space a discrete parametric programming problem is then solved in this direction to provide the dm with a number of alternatives from amongst which he she can select the most preferred solution on the basis of his her preference structure illustrative examples taken from literature have been solved using the proposed method

a bm lambda cut and goal programming based algorithm for fuzzy linear multiple objective bilevel optimization bilevel programming techniques are developed to handle decentralized problems with two level decision makers which are leaders and followers who may have more than one objective to achieve this paper proposes a cut and goal programming based algorithm to solve fuzzy linear multiple objective bilevel flmob decision problems first based on the definition of a distance measure between two fuzzy vectors using cut a fuzzy linear bilevel goal flbg model is formatted and related theorems are proved then using a cut for fuzzy coefficients and a goal programming strategy for multiple objectives a cut and goal programming based algorithm to solve flmob decision problems is presented a case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm finally experiments are carried out to discuss and analyze the performance of this algorithm

stable neurovisual servoing for robot manipulators in this paper we propose a stable neurovisual servoing algorithm for set point control of planar robot manipulators in a fixed camera configuration an show that all the closed loop signals are uniformly ultimately bounded uub and converge exponentially to a small compact set we assume that the gravity term and jacobian matrix are unknown radial basis function neural networks rbfnns with online real time learning are proposed for compensating both gravitational forces and errors in the robot jacobian matrix the learning rule for updating the neural network weights similar to a back propagation algorithm is obtained from a lyapunov stability analysis experimental results on a two degrees of freedom manipulator are presented to evaluate the proposed controller

fuzzy programming approach to multi objective stochastic linear programming problems abstract this paper presents an application of fuzzy programming approach to the multi objective stochastic linear programming problem after converting the proposed stochastic programming problem into a deterministic problem which may be linear or non linear fuzzy programming approach is applied to find the compromise solution assuming the coefficients of the decision variables in the objective functions and in the constraints and the right hand side parameters in the constraints as normal random variables a methodology is presented to convert the probabilistic problem into a deterministic problem then fuzzy programming is applied using linear as well as non linear membership functions the method leads to an efficient solution as well as an optimal compromise solution numerical example is also presented to illustrate the methodology

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

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

fuzzy goal programming algorithm for solving decentralized bi level multi objective programming problems this paper presents fuzzy goal programming fgp algorithm for solving decentralized bi level multi objective programming dbl mop problems with a single decision maker at the upper level and multiple decision makers at the lower level a fgp algorithm for dbl multi objective linear programming dbl molp problems is proposed this algorithm is extended to solve bi level multi objective linear fractional programming dbl molfp problems in the proposed algorithm the membership functions for the defined fuzzy goals of all objective functions at the two levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by uldm are developed in the model formulation of the problem then fgp approach is used to achieve highest degree of each of the membership goals by minimizing their deviational variables and thereby obtaining the most satisfactory solution for all decision makers illustrative numerical examples are given to demonstrate the proposed algorithm

solving a bilevel linear program when the inner decision maker controls few variables abstract this paper presents an algorithm that always finds an optimum of a bilevel linear program blp problem if one exists moreover if the inner decision maker does not control too many variables the algorithm is efficient in particular if the number of variables controlled by the inner decision maker can be considered to be constant then the algorithm is a polynomial time algorithm the algorithm is also well suited to parallel implementation

on fuzzy linear programming abstract fuzzy multi objective and fuzzy goal programming are discussed in connection with several membership functions which are used to transform the original problem into three equivalent linear programming problems existence and uniqueness theorems are given fuzzy duality is presented and an extension of the initial fuzzy problem arises immediately from it

a study of fuzzy parametric on multiobjective nonlinear programming problems without differentiability this paper deals with multiobjective nonlinear programming problems with fuzzy parameters in the objective functions without differentiability these fuzzy parameters are characterized by fuzzy numbers the existing results concerning the stability notions of parametric convex programs are reformulated to study the stability of multiobjective nonlinear programming problems under the concept of pareto optimality without differentiability on the functions considered

on bilevel programming part i general nonlinear cases this paper is concerned with general nonlinear nonconvex bilevel programming problems blpp we derive necessary and sufficient conditions at a local solution and investigate the stability and sensitivity analysis at a local solution in the blpp we then explore an approach in which a bundle method is used in the upper level problem with subgradient information from the lower level problem two algorithms are proposed to solve the general nonlinear blpp and are shown to converge to regular points of the blpp under appropriate conditions the theoretical analysis conducted in this paper seems to indicate that a sensitivity based approach is rather promising for solving general nonlinear blpp