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

multiple objective programming problems with possibilistic coefficients abstract we consider the problem of incorporating possibilistic data into a multiple objective linear programming framework a solution concept that is attractive from the standpoints of feasibility and efficiency is specified a necessary and sufficient condition for such a solution is established and ways to single out some satisfying alternative in this context are described a numerical example is also included for the sake of illustration throughout the paper we indicate topics for further research

linear programming with a possibilistic objective function abstract this paper proposes some ways for dealing with a linear program when the coefficients of the objective function are subject to possibilistic imprecision i e they are characterized by fuzzy restrictions emphasis is placed upon a passive approach that yields a satisfying solution via an appropriate semi infinite program and an active one that allows to reach a solution with a high possibility level of optimality extensions to the possibilistic constraints case and to the case of multiple objective programming problems with possibilistic coefficients are also hinted we end up with some concluding remarks and indicate axes for further developments

fuzzy random programming with equilibrium chance constraints to model fuzzy random decision systems this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of sugeno then a new class of fuzzy random programming problems is presented based on equilibrium chances also some convex theorems about fuzzy random linear programming problems are proved the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply after that a solution approach which integrates simulations neural network and genetic algorithm is suggested to solve general fuzzy random programming problems at the end of this paper three numerical examples are provided since the equivalent stochastic programming problems of the three examples are very complex and nonconvex the techniques of stochastic programming cannot apply in this paper we solve them by the proposed hybrid intelligent algorithm the results show that the algorithm is feasible and effectiveness

membership function elicitation in possibilistic programming problems in this paper we propose an elicitation method for membership functions in the setting of possibilistic programming each possibility distribution is defined by several possible domains with different possibility degrees taking advantage of the properties of possibility and necessity measures a nested target table for the objective function and for each constraint is elicited from a decision maker to aggregate all the goals an additional nested target table is established through those nested target tables membership functions can be determined it is emphasized that the information of nested target tables is much more important than that of membership values in the setting of possibilistic programming the membership functions in possibilistic programming are not assumed to be cardinal but ordinal in this sense the decision making via possibilistic programming can be regarded as a qualitative one

periodic boundary value problems for second order impulsive differential systems on etudie le probleme aux valeurs limites periodiques pour un systeme d equations differentielles d ordre 2 faiblement couplees avec impulsion

deformation measurement of a birdlike airfoil with optical flow and numerical simulation a lucas kanade optical flow technique was developed to measure the deformation of a flexible birdlike airfoil undergoing an increasing angle of attack at reynolds number 100 000 a pyramidal scheme was used to allow large displacements a nonlinear structure tensor diffusion was introduced to preserve image intensity discontinuities the accuracy and convergence of this lucas kanade method was studied then this optical flow method was adapted for a wind tunnel experimental setup to estimate the vertical deformation of a newly designed flexible birdlike airfoil with an improved wing loading at last the proposed optical flow method was compared to image correlation and numerical simulation results that were carried out solving the fluid structural interaction problem through a well validated coupling environment with conservative load transfer and a partitioned coupling approach

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

impulsive degenerate nonlinear parabolic functional differential inequalities abstract the aim of the paper is to give a theorem about impulsive degenerate strong nonlinear parabolic functional differential inequalities in arbitrary parabolic domain and two corollaries about weak and strong inequalities the paper is a direct generalization and a continuation among other things of the author s previous work the results obtained in this paper can be applied for some impulsive problems in the theories of diffusion and heat conduction with better effects than analogous known classical parabolic problems

existence results for boundary value problems of second order impulsive differential equations abstract with the help of lower and upper solutions the extremal solutions of a second order impulsive differential equation are obtained as limits of monotone iterates several existence results for the second order impulsive differential equation subject to nonlinear boundary conditions which include the usual periodic and linear separated boundary conditions are also established

multi objective particle swarm optimization based on fuzzy pareto dominance for possibilistic planning of electrical distribution systems incorporating distributed generation this paper presents a multi objective planning approach for electrical distribution systems under uncertainty in load demand incorporating distributed generation dg both radial and meshed systems are considered the overall influence of load demand uncertainty on planned networks is investigated in detail uncertainty in load demand is possibilistically modeled using a fuzzy triangular number the two objectives in system planning are i minimization of total installation and operational costs and ii minimization of the risk factor the risk factor is a function of the contingency load loss index clli which measures load loss under contingencies and the degree of network constraints violations clli minimization improves network reliability the network variables optimized are i the network structure type radial or meshed ii the number of feeders and their routes and iii the number and location of sectionalizing switches the optimization tool is a multi objective particle swarm optimization mopso variant that uses heuristic selection and assignment of leaders or guides for efficient identification of non dominated solutions the optimal number location and size of the dg units are determined in another planning stage performance comparisons between the planning approaches with possibilistic and deterministic load models highlight the relative merits and demerits the advantages of networks obtained using the proposed planning approach in the context of dg integration are described the proposed planning approach is validated using three typical distribution systems

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

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

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

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

duality in linear programming with fuzzy parameters and matrix games with fuzzy pay offs abstract a dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay offs is equivalent to a primal dual pair of such fuzzy linear programming problems further certain difficulties with similar studies reported in the literature are discussed

relative modalities and their use in possibilistic linear programming abstract the relative modalities defined by possibility necessity impossibility and contingency of fuzzy sets in modal semantics are investigated decision procedures based on the modal concept are introduced and classified into eight classes the relation between each decision procedure and the attitude of the decision maker toward uncertainty is discussed lastly possibilistic linear programming relying on these decision procedures is formulated and a solution algorithm is proposed a numerical example is given

fuzzy goal programming with nested priorities abstract this paper proposes a new approach to formulating fuzzy priorities in a goal programming problem the proposed methodology remedies certain shortcomings of the composite membership function approach discussed in previous works 7 10 the principal advantage of the proposed method is that it leads to a formulation in which tradeoffs between goals more closely reflect the decision maker s intentions than in other noninteractive approaches 8 9 10 14 in some of which a fixed hierarchy of goals is assumed

boundary value problems for nonlinear impulsive integrodifferential equations we consider boundary value problems for nonlinear impulsive integrodifferential equations in which impulses occur at fixed times by suitably modifying the notions of upper and lower solutions we establish existence results in a sector then develop the monotone method and prove the existence of extremal solutions of the impulsive integrodifferential equations as an application we derive some existence results for a boundary value problem for a third order impulsive differential equation

possibilistic linear programming with triangular fuzzy numbers abstract we consider a mathematical programming problem where all the parameters may be fuzzy variables specified by their possibility distribution and we define the possibility distribution of the objective function the ideas are illustrated on possibilistic linear programming

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

possibility and necessity in optimization abstract we employ possibility and necessity in fuzzy programming and in other optimization problems that traditionally use random variables the possibility approach to multiobjective programming produces the same results as fuzzy programming a detailed example is presented to illustrate the use of possibility and necessity in optimization problems that usually employ random variables to describe uncertainty

linear programming problems and ranking of fuzzy numbers abstract in this paper linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered because of fuzzy coefficients in both members of each constraint ranking methods for fuzzy numbers must be considered the diversity of such methods provides a lot of different models of conventional linear programming problems from which fuzzy solutions to the former problem can be obtained

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

solutions of impulsive boundary value problems on the half line abstract this paper presents some existence results for a class of impulsive boundary value problems with nonhomogeneous boundary data on the half line by applying fixed point theorems on cones we obtain the existence of positive bounded and unbounded solutions our methods are integral equations approximate solutions a priori bounds and modified arzela techniques

invariance under the dihedral group and application to bifurcation problems soit un groupe d ordre agissant lineairement sur r s et soient 1 2 t des generateurs homogenes de r x 1 x s l algebre de tous les polynomes invariants a s variables si f est une fonction invariante de classe c m sur r s avec 0 m alors il existe une fonction f c p r t telle que f f 1 t avec p sup 0 m s 1 on considere ici le cas s 2 d n le groupe diedre d ordre 2n avec n 2

material requirement planning with fuzzy constraints and fuzzy coefficients we propose a new fuzzy mathematical programming model for production planning under uncertainty in an industrial environment this model considers fuzzy constraints related to the total costs the market demand and the available capacity of the productive resources and fuzzy coefficients for the costs due to the backlog of demand and for the required capacity the main goal is to determine the master production schedule of each product the mrp material requirement planning for each raw component in each period stock levels demand backlog and capacity usage levels over a given planning horizon finally the proposed model is tested by using data from an automobile seat assembler and compared with other fuzzy mathematical programming approaches the experiment shows that the proposed model has not got a better behaviour than more simple fuzzy models but the advantage is that both types of uncertainties fuzziness and lack of knowledge or epistemic uncertainty can be considered in a model with fuzzy constraints and fuzzy coefficients

modality constrained programming problems a unified approach to fuzzy mathematical programming problems in the setting of possibility theory abstract in this paper fuzzy mathematical programming problems are formulated based on the idea analogous with the chance constrained programming problem the difference in meaning between the ambiguity of the coefficients and that of the decision maker s preference is emphasized the constraints with fuzzy coefficients are treated as the restriction that should be satisfied properly rather than perfectly the objective functions with fuzzy coefficients are treated variously depending on the interpretations i e the optimization of the modalities the optimization of the fractile the minimization of the ambiguity and so forth the deterministic equivalent constraints and the deterministic equivalent problems are shown when the constraints and the objective functions are linear a numerical example is given to illustrate the proposed formulations

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

necessity measure optimization in linear programming problems with fuzzy polytopes in this paper we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes the problem is formulated as a necessity measure optimization model it is shown that the problem can be reduced to a semi infinite programming problem and solved by a combination of a bisection method and a relaxation procedure an algorithm in which the bisection method and the relaxation procedure converge simultaneously is proposed a simple numerical example is given to illustrate the solution procedure

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

portfolio selection under independent possibilistic information this paper deals with a portfolio selection problem with independently estimated possibilistic return rates under such a circumstance a distributive investment has been regarded as a good solution in the traditional portfolio theory however the conventional possibilistic approach yields a concentrated investment solution considering the reason why a distributive investment is advocated a new approach to the possibilistic portfolio selection is proposed

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described