introduction to fuzzy partial differential equations this paper considers solutions to elementary fuzzy partial differential equations we follow the same strategy as in buckley and feuring fuzzy sets and systems to appear which is 1 first check to see if the buckley feuring method produces a solution and 2 if the buckley feuring method does not give a solution then see if the seikkala procedure generates a solution examples are presented showing the buckley feuring solution and the seikkala solution

design of a fuzzy finite capacity queuing model based on the degree of customer satisfaction analysis and fuzzy optimization due to uncontrollable factors the parameters in the queuing models may be uncertain and so in this paper we present the design of a fuzzy finite capacity queuing model in which the arrival pattern and the service pattern follow an exponential distribution under uncertain parameter as for the design of the system the criterion of optimization proposed is aimed at the optimum selection of the number of servers with the goal of providing a high degree of satisfaction to clients when they join the system this optimization process will be solved through markov chains with fuzzy state the validity of the procedure proposed to incorporate fuzzy data in this queuing system is confirmed by a fuzzy simulation experiment of the differential equations which govern the behaviour of the model by the bontempi s qua si iii algorithm the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informative results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite capacity queuing models with uncertain data can have a broader range of applications

a differential quadrature based approach a la picard for systems of partial differential equations associated with fuzzy differential equations departing from a numerical method designed to solve ordinary differential equations in this manuscript we extend such approach to solve problems involving fuzzy partial differential equations the method proposed in this work is a non recursive technique that combines differential quadrature rules and a picard like scheme in order to obtain general solutions of systems of partial differential equations derived from a general fuzzy partial differential model the property of stability and a bound for the hausdorff distance are established under suitable conditions several numerical examples are provided in order to show the effectiveness of the proposed technique

existence and roughness of exponential dichotomies of linear dynamic equations on time scales in this paper we define the exponential dichotomy of linear dynamic equations on time scales then we present perturbation theorems on the roughness of exponential dichotomy and develop several explicit sufficient criteria for linear dynamic equations to have an exponential dichotomy as applications of the criteria of exponential dichotomy we derive some new sufficient conditions for the existence of periodic solutions of semi linear dynamic equations and nonlinear dynamic equations on time scales

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

a lagrangean heuristic for the capacitated concave minimum cost network flow problem we propose a heuristic solution technique for the capacitated concave minimum cost network flow problem based on a lagrangean dualization of the problem despite its dual character the algorithm guarantees the generation of primal feasible solutions which are local optima and therefore candidates of being the global optimum the lagrangean dual is solved by a subgradient search procedure and provides a lower bound to the optimal value the lower bound is in general stronger than the one obtained by a linear approximation of the original problem it can be used as a judgement of the quality of the solution or in a branch and bound procedure computational results from randomly generated problems are presented

min and max operators for gradual intervals this paper presents a new and a more general formulation of the min and max operations for gradual intervals initially proposed for the special case of triangular fuzzy intervals gradual intervals generalize the conventional interval representation by increasing its specificity thereby making it possible to represent the imprecision and the uncertainty via the notion of gradualness in this context a new interpretation of fuzzy intervals through the notion of gradual intervals is developed the originality of the proposed methodology lies in the extension of inter interval relations to the gradual case according to midpoint radius representation

a priori error analysis and spring arithmetic error analysis is defined by the following concern bounding the output variation of a nonlinear function with respect to a given variation of the input variables this paper investigates this issue in the framework of interval analysis the classical way of analyzing the error is to linearize the function around the point corresponding to the actual input but this method is local and not reliable both drawbacks can be easily circumvented by a combined use of interval arithmetic and domain splitting however because of the underlying linearization a standard interval algorithm leads to a pessimistic bound and even simply fails i e returns an infinite error in case of singularity we propose an original nonlinear approach where intervals are used in a more sophisticated way through the so called springs this new structure allows one to represent an infinite set of intervals constrained by their midpoints and their radius the output error is then calculated with a spring arithmetic in the same way as the image of a function is calculated with interval arithmetic our method is illustrated on two examples including an application of geopositioning

numerically solution of fuzzy differential equations by adomian method in this paper a method for numerical approximation of fuzzy first order initial value problem is presented buckly and feruing fuzzy sets syst 110 2000 43 have solved fuzzy first order initial value problem they solved problem in crisp case and then extend the solution to fuzzy case in this paper we use adomian method to find the approximate solution in crisp case and extend it to fuzzy case using this method we solve problems that the classical methods could not be applied for them in crisp case

exponential dichotomies almost periodic structurally stable differential systems and an example abstract in this paper we introduce concepts of almost periodic topological in short apt equivalence and almost periodic structural in short aps stability of differential systems and a necessary and sufficient condition for aps stability of differential systems furthermore we discuss the inheritability of the aps stability and density of aps stable differential systems in a certain space of uniformly almost periodic differential systems

probabilistic local search algorithms for concave cost transportation network problems in practice concave cost transportation problems are characterized as np hard therefore cost functions are usually simplified as linear in order to facilitate problem solving however linear cost functions may not reflect actual operations which generally results in decreased operational performance this research employs the techniques of simulated annealing and threshold accepting to develop several heuristics that would efficiently solve these concave cost transportation network problems a network generator has also been designed to generate many instances on an hp workstation to test the heuristics the preliminary results show that these heuristics are potentially useful

optimizing a priority discipline queueing model using fuzzy set theory the aim of this paper is to provide a more realistic description of priority discipline queueing models by using fuzzy set theory it develops and optimizes two fuzzy queueing models with priority discipline a model with nonpreemptive priorities system and a model with preemptive priorities system denoted by m i m i 1 and m i f i 1 the first symbol is for a queueing system where arrivals and services from a single server follow a poisson process with fuzzy parameter and the last symbol is for a queueing model with arrivals follows a poisson process with fuzzy rate and fuzzy deterministic service rate zadeh s extension principle is the basic approach to this research into fuzzy stochastic processes our results are the basis for a discussion of optimal selection of priority discipline two fuzzy queueing systems that are commonly found in real situations are solved and serve as examples that highlight the validity of the procedure we propose fuzzy queueing models are more realistic than the crisp queues that are commonly used in reality furthermore extending queueing models to the fuzzy environment widens their scope of application

steepest descent method for solving fuzzy nonlinear equations in this paper we propose the numerical solution for a fuzzy nonlinear equation by steepest descent method the fuzzy quantities are presented in parametric form some numerical illustrations are given to show the efficiency of steepest descent method

fuzzy analysis of statistical evidence bayesian classifiers are effective methods for pattern classification although their assumptions on the belief structure among attributes are not always justified in this paper we introduce a new classification method based on the possibility measure which does not require a precise belief model and in a sense it includes the bayesian classifiers as special cases this new classification method uses the fuzzy operators to aggregate attributes information evidence and it is referred to as fuzzy analysis of statistical evidence fase fase has several nice properties it is noise tolerant it can handle missing values with ease and it can extract statistical patterns from the data and represent them by knowledge of beliefs which in turn are propositions for an expert system thus from pattern classification to expert systems fase provides a linkage from inductive reasoning to deductive reasoning

lyapunov type characterization of hyperbolic behavior abstract we give a complete characterization of the uniform hyperbolicity and nonuniform hyperbolicity of a cocycle with values in the space of bounded linear operators acting on a hilbert space in terms of the existence of appropriate quadratic forms our work unifies and extends many results in the literature by considering the general case of not necessarily invertible cocycles acting on a hilbert space over an arbitrary invertible dynamics as a nontrivial application of we study the persistence of hyperbolicity under small linear perturbations

exponential separation exponential dichotomy and almost periodicity of linear difference equations abstract in this paper we study the relation between the concept of exponential separation and those of reducibility exponential dichotomy and almost periodicity of linear difference equations

topological equivalence and structural stability for linear difference equations abstract in this paper first we prove that if two linear difference equations with invertible coefficient matrices are topologically equivalent and one of them has bounded coefficient matrix together with its inverse then the coefficient matrix of the other equation is also bounded together with its inverse we also prove that if a linear difference equation with bounded and invertible coefficient matrix is structurally stable then the inverse of the coefficient matrix is also bounded

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

on estimating frequency response function envelopes using the spectral element method and fuzzy sets abstract the influence of uncertain input data on response spectra of dynamic structures is considered traditionally frequency response analyses are based on finite or boundary element models of the objective structure in the case of the mid frequency range problem however a very fine mesh is required to correctly approximate the frequency response this is particularly problematic in uncertainty modeling where the computational effort is usually increased significantly by the need for multiple runs e g when conducting a monte carlo analysis to achieve reliable results in this paper the spectral element method combined with a fuzzy set based uncertainty modeling approach is presented as an appealing alternative provided that the models are simple enough to yield a spectral element representation to conduct the fuzzy analysis part three different implementations of the extension principle of fuzzy arithmetic are applied and compared the suitability of each method depends on the number of uncertain parameters the problem characteristics and the required accuracy of the results the performance of the proposed approach is illustrated by two test problems a simple coupled rod and a reinforced plate model to verify the fuzzy valued results a monte carlo simulation has also been included

optimal selection of the service rate for a finite input source fuzzy queuing system finite input source queuing models have a wide range of applications in many practical situations and are frequently found in machine maintenance and repair operations owing to uncontrollable factors finite input source queuing problems parameters may contain uncertainty that is why to begin with in this paper it is proposed the analysis development and design of a fuzzy queuing model with finite input source in which the arrival pattern as well as the service pattern follow an exponential distribution under uncertain parameter in order to design the system the established optimization criterion consists in determining the optimal number of servers so as to minimize the expected total cost function per unit time to choose among uncertain alternatives three techniques to make decisions under uncertainty are proposed this type of systems has a finite waiting line as a result the system of differential equations that governs the model s behaviour consists of a finite number of equations in the second place this feature of the finite input source queuing systems enables us to bring forward in this paper two new contributions i in the first one the following doubt has been raised and solved if the convergence of the probabilities email protected i t obtained from the fuzzy differential equations that govern the behaviour of the finite source system is worked out does the result match the steady state fuzzy probabilities obtained by applying zadeh s extension principle to the classic queuing model and ii it has been performed a fuzzy simulation experiment on the differential equations using bontempi s qua si iii algorithm this enables us to know the time evolution of the probabilities email protected i t and its convergence on the one hand on the other we can compare the results of the simulation to those analytically obtained by applying zadeh s extension principle this way the validity of the proposed procedure for the simulation is verified by means of the theoretical results the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informing results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite input source queuing models with uncertain data can be of more use and can have a broader range of applications

neural net solutions to fuzzy problems the quadratic equation abstract this paper continues our research on using neural nets to solve fuzzy equations after outlining our general method of employing neural nets to solve fuzzy problems we concentrate on solving the fuzzy quadratic equation we show how neural nets can produce both real and complex fuzzy number solutions

exponential dichotomy and trichotomy for difference equations abstract in this paper a roughness theorem of exponential dichotomy and trichotomy of linear difference equations is proved it is also shown that if an almost periodic difference equation has an exponential dichotomy on a sufficiently long finite interval then it has one on

analysis of uncertain structural systems using interval analysis the imprecision or uncertainty present in many engineering analysis design problems can be modeled using probabilistic fuzzy or interval methods this work considers the modeling of uncertain structural systems using interval analysis by representing each uncertain input parameter as an interval number a static structural analysis problem can be expressed in the form of a system of linear interval equations in addition to the direct and gaussian elimination based solution approaches a combinatorial approach based on an exhaustive combination of the extreme values of the interval numbers and an inequality hased method are presented for finding the solution of interval equations the range or interval of the solution vector response parameters is found to increase with increasing size of the problem in all of the methods an interval truncation approach is proposed to limit the growth of intervals of response parameters so that realistic and accurate solutions can be obtained in the presence of large amounts of uncertainty numerical examples are presented to illustrate the computational aspects of the methods and also to indicate the importance of the truncation approach in practical problems the utility of interval methods in predicting the extreme values of the response parameters of structures is discussed

dichotomies and asymptotic behaviour for linear differential systems sufficient conditions that a system of differential equations x a t x have a dichotomy usually require that the matrix a t be bounded or at least that some restriction be placed on the rate of growth or decay of solutions here three sets of necessary and sufficient conditions for a dichotomy which do not impose such a restriction are given in terms of liapunov functions each of the theorems gives practical criteria for a dichotomy including the extension to unbounded matrices of criteria which depend on a concept of diagonal dominance for a t an asymptotic analysis is also given for subspaces of the solution set by means of the associated compound equations

dichotomies in terms of lyapunov functions for linear difference equations abstract necessary and sufficient conditions that a linear difference equation have an exponential dichotomy on the set of the integer numbers are given in terms of lyapunov functions

time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness abstract this paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed random and fuzzy uncertainties that result from unreliable systems to consider different types of delay time values the system states are appropriately and carefully identified and defined and a cost based fuzzy decision model that incorporates several unreliability factors is constructed then the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level to identify the lower and upper bounds on the minimal total cost per unit time at and thus construct the membership function to provide analytical expressions a special case with analytical results is also presented in contrast to existing studies the results derived from the proposed solution procedure conserve the fuzziness of the input information representing a significant difference from the crisp results obtained using approaches based on probability theory the results indicate that the proposed approach can provide more precise information to managers and improve decision making in practical system design

simulation of discrete linear time invariant fuzzy dynamic systems in this paper a new approach to simulation of discrete linear time invariant dynamic systems with parameters and initial conditions described by fuzzy numbers is proposed this approach solves the problem of fuzzy simulation by determining at each iteration a nested family of intervals corresponding to different levels of certainty a cuts that enclose the possible system states using optimisation the originality of this approach consists in considering uncertain parameters as time invariant during the simulation process the optimisation problems associated with the approach proposed must be solved globally in order to guarantee that the minimum volume box enclosing the region of system states for each level of certainty has been derived then a global optimisation algorithm based on the theory of moments and linear matrix inequality relaxations suitable for the type of problems polynomial programs that appear in the fuzzy simulation algorithm is used finally two real engineering application examples allow assessing the performance of the approach proposed

robustness of nonuniform μ ν dichotomies in banach spaces abstract this paper focuses on the linear perturbation of dynamical systems in banach spaces which corresponds to a nonautonomous dynamical system admitting a nonuniform dichotomy we establish the robustness or roughness of nonuniform dichotomies in the sense that the linear dynamical system persists under a sufficiently small linear perturbation

fuzzy hierarchical analysis revisited abstract we present a new method of finding the fuzzy weights in fuzzy hierarchical analysis which is the direct fuzzification of the original method used by saaty in the analytic hierarchy process we test our new procedure in two cases where there are formulas for the crisp weights an example is presented where there are five criteria and three alternatives

necessary and sufficient criteria for the existence of exponential dichotomy on time scales necessary and sufficient criteria are established for the existence of exponential dichotomies for linear dynamic equations on time scales and are applied to derive some perturbation theorems on the roughness of exponential dichotomy

a note on nguyen fuller keresztfalvi theorem and zadeh s extension principle this paper is devoted to the analysis of the generalised form of the nguyen fuller keresztfalvi theorem nfk theorem the classical nfk theorem expresses the zadeh extension principle in terms of a cuts of fuzzy sets but it is subjected to some constraining assumptions these assumptions concern all data in the problem shape of fuzzy sets topology of underlying spaces and regularity of functions and t norms in this paper we analyse consequences of dropping these assumptions in order to prove the generalised version of the nfk theorem we introduce a notion of level sets as a generalisation of the collection of a cuts we discuss properties of the level sets and then we formulate the general nfk theorem which does not require assumptions on the shape of fuzzy sets t norms nor topology of underlying spaces finally we return to the classical formulation of the nfk theorem and we show that it can be extended to the class of fuzzy sets with unbounded supports

fuzzy initial value problem for n th order linear differential equations we present two methods of solving nth order linear differential equation that have fuzzy initial conditions for the second order constant coefficient case we show that 1 the first method always gives a solution and 2 the second solution quite often does not exist and when it does exist it may be equal to the solution determined using the first method we apply the first method to three example problems including an electrical circuit and a vibrating mass

linear and non linear fuzzy regression evolutionary algorithm solutions given some data which consists of pairs of fuzzy numbers our evolutionary algorithm searches our library of fuzzy functions which includes linear polynomial exponential and logarithmic for a fuzzy function which best fits the data tests of our fuzzy regression package are given for each of the four cases linear polynomial exponential and logarithmic for the linear model we also consider multiple independent variables in all cases we use data generated with and without noise we prove that fuzzy polynomial regression can model the extension principle extension of continuous real valued functions

reducibility of linear dynamic equations on measure chains the concepts of reducibility and kinematic similarity are of major significance in the theory of stability of linear differential and difference equations in this paper we generalize some fundamental results on reducibility from the finite dimensional differential equations context to dynamic equations on measure chains in arbitrary hilbert spaces in fact we derive sufficient conditions for dynamic equations to be kinematically similar to an equation with zero right hand side or to an equation in hermitian or block diagonal form

smooth linearization near a fixed point in this paper we extend a theorem of sternberg and bi leckii we study a vector field or a diffeomorphism in the vicinity of a hyperbolic fixed point we assume that the eigenvalues of the linear part a at the fixed point satisfy qth order algebraic inequalities where q 2 2 then there is ck linearization in the vicinity of the fixed point where k is the q smoothness of a we give an explicit and simple algorithm for com puting k an illustrative example from celestial mechanics is included which shows that our main theorem is an improvement over previously known theories we also show that if the vector field or diffeomorphism depends smoothly on a parameter then the linearizing conjugation de pends smoothly on the parameter

solving systems of linear fuzzy equations abstract in this paper we wish to construct solutions for x to the fuzzy matrix equation ax b when the elements in a and b are triangular fuzzy numbers a is square and always non singular we argue that the previous method of solving for x based on the extension principle and regular fuzzy arithmetic should be abandoned since it too often fails to produce a solution we present six new solutions of which we show that five are identical we then adopt the common value x of these five new solutions as our solution to ax b we show that x is a fuzzy vector which is the generalization to rn of real fuzzy numbers we also show how these results pertain to and extend previous research on this problem within the area of interval analysis

discretization of semilinear differential equations with an exponential dichotomy abstract a structural stability result for one step discretizations of semilinear differential equations with an exponential dichotomy in its linear part is presented and interpreted as a shadowing result estimates are given in terms of the stepsize and of the order of the discretization method chosen

solving fuzzy equations in economics and finance abstract in this paper we apply our new solution procedure for solving fuzzy equations linear non linear differential to three problems in economics and finance the three applications are 1 leontief s input output model 2 the internal rate of return and 3 a dynamic supply demand model where price and supply are governed by a system of differential equations

methods for global concave minimization a bibliographic survey the global concave minimization problem is to find the constrained global minimum of a concave function since such a function may have many local minima finding the global minimum is a computationally difficult problem in this bibliographic survey which includes most of the recent papers on constrained global concave minimization we have attempted to briefly summarize the main ideas in each paper these recent papers include those concerned with large scale global concave minimization and bilinear programming

temporal reasoning based on semi intervals abstract a generalization of allen s interval based approach to temporal reasoning is presented the notion of conceptual neighborhood of qualitative relations between events is central to the presented approach relations between semi intervals rather than intervals are used as the basic units of knowledge semi intervals correspond to temporal beginnings or endings of events we demonstrate the advantages of reasoning on the basis of semi intervals 1 semi intervals are rather natural entities both from a cognitive and from a computational point of view 2 coarse knowledge can be processed directly computational effort is saved 3 incomplete knowledge about events can be fully exploited 4 incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps 5 there is no trade off in computational strength for the added flexibility and efficiency 6 for a natural subset of allen s algebra global consistency can be guaranteed in polynomial time 7 knowledge about relations between events can be represented much more compactly

applying a fuzzy set based method for robust estimation of coupling loss factors finite element models have been used by many authors to provide accurate estimations of coupling loss factors although much progress has been achieved in this area little attention has been paid to the influence of uncertain parameters in the finite element model used to estimate these factors it is well known that in the mid frequency range uncertainty is a major issue in this context a spectral element method combined with a special implementation of a fuzzy set based method which is called the transformation method is proposed as an alternative to compute coupling loss factors the proposed technique is applied to a frame type junction which can consist of two beams connected at an arbitrary angle in this context two problems are investigated in the first one the influence of the confidence intervals of the coupling loss factors on the estimated energy envelopes assuming a unit power input is considered in the other problem the influence of the envelope of the input power obtained considering the confidence intervals of the coupling loss factors is also taken into account the estimates of the intervals are obtained by using the spectral element method combined with a fuzzy set based method results using a monte carlo analysis for the estimation of the coupling loss factors under the influence of uncertain parameters are shown for comparison and verification of the fuzzy method

uniformly rd piecewise almost periodic functions with applications to the analysis of impulsive δ dynamic system on time scales we introduce some new concepts of uniformly rd piecewise almost periodic functions on time scales and obtain some properties some new estimation inequalities and completely new theorems are established on time scales for impulsive dynamic systems several applications are given to illustrate our feasible results in the present work we introduce two equivalent concepts of uniformly rd piecewise almost periodic functions on time scales and their equivalence is proved based on this some basic properties of them are obtained then some new criteria of exponential dichotomy are established for homogeneous dynamic system on time scales also some completely new theorems are established on time scales for impulsive almost periodic dynamic systems such as favard s theorem and exponential dichotomy theorem as applications we provide a method to obtain an almost periodic solution for a given nonhomogeneous impulsive dynamic system furthermore we introduce an impulsive non autonomous nicholson s blowflies system model with patch structure and multiple nonlinear harvesting terms for which the existence and exponential stability of almost periodic solutions are studied which shows that our results can be applied feasibly and effectively

exponential dichotomy integral separation and diagonalizability of linear systems of ordinary differential equations abstract this paper is concerned with linear systems of ordinary differential equations a criterion for integral separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half line is integrally separated if and only if the system corresponding to its diagonal is we then show that a diagonal system on a half line is integrally separated if and only if a certain perturbed system is diagonalizable using this result we are able to deduce that the interior of the set of diagonalizable systems on a half line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half lines

interval arithmetic based simple linear regression between interval data discussion and sensitivity analysis on the choice of the metric the prediction of a response random interval valued set from an explanatory one has been examined in previous developments these developments have considered an interval arithmetic based linear model between the random interval valued sets and a least squares regression analysis the least squares approach involves a generalized l 2 metric between interval data this metric weights squared distances between data location mid points centers and squared distances between data imprecision spread radius as a consequence estimators of the parameters in the linear model depend on the choice of the weights in the metric to investigate about a suitable choice of weighting in the generalized mid spread metric a theoretical conclusion is first obtained finally the impact of varying the weights is discussed by considering a monte carlo simulation study

iteration algorithms for solving a system of fuzzy linear equations abstract in this paper we discuss the solution of a system of fuzzy linear equations x ax u and its iteration algorithms where a is a real n n matrix the unknown vector x and the constant u are all vectors consisting of n fuzzy numbers and the addition scale multiplication are defined by zadeh s extension principle after introducing a metric between two fuzzy vectors we prove that the system has unique solution if a we also give the convergence and the error estimation for using simple iteration to obtain the solution finally we give the convergence and the error estimation of successive iteration sequence for obtaining the solution

approximating a cuts with the vertex method if f rn r is continuous and monotonic in eachvariable and if i is a fuzzy number on the ith coordinate then the membership on r induced by and by the membership onfrn given by x min 1 x1 n xn can be evaluated by determining the membership at the endpoints of the level cuts of each i here more general conditions are given for both the function and the manner in which the fuzzy numbers i are combined so that this simple method for computing induced membership may be used in particular a geometric condition is given so that the cuts computed when the fuzzy numbers are combined using min is an upper bound for the actual induced membership

universal approximators for fuzzy functions abstract we show how to construct a large class of universal approximators for fuzzy functions which continuously map fuzzy numbers into fuzzy numbers and are the extension principle extensions of continuous real valued functions one important application is that layered feedforward neural nets with real weights and bias terms and fuzzy signals whose output is computed using the extension principle are universal approximators for these functions

send and split method for minimum concave cost network flows many problems from inventory production and capacity planning and from network design exhibit scale economies and can be formulated in terms of finding minimum additive concave cost nonnegative network flows we reduce the problem to an equivalent one in which the arc flow costs are nonnegative and give a dynamic programming method called the send and split method to solve it the main work of the method entails repeatedly solving set splitting and minimum cost chain problems in uncapacitated networks with n nodes a arcs and d 1 demand nodes i e nodes with nonzero exogenous demand the algorithm requires up to n2 13d s2d operations additions and comparisons where s n log2n 3a is the number of operations required to solve a minimum cost chain problem with nonnegative arc costs on the augmented graph formed by appending a node and an arc thereto from each node in the graph if also the network is k planar i e the graph is planar with all demand nodes lying on the boundary of k faces the method requires at most n2 kd3k sd2k operations the algorithm can be applied to capacitated networks because they can be reduced to equivalent uncapacitated ones these results unify significantly generalize e g to cyclic problems and sometimes improve upon e g for tandem facilities known polynomial time dynamic programming algorithms for wagner and whitin s wagner h m whitin t m 1958 dynamic version of the economic lot size model management sci 5 89 96 dynamic economic order quantity problem zangwill s zangwill w i 1969 a backlogging model and a multi echelon model of a dynamic economic lot size production system a network approach management sci 15 506 527 generalization to tandem facilities and veinott s veinott jr a f 1969 minimum concave cost solution of leontief substitution models of multi facility inventory systems oper res 17 262 291 increasing capacity warehousing problem the networks for the finite period versions of these problems are each 1 planar the method improves upon zangwill s zangwill w i 1968 minimum concave cost flows in certain networks management sci 14 429 450 related oand running time dynamic programming method for finding minimum additive concave cost non negative flows in circuitless single source networks we also implement the method to solve in polynomial time the d 1 demand node and k planar versions of the minimum cost forest and steiner problems in graphs the running time for the d 1 demand node steiner problem in graphs is comparable to that of dreyfus and wagner s dreyfus s e wagner r a 1971 the steiner problem in graphs networks1 195 207 method

a characterization of exponential separation in terms of reducibility for linear difference equations abstract the main aim of this paper is to show that a linear difference equation is exponentially separated if and only if all neighboring equations are reducible

exponential separation exponential dichotomy and spectral theory for linear systems of ordinary differential equations abstract this paper is concerned with linear nonautonomous systems of ordinary differential equations a criterion for exponential separation in terms of exponential dichotomy is given as corollaries we obtain the roughness theorem for exponential separation and the new result that an upper triangular system on a half line is exponentially separated if and only if the system corresponding to its diagonal is a minimal decomposition into exponentially separated subspaces is defined it turns out that it is in general finer than the sacker sell spectral decomposition but that the two decompositions coincide for almost periodic systems

structural stability via the density of a class of linear discrete systems abstract in this paper we prove that the set of multiplicatively separated linear discrete systems is dense in the set of linear systems and we find a relationship between the set of structurally stable systems and the set of the systems which have an exponential dichotomy

a new lagrangian relaxation approach to the generalized assignment problem abstract in this paper we present a new lagrangian relaxation approach to the generalized assignment problem gap the new approach is based on a reformulation of gap into an equivalent problem which is then relaxed by traditional lagrangian relaxation techniques the reformulation is created by introducing a set of auxiliary variables and a number of coupling constraints by relaxing the coupling constraints we get subproblems where both types of constraint structures present in the gap are active the lower bound from the lagrangian dual of this approach is shown to be at least as strong as that from the best of the traditional lagrangian relaxation approaches an important feature is also the possibility of generating upper bounds quite easily the new approach has been tested on 10 problems of size m 4 n 25 i e 100 0 1 variables and the results have been compared with the traditional approaches

calculating insurance claim reserves with fuzzy regression claim provisions are crucial for the financial stability of insurance companies this is why actuarial literature has proposed numerous claim reserving methods which are usually based on statistical concepts however the mutant and uncertain behaviour of insurance environments does not make advisable to use a wide data base when calculating claim reserves on the one hand this involves a considerable loss in reliability of statistical methods but on the other it makes the use of fuzzy set theory very attractive in this paper then we propose a claim reserving method that combines the extension by ishibuchi and nii of tanaka s classical fuzzy regression method with sherman s claim reserving scheme

diagrammatic representation for interval arithmetic abstract the paper presents a diagrammatic representation of a standard interval space the so called mr diagram and shows how to represent and perform interval arithmetic and derive its various properties using the diagram the representation is an extension and refinement of the is diagram representation devised earlier by the author to represent interval relations first the mr diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations second diagrammatic constructions for all standard arithmetic operations are presented several examples of the use of these constructions to aid reasoning about various simple though nontrivial properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties

solving fuzzy equations we start in the next section 10 2 with looking at possible solutions to the simple fuzzy linear equation overline a cdot overline x overline b overline c we discuss three different types of solution which we have studied before in solving fuzzy equations then we present a fourth type of solution based on our fuzzy monte carlo method in section 10 2 2 this new solution is based on random fuzzy numbers in section 10 3 we look at only classical solutions to the fuzzy quadratic equation and apply our fuzzy monte carlo method to obtain new solutions then in section 10 4 we consider the fuzzy matrix equation overline a cdot overline x overline b and a number of solution types for overline x and then another solution based on fuzzy monte carlo techniques the last section contains a brief summary and our conclusions

engineering design calculations with fuzzy parameters uncertainty in engineering analysis usually pertains to stochastic uncertainty i e v ariance in product or process parameters characterized by probability uncertainty in truth methods for calculating under stochastic uncertainty are well documented it has been proposed by the authors that other forms of uncertainty exist in engineering design imprecision or the concept of uncertainty in choice is one such form this paper considers real time techniques for calculating with imprecise parameters these techniques utilize interval mathematics and the notion of cuts from the fuzzy calculus the extremes or anomalies of the techniques are also investigated particularly the evaluation of singular or multi valued functions it will be shown that realistic engineering functions can be used in imprecision calculations with reasonable computational performance

inverse controller design for fuzzy interval systems this paper aims at designing and analyzing an inverse controller for stable inversible minimum phase fuzzy interval linear and or multilinear systems the controller is designed from the fuzzy interval ranges of the system parameters using an spl alpha cut methodology indeed for a given spl alpha cut of the fuzzy system parameters representing an uncertainty level the control objective can be viewed as maintaining the system output within a tolerance envelope around the exact trajectory specified by the degree of preference spl alpha on the fuzzy trajectory the stability is ensured in the way that the controller restricts the system output divergence within the tolerance envelope the validity of the proposed method is illustrated by simulation examples

conditions for kinematical similarity of a linear difference equation to a block upper triangular equation abstract in this paper we consider a linear difference equation in which the coefficient matrix is variable and depends on a positive parameter under some conditions we prove that the above equation is kinematically similar to a block upper triangular equation

joint solution to fuzzy programming problems we propose a new solution concept for fuzzy programming problems it is based on our new method of solving fuzzy equations 101 for simplicity we discuss in detail only fuzzy linear programming in this paper we define and obtain the basic properties of the joint solution a fuzzy vector in rn and the optimal value of the objective function a fuzzy number three examples are presented illustrating these concepts

estimating a fuzzy term structure of interest rates using fuzzy regression techniques abstract several papers in the financial literature propose using fuzzy numbers fns to model interest rate uncertainty however in our opinion the first problem to be solved is how to estimate these rates with fns in this paper we attempt to provide a solution to this question with a method for adjusting the temporal structure of interest rates tsir that is based on fuzzy regression techniques this method will enable to quantify the anticipated rates in the fixed income markets for the future with fns in particular we discuss how to estimate the tsir with triangular fuzzy numbers because of their desirable properties