investigation of natural frequencies and mode shapes of buckled beams the linear modes of vibration of buckled beams are investigated analytically and experimentally assuming a static buckled shape corresponding to the nth buckling mode an exact solution is obtained for the linear modes and associated frequencies of initially buckled beams with fixed fixed fixed hinged and hinged hinged boundary conditions the analytical solution for a first mode buckled beam is validated experimentally for the fixed fixed case the analytically obtained natural frequencies are in excellent agreement with those obtained experimentally these exact linear modes provide a basis from which to study the nonlinear vibrations of buckled beams

a new method for solving interval and fuzzy equations linear case a new approach to the solution of interval and fuzzy equations based on the generalized procedure of interval extension called interval extended zero method is proposed the central for the proposed approach is the treatment of the interval zero as an interval centered around zero it is shown that such proposition is not of heuristic nature but is the direct consequence of the interval subtraction operation some methodological problems concerned with this definition of interval zero are discussed it is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number an important advantage of a new method is that it substantially decreases the excess width effect on the other hand we show that it can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them the features of the method are illustrated by the example of the solution of the well known leontief input output problem in the interval setting

folds and cusps in banach spaces with applications to nonlinear partial differential equations ii on considere le probleme de dirichlet non lineaire inhomogene u u u 3 g sur u 0 ou r n n 4 est un domaine borne on etudie aussi un systeme elliptique non lineaire les equations de von karman

computing real solutions of fuzzy polynomial systems abstract this paper presents an efficient algorithm called solvefuzzysystem or sfs for finding real solutions of polynomial systems whose coefficients are symmetrical l r fuzzy numbers with bounded support for which the spread functions l and r are bijective the real solutions of such a system are deduced from solutions of some polynomial systems with real coefficients this algorithm is based on new results that are universal because they are independent from the spread functions these theoretical results include the management of the fuzzy system s solutions signs an implementation in the fuzzy package of the free computer algebra software sagemath and a parallel version of the algorithm are described

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

numerical solution of a system of fuzzy polynomials by fuzzy neural network in this paper a new approach for solving systems of fuzzy polynomials based on fuzzy neural network fnn is presented this method can also lead to improve numerical methods in this work an architecture of fuzzy neural networks is also proposed to find a real root of a system of fuzzy polynomials if exists by introducing a learning algorithm finally we illustrate our approach by numerical examples

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

free vibrations of a non uniform beam with general elastically restrained boundary conditions abstract a simple and efficient method is presented to study the problem of free vibration of a non uniform bernoulli euler beam with general elastic restraints at boundary points with one set of particularly chosen fundamental solutions of the system the frequency equation is derived and expressed in concise form if the closed form fundamental solutions of the system are not available the approximate fundamental solutions can be obtained through a newly developed algorithm which is shown to be efficient convenient and accurate finally several limiting cases of the general system are examined and some examples are presented to illustrate the validity and accuracy of the proposed method

nonlinear vibration of buckled beams some exact solutions in this paper exact solutions are obtained for the dynamics of buckled beams with different types of end conditions the differential equation for the vibrations of buckled beams with restrictions on axial stretch is nonlinear using the modes of the corresponding linear problem which readily satisfy the boundary conditions the natural frequencies are obtained for the nonlinear problem by using jacobi elliptic functions analytical solutions for the dynamics of buckled beams with various rotational restraints are presented

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

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

stability analysis of neural net controllers using fuzzy neural networks neural networks can only be trained with a crisp and finite data set therefore the approximation quality of a trained network is hard to verify so a common way in proving stability of a trained neural net controller is to demonstrate the existence of a lyapunov function in this article we propose a new method how stability of a neural net controller used as a closed loop feedback controller can be proven instead of finding a lyapunov function conditions for a fuzzy training set are developed if a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error after defuzzification of the fuzzy net finite stability of the process can be concluded

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

analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials for the given fuzzy valued function j rn f0 r the fuzzy valued bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set u rn some equivalent condition for the continuous fuzzy function f f0 r n f0 r that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set u f0 r n are presented

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

universal approximations of continuous fuzzy valued functions by multi layer fuzzy neural networks abstract the fact that four layer feedforward regular fuzzy neural networks with sigmoid function in the first hidden layer are capable of approximately representing continuous fuzzy valued functions on any compact set of r is shown at first bernstein polynomials associated with fuzzy valued functions are employed to approximate continuous fuzzy valued function defined on a compact set secondly by the conclusions related to standard feedforward networks universal approximations of continuous fuzzy valued functions by regular fuzzy neural networks are obtained

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

can neural nets be universal approximators for fuzzy functions abstract we first argue that the extension principle is too computationally involved to be an efficient way for a computer to evaluate fuzzy functions we then suggest using cuts and interval arithmetic to compute the valued of fuzzy functions using the method of computing fuzzy functions we then show that neural nets are universal approximators for computable fuzzy functions when we only input non negative or non positive fuzzy numbers

analysis of buckled and pre bent fixed end columns used as vibration isolators the use of a buckled or pre bent column with fixed ends as a vibration isolator is analyzed the column is designed to have a high axial stiffness under the weight that it supports so that the static displacement of the weight is not excessive and then to have a low stiffness during excitation the base of the column is assumed to have an axial motion which is simple harmonic or a linear combination of two simple harmonic functions the column is modeled as an elastica first the equilibrium shape under the supported weight is determined then small steady state vibrations about the equilibrium configuration are obtained numerically using a shooting method the inertia of the supported weight and the transverse and axial inertias of the column are included the axial displacement transmissibility is computed and the effects of external and internal damping column stiffness supported weight and initial curvature are investigated for the two frequency excitation the effects of the relative amplitudes and frequencies of the excitation components are considered

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

numerical solution of fuzzy polynomials by fuzzy neural network in this paper an architecture of fuzzy neural networks is proposed to find a real root of fuzzy polynomials if exists by introducing a learning algorithm we proposed a learning algorithm from the cost function for adjusting of crisp weights finally we illustrated our approach by numerical examples

jacobi elliptic functions a review of nonlinear oscillatory application problems abstract this review paper is concerned with the applications of jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and or quadratic nonlinearity first geometric interpretations of three basic jacobi elliptic functions are given and their characteristics are discussed it is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators these forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators an illustrative example is provided further two types of externally forced nonlinear oscillators are reviewed i those that are excited by elliptic type excitations with different exact and approximate solutions ii those that are damped and excited by harmonic excitations but their approximate response is expressed in terms of jacobi elliptic functions characteristics of the steady state response are discussed and certain qualitative differences with respect to the classical duffing oscillator excited harmonically are pointed out parametric oscillations of the oscillators excited by an elliptic type forcing are considered as well and the differences with respect to the stability chart of the classical mathieu equation are emphasized the adjustment of the melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic type forcing is provided and compared with those corresponding to harmonic excitations advantages and disadvantages of the use of jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given

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

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

neural network approach to solving fuzzy nonlinear equations using z numbers in this article the fuzzy property is described by means of the z number as the coefficients and variables of the fuzzy equations this alteration for the fuzzy equation is appropriate for system modeling with z number parameters in this article the fuzzy equation with z number coefficients and variables is tended to be used as the models for the uncertain systems the modeling issue related to the uncertain system is to obtain the z number coefficients and variables of the fuzzy equation nevertheless it is extremely hard to get the z number coefficients of the fuzzy equations in this article in order to model the uncertain nonlinear systems a novel structure of the multilayer neural network is utilized in such a manner that it is able to obtain the z number coefficients of the fuzzy equation the suggested technique is validated by some examples with applications

can fuzzy neural nets approximate continuous fuzzy functions abstract we first argue that regular fuzzy neural nets based on standard fuzzy arithmetic and the extension principle cannot be universal approximators this negative result is surprising since regular neural nets are universal approximators we then argue that hybrid fuzzy neural nets not necessarily based on standard fuzzy arithmetic can be universal approximators

evaluation of fuzzy regression models by fuzzy neural network in this paper a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients parameters of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs is presented here a neural network is considered as a part of a large field called neural computing or soft computing moreover in order to find the approximate parameters a simple algorithm from the cost function of the fuzzy neural network is proposed finally we illustrate our approach by some numerical examples

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

investigation on non linear vibration in arched beam for bridges construction via agm method analyzing and modeling the vibrational behavior of arched bridges during earthquake in order to decrease the exerted damages to the structure is a very hard task to do in the present paper this item has been performed analytically for the first time due to the importance of arched bridges building as a great structure in the human being civilization and its specifications such as transferring vertical loads to its arcs and the lack of bending moments and shearing forces this case study is devoted to this special issue therefore the nonlinear vibration of arched bridges has been modeled and simulated by an arched beam with harmonic vertical loads and its behavior has been investigated by analyzing a nonlinear partial differential equation governing on the system it is notable that the procedure has been done analytically by agm akbari ganji s method it has found that angular frequency is increased significantly by escalating the amount of the center outlet furthermore comparisons have been made between the obtained results by numerical method rkf 45 and agm in order to assess the scientific validity obtained results indicate the precision of the achieved answers by agm method

exact enclosures of roots of interval quadratic equations by sridhara s and fagnano s or modified fagnano s formulas in this study we investigate the question of accurate determination of the root enclosures of quadratic equations whose coefficients constitute interval variables we treat several special cases where either sridhara s classical formula or fagnano s alternative expression provide exact interval enclosures for the roots of the quadratic equation in the case of a single coefficient serving as an interval it is shown that the classical interval analysis by either sridhara s fagnano s or specifically modified fagnano s formulas provide lower and upper bounds of roots then we follow with the case of two coefficients being intervals whereas the third coefficient is a deterministic quantity numerous examples are provided in which the solutions are compared with the direct numerical evaluation of the roots enclosures in three arising cases either sridhara s or fagnano s expressions suffice to obtain exact enclosures

fuzzy complex numbers abstract this paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations it is shown that arithmetic of fuzzy complex numbers may be performed in terms of cuts next two special types of fuzzy complex numbers based on the forms z x iy and z re i for regular complex numbers are investigated introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions

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

on the number of solutions of some semilinear elliptic boundary value problems where r is an open bounded subset of rd y is a linear real valued uniformly elliptic differential operator 9 is a linear differential boundary operator and the pair y 9 is formally self adjoint it is well known that given l t r and 1 cc r r may have a nonunique solution or may not have any solution at all recently some authors have studied the problem of finding the exact number of solutions of for some special classes of 3 99 and f see e g ambrosetti and prodi l amann 121 ambrosetti and mancini 131 berger 4 berestycki s and the references therein the main purpose of the present paper is to continue this study however in the last two sections we turn to somewhat different problems let a and iz be the first and the second eigenvalue of y i with i simple suppose that j t is convex for t 0 concave for 1 0 and f o f o 0 furthermore let

solving linear and quadratic fuzzy equations abstract we present necessary and sufficient conditions for some linear and quadratic equations to have a solution when the parameters are either real or complex fuzzy numbers the solution will be a real or complex fuzzy number applications in chemistry economics finance and physics are presented for these types of equations

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

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

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

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

neural net solutions to fuzzy linear programming we show how a neural net with sign restrictions on its weights can be trained to produce approximate solutions to fuzzy linear programming problems the neural net approximates the joint solution buckley 1995 to the fuzzy linear program

solving fuzzy equations a new solution concept abstract we have previously shown 2 that many fuzzy equations do not have solutions when the solution concept is based on the extension principle we therefore introduce two new solution procedures one based on the unified extension 6 and the other based on possibility theory after we solve the non fuzzy equation for the unknown variable we show for many types of equations that 1 the two new solutions are identical 2 the solution is either a real or generalized complex fuzzy number all uncertain parameters are modeled as real fuzzy numbers and 3 the previous solution based on the extension principle when it exists is a subset of the new solution in particular we show that the fuzzy quadratic equation with real fuzzy number coefficients always has a new solution

solving fuzzy equations using neural nets abstract in this paper we show how a neural net can be used to solve ax c for x even though for some values of a and c there is no fuzzy arithmetic solution for x the neural net solution is identified with our new solution 6 to fuzzy equations

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

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

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

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