first order linear fuzzy differential equations under generalized differentiability first order linear fuzzy differential equations are investigated we interpret a fuzzy differential equation by using the strongly generalized differentiability concept because under this interpretation we may obtain solutions which have a decreasing length of their support which means a decreasing uncertainty in several applications the behaviour of these solutions better reflects the behaviour of some real world systems derivatives of the h difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations using different versions of the variation of constants formula some examples show the rich behaviour of the solutions obtained

fuzzy differential equations and the extension principle we study the cauchy problem for differential equations considering its parameters and or initial conditions given by fuzzy sets these fuzzy differential equations are approached in two different ways a by using a family of differential inclusions and b the zadeh extension principle for the solution of the model we conclude that the solutions of the cauchy problem obtained by both are the same we also provide some illustrative examples

brief note on the variation of constants formula for fuzzy differential equations this note gives a theory of state transition matrices for linear systems of fuzzy differential equations this is used to give a fuzzy version of the classical variation of constants formula a simple example of a time independent control system is used to illustrate the methods while similar problems to the crisp case arise for time dependent systems in time independent cases the calculations are elementary solutions of eigenvalue eigenvector problems in particular for nonnegative or nonpositive matrices the problems at each level set can easily be solved in matlab to give the level sets of the fuzzy solution

existence theorem to the cauchy problem of fuzzy differential equations under compactness type conditions kaleva fuzzy sets and systems 35 1990 389 396 has concluded that the peano theorem does not hold for fuzzy differential equations on en d this paper deals with the cauchy problem of fuzzy differential equations the existence theorems under compactness type conditions are obtained

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

numerical solution of fuzzy differential equations by predictor corrector method in this paper three numerical methods to solve the fuzzy ordinary differential equations are discussed these methods are adams bashforth adams moulton and predictor corrector predictor corrector is obtained by combining adams bashforth and adams moulton methods convergence and stability of the proposed methods are also proved in detail in addition these methods are illustrated by solving two fuzzy cauchy problems

homotopy perturbation method a new nonlinear analytical technique in this paper a new perturbation method is proposed in contrast to the traditional perturbation methods this technique does not require a small parameter in an equation in this method according to the homotopy technique a homotopy with an imbedding parameter email protected 0 1 is constructed and the imbedding parameter is considered as a small parameter so the method is called the homotopy perturbation method which can take the full advantages of the traditional perturbation methods and homotopy techniques to illustrate its effectiveness and its convenience a duffing equation with high order of nonlinearity is used the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter and is more accurate than the perturbation solutions

scattering theory for nonlinear schrodinger equations with inverse square potential abstract we study the long time behavior of solutions to nonlinear schrodinger equations with some critical rough potential of a x 2 type the new ingredients are the interaction morawetz type inequalities and sobolev norm property associated with p a a x 2 we use such properties to obtain the scattering theory for the defocusing energy subcritical nonlinear schrodinger equation with inverse square potential in energy space h 1 r n

existence and uniqueness of solution for fuzzy random differential equations with non lipschitz coefficients in this paper a class of fuzzy random differential equations with non lipschitz coefficients is studied the existence and uniqueness of solutions for fuzzy random differential equations with non lipschitz coefficients is first proved then the dependence of fuzzy random differential equations on initial values is discussed finally the non confluence property of the solution for fuzzy random differential equation is investigated our main tool is the gronwall lemma

global existence of solutions to fuzzy differential equations abstract the local existence and uniqueness theorems are investigated by wu et al j math anal appl 202 1996 629 644 for the cauchy problem of the fuzzy valued mappings of a real variable whose values are in the fuzzy number space e n d in this paper we point out a variety of results which assure global existence of solutions to fuzzy differential equations

numerical methods forfuzzy differential inclusions in this paper a numerical method for solving fuzzy differential inclusions is considered fuzzy reachable set can be approximated by proposed method with complete error analysis which is discussed in detail the method is illustrated by solving some linear and nonlinear fuzzy initial value problems

robust stabilization in the gap metric controller design for distributed plants the problem of robustness in the gap metric for infinite dimensional systems is considered the problem of computing the optimal controller and the optimal robustness radius for a class of systems whose normalized coprime factors have elements which are h sub infinity functions with continuous boundary values is studied the underlying hankel and related operators which are important in the gap optimization problem are studied and relations between their singular values and vectors are established a computational approach to the optimal robustness problem is developed for single input single output systems whose transfer function is an inner function in h sub infinity times a rational function the procedure is applied to a general first order delay system and a closed form formula is obtained for the optimal controller the frequency response plots of the compensated system for various values of time delay are examined

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

the extension principle and a decomposition of fuzzy sets we give an algorithm to decompose a fuzzy interval u using this decomposition and the multilinearization of a univariate function f we obtain an approximation of the fuzzy interval where is obtained from f by applying the extension principle we provide approximation bounds some numeric illustration is provided

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

simulating continuous fuzzy systems abstract in previous studies we concentrated on utilizing crisp numeric simulation to produce discrete event fuzzy systems simulations then we extended this research to the simulation of continuous fuzzy systems models in this study we continue our study of continuous fuzzy systems using crisp continuous simulation consider a crisp continuous system whose process of evolution depends on differential equations such a system contains a number of parameters that must be estimated usually point estimates are computed and used in the model however these point estimates typically have uncertainty associated with them we propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters fuzzy parameters convert the crisp system into a fuzzy system trajectories describing the behavior of the system become fuzzy curves we will employ crisp continuous simulation to estimate these fuzzy trajectories three examples are discussed

comparison results for fuzzy differential equations in this paper we present several comparison results for the solutions of fuzzy differential equations by using the hukuhara derivative these results constitute the extension to the fuzzy context of some comparison results for the solutions of linear differential equations besides some side results about the hukuhara difference and the partial orderings are given we illustrate the applicability of the new results by showing several examples

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

numerical solutions of fuzzy differential equations abstract numerical algorithms for solving fuzzy ordinary differential equations fode are considered a scheme based on the classical euler method is discussed in detail and this is followed by a complete error analysis the algorithm is illustrated by solving several linear and nonlinear fuzzy cauchy problems

on solving the initial value problems using the differential transformation method in this paper initial value problems are solved by the differential transformation method the differential transformation method of fixed grid size is used to approximate solutions of linear and nonlinear initial value problems an adaptive grid size mechanism based on the fixed grid size technique is also proposed the proposed adaptive grid size procedure provides concise adjustment policy and raises computational efficiency of using differential transformation method

existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument in this paper we study the existence the uniqueness and the asymptotic behavior of the solutions of the fuzzy differential equation of the form x t px t qx t email protected 0 where p q are constant real numbers and the initial value x 0 is a fuzzy number

solving partial differential equations by two dimensional differential transform method using two dimensional differential transform to solve partial differential equations pde is proposed in this study first the theory of two dimensional differential transform is introduced second taking two dimensional differential transform of a pde problem a set of difference equations is derived doing some simple mathematical operations on these equations we can get a closed form series solution or an approximate solution quickly finally three pde problems with constant and variable coefficients are solved by the present method the calculated results are compared very well with those obtained by other analytical or approximate methods

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

towards fuzzy differential calculus part 3 differentiation this paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation of fuzzy valued functions at a nonfuzzy point in both cases the concept of differentiation is extended and the problem of the linearity is addressed in the second case practical methods of computation are presented in practical situations the available knowledge about mappings may be fuzzy it is the motivation of this work

existence of the solutions of fuzzy differential equations with parameters in this paper we study the existence of the solutions of fuzzy differential equations with parameters by the topological degree method

fuzzy differential equations we will concentrate on the second order linear constant coefficient ordinary differential equation for x in interval i i can be 0 t for t 0 or i can be 0 the initial conditions are y 0 0 y 0 1 we assume g is continuous on i

an efficient technique for superfamily classification of amino acid sequences feature extraction fuzzy clustering and prototype selection in this article we propose an efficient technique for classifying amino acid sequences into different superfamilies the proposed method first extracts 20 features from a set of training sequences the extracted features are such that they take into consideration the probabilities of occurrences of the amino acids in the different positions of the sequences thereafter a genetic fuzzy clustering approach is used to automatically evolve a set of prototypes representing each class the characteristic of this clustering method is that it does not require the a priori information about the number of clusters and is also able to come out of locally optimal configurations finally the nearest neighbor rule is used to classify an unknown sequence into a particular superfamily class based on its proximity to the prototypes evolved using the genetic fuzzy clustering technique this results in a significant improvement in the time required for classifying unknown sequences results for three superfamilies namely globin trypsin and ras demonstrate the effectiveness of the proposed technique with respect to the case where all the training sequences are considered for classification using the same set of features comparison with the well known technique blast also shows that the proposed method provides a significant improvement in terms of the time required for classification while providing comparable classification performance

numerical solutions for linear system of first order fuzzy differential equations with fuzzy constant coefficients in this paper a novel iterative method is proposed to obtain approximate analytical solutions for the linear systems of first order fuzzy differential equations fdes with fuzzy constant coefficients fccs while avoiding the complexities of eigen value computations a theorem for the convergence and the validity of the approach is also presented in detail numerical experiments and comparisons with exact solutions reveal that the proposed method is capable of generating accurate results

note on numerical solutions of fuzzy differential equations by predictor corrector method in the present note it is shown that the examples presented in a recent paper by allahviranloo et al are incorrect namely the exact solutions proposed by the authors are not solutions of the given fuzzy differential equations fdes the correct exact solutions are also presented here together with some results for characterizing solutions of fdes under hukuhara differentiability by an equivalent system of odes in this way a new direction for the numerical solutions of fdes is proposed

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation