on a class of fuzzy functional differential equations in this paper we establish the local and global existence and uniqueness results for fuzzy functional differential equations for the local existence and uniqueness we use the method of successive approximations and for global existence and uniqueness we use the contraction principle also we apply these results to fuzzy differential equations with distributed delays and fuzzy population models

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

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

periodic boundary value problems for first order linear differential equations with uncertainty under generalized differentiability we study the existence of solutions to a class of first order linear fuzzy differential equations subject to periodic boundary conditions from the point of view of generalized differentiability the objective of this paper is to show that fuzzy differential equations under generalized differentiability can be used in the study of periodic phenomena by considering a combination of two types of derivatives with a switching point we provide sufficient conditions which guarantee that the piecewise defined solutions match adequately and illustrate through some examples the process of construction and calculation of solutions

open fuzzy cubature rule with application to nonlinear fuzzy volterra integral equations in two dimensions abstract in this paper we propose an open fuzzy cubature formula and as application we construct an iterative numerical method for solving nonlinear fuzzy volterra integral equations in two dimensions the convergence of the method is proved by providing the error estimate and it is tested on two numerical experiments

the s differentiability of a fuzzy valued mapping several approaches to define the differential of fuzzy valued mappings can be found in the literature in this paper we introduce a new concept of differential of a fuzzy valued mapping which is based on the notion of differential of the support function associated with such a mapping properties of the new concept as well as the relation between it and previous approaches are also analyzed in detail

on the solutions to first order linear fuzzy differential equations in this paper we study different formulations of first order linear fuzzy differential equations using the concept of generalized differentiability we present sufficient conditions for the existence of solutions and obtain the general expression of these solutions which exhibit different behavior some examples are given to illustrate our results

on differential equations with interactive fuzzy parameter via t norms abstract in this paper we study fuzzy differential equations with uncertain parameters modeled by interactive fuzzy numbers the interactivity is formalized with the help of upper semicontinuous t norms to obtain solutions to fuzzy differential equations we use two different approaches the first uses a family of differential inclusions while the second is the fuzzification of the deterministic problem using the zadeh extension principle we show that the solutions obtained by the two methods are equal interactivity among the parameters and variable of the problem are studies with respect two methods we show that a hierarchy in uncertainties of the solutions arises when we chose one of the basic t norm the minimum the t norm of the product the t norm of lukasiewicz and t norm of the drastic product to model the interaction between parameters finally to illustrate the concepts introduced in the paper we study the malthusian model with interactive parameters

unfold fold transformation of stratified programs abstract this paper describes some extensions of tamaki sato s 1984 unfold fold transformation of definite programs we first propose unfold fold rules also preserving the finite failure set by sld resolution of a definite program which the original rules proposed by tamaki and sato do not then we show that our unfold fold rules can be extended to rules for stratified programs and prove that both the success set and the finite failure set by sldnf resolution of a stratified program are preserved preservation of equivalence of the perfect model semantics przymusinski 1988 is also discussed

fuzzy fractional functional integral and differential equations this paper is devoted to considering the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle moreover the approach is followed to prove the existence and uniqueness of solutions for the fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives finally the solution to fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives by a modified fractional euler method mfem is presented the method is illustrated by solving some examples

improved predictor corrector method for solving fuzzy initial value problems in this paper an improved predictor corrector ipc method is proposed to solve the fuzzy initial value problem the ipc method is generated by combining an explicit three step method and an implicit two step method the methods are compared with the methods discussed in t allahviranloo n ahmady e ahmady numerical solution of fuzzy differential equations by predictor corrector method information sciences 177 7 2007 1633 1647 and are shown to be more accurate the convergence and stability of the proposed methods are also presented in detail these methods are illustrated by solving some examples

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

a continuous time dynamic fuzzy system ii fuzzy potentials abstract this paper is a sequel of yoshida 9 fuzzy potentials are introduced in a continuous time dynamic fuzzy system and a fuzzy relational differential equation is given to characterize the fuzzy potentials

initial and boundary value problems for fuzzy differential equations we prove a wintner type result for fuzzy ivps and a superlinear type result for fuzzy bvps both results rely on a generalized schauder theorem in metric spaces

generalized convexity in fuzzy vector optimization through a linear ordering in this article we study efficiency and weakly efficiency in fuzzy vector optimization after formulating the problem we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized hukuhara differentiability pseudoinvexity i and pseudoinvexity ii we prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem we give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex i and ii moreover we present some examples to illustrate the results lastly we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models

characterizations of generalized differentiable fuzzy functions this article deals with generalized differentiable fuzzy functions specifically we give some characterizations of generalized hukuhara differentiable fuzzy functions through the differentiability of their endpoint functions then we introduce a differentiability concept that is more general than the generalized hukuhara differentiability and extend the above characterization to this new type of differentiability as well as to g differentiable fuzzy functions these characterizations are useful tools for the calculus of derivatives of fuzzy functions

universal distributed estimation over multiple access channels with constant modulus signaling a distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered the proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i i d case both for a per sensor power constraint and a total power constraint when the distributions of the sensing noise are not identical a bound on their variances is shown to establish strong consistency the estimator is shown to be asymptotically normal with a variance asv that depends on the characteristic function of the sensing noise optimization of the asv is considered with respect to a transmission phase parameter for a variety of noise distributions exhibiting differing levels of impulsive behavior the robustness of the estimator in the sense of degrading gracefully when the sensing noise deviates from the gaussian distribution to impulsive sensing noise distributions such as those with positive excess kurtosis or those that do not have finite moments is shown the proposed estimator is favorably compared with the amplify and forward scheme under an impulsive noise scenario the effect of fading and phase error at the sensors are shown to not affect the consistency of the estimator but to degrade the asymptotic variance by terms that depend on the fading and phase error distributions simulations corroborate our analytical results

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

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

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

distributed snr estimation with power constrained signaling over gaussian multiple access channels a sensor network is used for distributed signal to noise ratio snr estimation in a single time snapshot sensors observe a signal embedded in noise and each observation is phase modulated using a constant modulus scheme and transmitted over a gaussian multiple access channel to a fusion center at the fusion center the mean and variance are estimated jointly using an asymptotically minimum variance estimator it is shown that this joint estimator decouples into simple individual estimators of the mean and the variance the constant modulus phase modulation scheme ensures a fixed transmit power robust estimation across several sensing noise distributions as well as an snr estimate that requires a single set of transmissions from the sensors to the fusion center the estimators are evaluated in terms of asymptotic variance which are then used to evaluate the performance of the snr estimator with gaussian and cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per sensor power constraint for each sensing noise distribution the optimal phase transmission parameters are also determined the asymptotic relative efficiency of the estimators is evaluated it is shown that among the noise distributions considered the estimators are asymptotically efficient only when the noise distribution is gaussian simulation results corroborate analytical results

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

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

stability in possibilistic linear programming with continuous fuzzy number parameters abstract we prove that possibilistic linear programming problems introduced by buckley in 2 with continuous fuzzy number parameters are well posed i e small changes of the membership function of the parameters may cause only a small deviation in the possibilistic distribution of the objective function

on the convergence of fuzzy sets three kind of convergences are defined on a space of fuzzy sets relationships between these convergences are studied some comments on the fixed point property are represented

oscillation property for fuzzy delay differential equations in this paper we obtain an oscillation criterion of solutions and the existence of nonoscillatory solutions to a class of fuzzy delay differential equation fdde of second order some examples are given to illustrate the main theorems

preservation of stronger equivalence in unfold fold logic program transformation abstract this paper shows that tamaki sato s unfold fold transformation of prolog programs preserves equivalence in a stronger sense that of the usual least herbrand model semantics which tamaki and sato originally showed conventionally the semantics of prolog program is defined by the least herbrand model however the least herbrand model does not always characterize what answer substitutions are returned this paper proves that any program obtained from an initial program by applying tamaki sato s transformation returns the same answer substitutions as the initial program for any given top level goal

periodic boundary value problems for impulsive fuzzy differential equations the peculiarity of the hukuhara derivative makes it impossible to find periodic solutions for fuzzy differential equations with the exception of very restrictive situations in this work we consider a boundary value problem associated with an impulsive fuzzy differential equation and approximate the extremal solutions in a fuzzy functional interval using the monotone method fuzzy comparison results are useful in our procedure and the expression of the solution for some impulsive periodic linear differential problems is also provided

sequential decentralized parameter estimation under randomly observed fisher information we consider the problem of decentralized scalar parameter estimation using wireless sensor networks with gaussian noise specifically we propose a novel framework based on level triggered sampling a non uniform sampling strategy and sequential estimation the proposed estimator can be used as an asymptotically optimal fixed sample size decentralized estimator when the observed fisher information i e fisher information without expectation is deterministic as an alternative to the one shot estimators commonly found in the literature it can also be used as an asymptotically optimal sequential decentralized estimator when the observed fisher information is random we show that the optimal centralized estimator under gaussian noise which is the maximum likelihood estimator is characterized by two processes namely the observed fisher information ut and the observed correlation vt it is noted that vt is always random even when ut is not in the proposed scheme each sensor computes its local random processes and sends a single bit to the fusion center fc whenever the local random processes passes certain predefined levels the fc upon receiving a bit from a sensor updates its approximation to the corresponding global random process and accordingly its estimate the sequential estimation process terminates when ut or the approximation to it reaches a target value we provide an asymptotic analysis for the proposed estimator and the one based on conventional uniform in time sampling under both deterministic and random ut and determine the conditions under which they are asymptotically optimal consistent and asymptotically unbiased analytical results together with simulation results demonstrate the superiority of the proposed estimator based on level triggered sampling over the traditional decentralized estimator based on uniform sampling

membership induced on manifolds by vector fields and flows abstract in many engineering and scientific applications the need arises to perform differential calculations on manifolds if such calculations involve imprecise data methods for computing with such data must be determined definitions and results are given for memberships on manifolds induced by differentiation along vector fields and by flows of vector fields with uncertain parameters examples are presented which illustrate the concepts

a class of linear differential dynamical systems with fuzzy matrices abstract this paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices we use a complex number representation of the level sets of the fuzzy system and obtain the solution by employing such representation it is applicable to practical computations and has also some implications for the theory of fuzzy differential equations we then present some properties of the 2 dimensional dynamical systems and their phase portraits some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear we finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems

fuzzy delay differential equations under generalized differentiability abstract we interpret a fuzzy delay differential equation using the concept of generalized differentiability in this setting we prove the existence of two fuzzy solutions each one corresponding to a different type of differentiability uniqueness is understood in the sense that the solutions considered do not have switching points the applicability of the theoretical results is illustrated with some real world examples

rules strategies for transforming lazy functional logic programs this work introduces a transformation methodology for functional logic programs based on needed narrowing the optimal and complete operational principle for modern declarative languages which integrate the best features of functional and logic programming we provide correctness results for the transformation system w r t the set of computed values and answer substitutions and show that the prominent properties of needed narrowing namely the optimality w r t the length of derivations and the number of computed solutions carry over to the transformation process and the transformed programs we illustrate the power of the system by taking on in our setting two well known transformation strategies composition and tupling we also provide an implementation of the transformation system which by means of some experimental results highlights the potentiality of our approach

analytical and numerical solutions of fuzzy differential equations in this paper we study analytical and numerical solutions of fuzzy differential equations based on the extension principle for linear fuzzy differential equations we state some results on the behaviour of the solutions and study their relationship with the generalised hukuhara derivative in order to approximate the solutions of linear and non linear fuzzy differential equations we propose a new fuzzification of the classical euler method and then incorporate an unconstrained optimisation technique this combination offers a powerful tool to tackle uncertainty in any numerical method an efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain several illustrative examples are given

variation of constant formula for first order fuzzy differential equations in this paper we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions we also correct and complete some previous results finally some examples are given to illustrate our results

on retarded fuzzy functional differential equations and nonabsolute fuzzy integrals abstract we prove a generalized convergence theorem for fuzzy henstock integrals based on the sequence of fuzzy number valued functions which are weak generalized uniformly absolute continuous u a c g to widen the applications of this convergence theorem we provide some existence theorems for the generalized solution for retarded fuzzy functional differential equations and the dependence of the solutions on a parameter under the assumption of the strong generalized derivative of the solution our results generalize existence results in a kaleva integral setting to a fuzzy henstock integral setting

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

initial value problem for fuzzy differential equations under dissipative conditions a new concept of inner product on the fuzzy space e n d is introduced studied and used to prove several theorems stating the existence uniqueness and boundedness of solutions of fuzzy differential equations a stability result is also proved in the same context

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

solution method for a boundary value problem with fuzzy forcing function in this paper we present a new approach to a non homogeneous fuzzy boundary value problem we consider a linear differential equation with real coefficients but with a fuzzy forcing function and fuzzy boundary values we assume that the forcing function is a triangular fuzzy function unlike previous studies we look for a solution that is a fuzzy set of real functions not a fuzzy valued function each of these real functions satisfies the boundary value problem with some membership degree we have developed a method that finds this solution and demonstrated its effectiveness using a test example to show that the approach can be extended to other types of fuzzy numbers we extended it to the trapezoidal case for a particular example we used the product t norm to demonstrate how a new solution type can be obtained

a survey on the initial value problems of fuzzy implicit fractional differential equations abstract the purpose of this paper is to present some basic theories of various classes of initial value problems of implicit fractional differential equation involving the caputo fuzzy type riemann liouville fuzzy type and hadamard fuzzy type concepts of fractional derivative in the case of the order 0 1 in particular the existence and uniqueness results of solution for the given initial value problems of implicit fractional differential equations is investigated in addition some results concerning continuous dependence of solutions on perturbations of the given parameters namely of the initial conditions of the function and parameters on the right hand side of the order of fractional derivative are analyzed finally some examples are given to illustrate our main results

the solvability of fuzzy fractional partial differential equations under caputo gh differentiability the foundation of the concepts of fuzzy fractional integral and caputo gh partial for fuzzy valued multivariable functions is defined as a result fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved we present two new results on the existence of two kinds of gh weak solutions of these problems the first result is based on the banach fixed point theorem with the lipschitz condition of functions on the right hand side of equations the second result is based on the nonlinear alternative of the schauder type for fuzzy valued continuous functions without the lipschitz condition moreover we indicate the boundedness and continuous dependence of solutions on the initial data of the problems our models are embedded in the sense of caputo gh differentiability some examples are presented to illustrate the results

interval cauchy problem with a second type hukuhara derivative in this paper we consider interval differential equations such the equations can be appropriate in modeling of dynamical systems under presence of uncertainty of parameters we study an interval initial value problem with a second type hukuhara derivative by an example of real world application we indicate the advantages of the usage of such a kind of interval valued derivative a continuous dependence of the solution on initial value and right hand side of the equation is shown the existence of approximate local solutions is proven and then it is used in the derivation of existence of at least one local solution to interval cauchy problem with second type hukuhara derivative the compactness of solutions set is also stated finally the explicit formulae for local solutions to linear interval differential equations are provided

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

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

a proof of the fisher information inequality via a data processing argument the fisher information j x of a random variable x under a translation parameter appears in information theory in the classical proof of the entropy power inequality epi it enters the proof of the epi via the de bruijn identity where it measures the variation of the differential entropy under a gaussian perturbation and via the convolution inequality j x y sup 1 spl ges j x sup 1 j y sup 1 for independent x and y known as the fisher information inequality fii the fii is proved in the literature directly in a rather involved way we give an alternative derivation of the fii as a simple consequence of a data processing inequality for the cramer rao lower bound on parameter estimation

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

on the efficiency of empirical characteristic function procedures summary the asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions

comparation between some approaches to solve fuzzy differential equations in this paper we study the class of fuzzy differential equations where the dynamics is given by a continuous fuzzy mapping which is obtained via zadeh s extension principle we get a fuzzy solution for this class of fuzzy differential equations and several illustrative examples are presented we also give some properties and we show the relationships with others interpretation finally we propose a numerical procedure for obtaining the fuzzy solution

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

almost periodic fuzzy number valued functions in this paper we develop a theory of almost periodic fuzzy functions i e of the almost periodic functions of real variable and with values fuzzy real numbers although the class of fuzzy real numbers does not form a linear normed space the majority of main properties of almost periodic functions with values in banach spaces are extended to this case applications to fuzzy differential equations and to fuzzy dynamical systems are given

on the asymptotic efficiency of distributed estimation systems with constant modulus signals over multiple access channels a distributed estimation problem is considered with multiple access channels between sensors and a fusion center the sensors phase modulate their noisy observations before transmitting them to the fusion center where a signal parameter is estimated the asymptotic efficiency of this estimator is then determined by using two inequalities that relate the fisher information and the characteristic function a necessary and sufficient condition for equality is found for the first time in the literature the loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions it is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is gaussian

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

new approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces abstract this study considers the solvability of nonlocal problems for fuzzy differential systems under gh differentiability using some linear transforms we convert partial differential equations into fuzzy integral systems before some similar results are obtained for fuzzy wave equations with nonlocal conditions as a consequence we give some further estimates of the convergence rates of approximation schemes to exact solutions the main tool used in our proofs is based on perov s fixed point principle which is applied to vector valued integral operators these operators appear as the sum of two integral operators where one is fredholm type and the other is of a volterra type that depends on the restriction of the domain the novel feature of this study is that we combine the matrix convergent to zero technique with calculations of fuzzy valued functions in generalized fuzzy metric spaces some examples are presented to demonstrate our theoretical results