In this paper, we apply the shooting method for solving the Fuzzy Boundary Value Differential Equations (FBVDEs) of the second order under generalized differentiability. By this method an FBVDE of …
In this paper, we apply the shooting method for solving the Fuzzy Boundary Value Differential Equations (FBVDEs) of the second order under generalized differentiability. By this method an FBVDE of the second order will be replaced with two fuzzy initial value differential equations and the answers of each of them are obtained by the Adomian method. Finally via linear combination of their solutions, the fuzzy solution will be obtained.
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. …
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data are given.
In this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. We use the generalized dierentiability concept and apply the exponent matrix to present …
In this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. We use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate our results.
In this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. We use the generalized dierentiability concept and apply the exponent matrix to present …
In this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. We use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. Finally, one example is given to illustrate our results.
In this paper, we apply the shooting method for solving the Fuzzy Boundary Value Differential Equations (FBVDEs) of the second order under generalized differentiability. By this method an FBVDE of …
In this paper, we apply the shooting method for solving the Fuzzy Boundary Value Differential Equations (FBVDEs) of the second order under generalized differentiability. By this method an FBVDE of the second order will be replaced with two fuzzy initial value differential equations and the answers of each of them are obtained by the Adomian method. Finally via linear combination of their solutions, the fuzzy solution will be obtained.
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. …
Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data are given.
In this paper, an analytic method (eigenvalue–eigenvector method) for solving nth order fuzzy differential equations with fuzzy initial conditions is considered. In this method, three cases are introduced, in each …
In this paper, an analytic method (eigenvalue–eigenvector method) for solving nth order fuzzy differential equations with fuzzy initial conditions is considered. In this method, three cases are introduced, in each case, it is shown that the solution of differential equation is a fuzzy number. In addition, the method is illustrated by solving several numerical examples.
In this survey main results in classical approximation theory such as Weierstrass and Stone and Weierstrass-type results, quantitative estimates in approximation by polynomials, interpolation results, best approximation results, etc. to …
In this survey main results in classical approximation theory such as Weierstrass and Stone and Weierstrass-type results, quantitative estimates in approximation by polynomials, interpolation results, best approximation results, etc. to fuzzy setting are generalized. Besides known results, several new results are proved.
A fuzzy mapping from X to Y is a fuzzy set on X × Y. The concept is extended to fuzzy mappings of fuzzy sets on X to Y, fuzzy …
A fuzzy mapping from X to Y is a fuzzy set on X × Y. The concept is extended to fuzzy mappings of fuzzy sets on X to Y, fuzzy function and its inverse, fuzzy parametric functions, fuzzy observation, and control. Set theoretical relations are obtained for fuzzy mappings, fuzzy functions, and fuzzy parametric functions. It is shown that under certain conditions a precise control goal can be attained with fuzzy observation and control as long as the observations become sufficiently precise when the goal is approached.
Traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations (DEs). A recent interpretation in terms of differential inclusions, expressed level setwise, …
Traditional formulations of fuzzy differential equations do not reproduce the rich and varied behavior of crisp differential equations (DEs). A recent interpretation in terms of differential inclusions, expressed level setwise, overcomes this deficiency and opens up for profitable investigation such properties as stability, attraction, periodicity, and the like. This is especially important for investigating continuous systems which are uncertain or incompletely specified. This paper studies attractors of fuzzy DEs in terms of cocycles and encompasses both the time-dependent and autonomous cases.
In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having …
In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability. Keywords—Fuzzy-valued function, Fuzzy initial value problem, Strongly generalized differentiability, Adomian decomposition method
We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret th-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy …
We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret th-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We present an example of a linear second-order fuzzy differential equation with initial conditions having four different solutions.