Fuzzy optimization issues have been discussed by many authors in recent articles, inspired by the concepts of generalized Hukuhara difference and generalized Hukuhara differentiability for one-dimensional functions from R to E, and have made considerable progress. In this paper, the concept of total generalized differentiability is introduced by using the concept of generalized difference from R^n to E for multi-dimensional mappings. Furthermore, the total generalized differentiability of the above is also examined and then the concept of directional generalized differentiability and Partial generalized differentiability for fuzzy multi-dimensional mappings is defined and discussed in detail. In addition, directional generalized differentiability and Partial generalized differentiability are expressed in terms of level-wise generalized differentiability. Also, the properties and the relationship between them are discussed. Finally, the relationships between total generalized differentiability, directional generalized differentiability and Partial generalized differentiability are shown to illustrate the power and ability of relationships between them by mentioning some examples.

In this paper, we study first order linear fuzzy differential equations with fuzzy coefficient and initial value. We use the generalized differentiability 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 research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations.The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [1], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability.

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example [5, 6]), but these methods have been done for fuzzy problems with triangular fuzzy initial value. Therefore by extending the r-cut solutions of the original problem we will obviate this deficiency. The presented idea is based on: if a second order fuzzy differential equation satisfy the Lipschitz condition then the initial value problem has a unique solution on a specific interval, therefore our main purpose is to present a method to find an interval on which the solution is valid.

An analytical fuzzy solution is achieved by means of the fuzzy d’, Alembert formula for the fuzzy one-dimensional homogeneous wave equation in a half-line considering the generalized Hukuhara Partial differentiability of the solution. In the current article, the exclusive solution and the stability of the homogeneous fuzzy wave equations are brought into existence. Eventually, given the various instances represented, the efficacy and accuracy of the method are scrutinized.

In this paper, a one-dimensional homogeneous fuzzy wave equation is solved with an analytical procedure using the fuzzy D’Alembert method by considering the generalized differentiability. Then, some definitions related to fuzzy numbers, theorems, and used lemmas are given. Additionally, the physical interpretation and dependency domain of fuzzy wave solutions are investigated by providing examples, where the fuzzy wave solutions are in the form of fuzzy standing, traveling, and recursive waves. The abstract of this article was presented in the 9th Iranian Joint Congress on Fuzzy and Intelligent Systems (2022, March 2-4), Bam, Kerman, Iran

In this paper, the (m+1) -step Adams-Bashforth, Adams-Moulton, and Predictor Corrector methods are used to solve first-order fuzzy linear ordinary differential equations. The concepts of fuzzy interpolation and generalized strongly differentiability are used, to obtain general algorithms. Each of these algorithms has advantages over current methods. Moreover, for each algorithm a convergence formula can be obtained. The convergence of these methods is proven in detail. Finally, these methods are illustrated using examples of initial value problems.

In this work, the Homotopy Perturbation Method (HPM) is implemented for finding approximate solution of the Fuzzy Initial Value Problem (FIVP) involving generalized differentiability.This method is based upon homotopy perturbation theory. The comparison of the exact solution with approximate solution obtained by HPM is in detail. The results reveal that the method is very effective and simple.