We propose a generalization of the Hukuhara di¤erence. First, the case of compact convex sets is examined; then, the results are applied to generalize the Hukuhara di¤erence of fuzzy numbers, using their compact and convex level-cuts. Finally, a similar approach is suggested to attempt a generalization of division for real intervals.

In this article, the concepts of gH-subgradient and gH-subdifferential interval-valued functions are illustrated. Several important characteristics a convex function, e.g., closeness, boundedness, chain rule, etc. studied. Alongside, we prove that gH-differentiable function contains only gH-gradient. It is observed directional gH-derivative maximum all products between gH-subgradients direction...

In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examp...

*Correspondence: [email protected] 1Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam Full list of author information is available at the end of the article Abstract In this paper the second-order random fuzzy differential equations (SRFDEs) under generalized Hukuhara differentiability are introduced. Un...

The fuzzy fractional differential equation explains more complex real-world phenomena than the does. Therefore, numerous techniques have been timely derived to solve various time-dependent models. In this paper, we develop two compact finite difference schemes and employ resulting obtain a certain solution for time-fractional convection–diffusion equation. Then, by making use of Caputo derivati...

The main focus of this paper is to develop an efficient analytical method obtain the traveling wave fuzzy solution for generalized Hukuhara conformable fractional equations by considering type differentiability solution. To achieve this, derivative based on defined, and several properties are brought topic, such as switching points chain rule. After that, a new applied find exact solutions two ...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

This article introduces the concept of weak sharp minima for convex interval-valued functions. To solve constrained and unconstrained IOPs by WSM, we provide primal dual characterizations set WSM. The characterization is given in terms gH-directional derivatives. On other hand, to derive characterizations, propose notions support function a subset $$I({\mathbb {R}})^{n}$$ gH-subdifferentiabilit...

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Huku...