Relationship Between Bede-Gal Differentiable Set-Valued Functions and Their Associated Support Functions

Abstract

In this study, we adapt the concept of the Bede-Gal derivative, which was initially suggested for fuzzy number-valued functions, to set-valued functions. We use an example to demonstrate that this concept overcomes some of the shortcomings of the Hukuhara derivative.

We prove some properties of Bede-Gal differentiable set-valued functions. We also study the relationship between a Bede-Gal differentiable set-valued function and its value's support function, which we call the associated support function. We provide examples of set-valued functions that are not Bede-Gal differentiable whereas their associated support functions are differentiable. We also present some applications of the Bede-Gal derivative to solving set-valued differential equations. (C) 2015 Elsevier B.V. All rights reserved.