Existence of Hukuhara differentiability of fuzzy-valued functions

TL;DR

This paper investigates the conditions under which fuzzy-valued functions are Hukuhara differentiable, exploring higher-order differentiability, effects of fuzzy modeling, and comparing gH- and H-differentiability through examples.

Contribution

It provides a detailed analysis of Hukuhara differentiability for fuzzy-valued functions, including higher-order cases and the impact of fuzzy modeling, with comparative insights on gH- and H-differentiability.

Findings

Fuzzy-valued functions can be one, two, or n-times H-differentiable.

Fuzzy modeling influences the existence of Hukuhara differentiability.

gH-differentiability has distinct properties compared to H-differentiability.

Abstract

In this paper, we discuss existence of Hukuhara differentiability of fuzzy-valued functions. Several examples are worked out to check that fuzzy-valued functions are one time, two times and n-times H-differentiable. We study the effects of fuzzy modelling on existence of Hukuhara differentiability of fuzzy-valued functions. We discuss existence of gH-differentiability and its comparison with H-differentiability.