Qualitative behavior of a higher-order fuzzy difference equation

Abstract

In this paper, we investigate the qualitative behavior of the fuzzy difference equation $ \begin{equation*} z_{n+1} = \frac{Az_{n-s}}{B+C\prod\limits_{i = 0}^{s}z_{n-i}} \end{equation*} $ where $ n\in \mathbb{N}_{0} = \; \mathbb{N} \cup \left\{ 0\right\}, \; (z_{n}) $ is a sequence of positive fuzzy numbers, $ A, B, C $ and the initial conditions $ z_{-j}, \; j = 0, 1, ..., s $ are positive fuzzy numbers and $ s $ is a positive integer. Moreover, two examples are given to verify the effectiveness of the results obtained.

Keywords

• fuzzy difference equations
• existence of positive solutions
• boundedness
• convergence