In this paper, we introduce fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (SFBM) which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The SFBM is an extension of the Brownian motion that retains many properties of fractional Brownian motion (FBM), but not the stationary increments. This property makes SFBM a possible candidate for models that include long-range dependence, self-similarity, and non-stationary increments which is suitable for the construction of stochastic models in finance and non-stationary queueing systems. We apply an approximation method to stochastic integrals, and a decomposition of the SFBM to find the existence and uniqueness of the solutions.

在本文中，我们引入了由次分数布朗运动（SFBM）驱动的模糊随机微分方程（FSDE），用于描述同时受到随机性和模糊性影响的现象。SFBM 是布朗运动的扩展，保留了分数布朗运动 (FBM) 的许多属性，但不保留平稳增量。这一特性使 SFBM 成为包含长程依赖、自相似性和非平稳增量的模型的可能候选者，适用于金融和非平稳排队系统中随机模型的构建。我们对随机积分应用近似方法，并对 SFBM 进行分解，以找出解的存在性和唯一性。