Qualitative analysis of symmetric fuzzy stochastic differential equations

In this paper, a special approach to stochastic differential equations is explored. Specifically, the values of the mappings involved are fuzzy sets, rather than the usual single values on the real line. Additionally, the equations under consideration are symmetric, meaning that the terms of drift and diffusion appear on both sides of the equation, which is crucial for the properties of the solutions. The primary goal of this paper is to establish certain qualitative results, such as the existence of a unique solution and stability of the solution. These results are obtained under the assumption that the coefficients of the equation satisfy a condition that is weaker than the standard Lipschitz condition. It is also noted that the results obtained can be applied to symmetric fuzzy random integral equations and deterministic symmetric fuzzy integral equations.