It is widely recognized that when formulating problems involving two or more independent variables, partial differential equations are employed. These equations are prevalent across various engineering and scientific disciplines, serving as fundamental tools for simulating real-world physics-based phenomena. Information is gathered from diverse sources through experiments, measurements, and reconciling conflicting perspectives, which is then incorporated as inputs into our models based on differential equations. Due to the inherent imprecision in the collected data, the utilization of fuzzy sets and fuzzy numbers becomes necessary. This chapter presents advancements in methods for solving sets of partial differential equations within a fuzzy environment, accounting for different forms of uncertainty. There are distinct types of partial differential equations elliptical, parabolic, and hyperbolic. In this chapter, we discuss the elliptical form. The Gauss–Seidel method is examined and applied to solve elliptic differential equations under uncertain conditions. Our work is validated through an example involving a temperature grid problem, wherein we explore fuzzy solutions at various time scales. Discrepancies between the numerical and exact solutions are visually depicted in a table.