Common fixed point theorem in partially ordered intuitionistic $\mathcal{L}$-fuzzy vector metric spaces

Abstract This paper formulates an intuitionistic non-Archimedean $\mathcal{L}$ L -fuzzy vector metric space in the context of intuitionism, Archimedeanism, and order structures. In doing so, we derive several essential auxiliary properties, such as left (right)-order continuity and orthogonality. Furthermore, a common fixed point theorem for commuting mappings is established in the space, equipped with a partial order. The method consists of synthesizing the iterative scheme of the contraction mapping principle with the monotone argument.