Computing markings for fuzzy minimax nets over the Gödel structure

Fuzzy minimax nets were recently introduced as a tool for computing the greatest fuzzy bisimulation and simulation between two finite fuzzy graph-based structures. In this work, we provide an efficient algorithm for computing the greatest correct marking of a finite fuzzy minimax net over the Gödel structure. Its time complexity is linear in the number of nodes and positive edges in the input net. Building on this result, we derive the first algorithm with time complexity $O((m+n)n)$ for computing the greatest fuzzy directed simulation between two finite fuzzy graphs over the Gödel structure, where $n$ and $m$ denote the total numbers of vertices and positive edges, respectively, in the input graphs.