Fuzzy Minimax Nets

In this article, we introduce fuzzy minimax nets as a novel tool to compute the greatest fuzzy bisimulation/simulation between two finite fuzzy labeled graphs. Fuzzy labeled graphs are a universal data structure for representing fuzzy systems, such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks, and fuzzy interpretations in description logic. The greatest fuzzy bisimulation between two such systems characterizes the similarity between their states, actors, or individuals. Using fuzzy minimax nets, we design the first algorithms for the mentioned computational problems in the case of using the product t-norm, as well as the first algorithms whose complexity order does not depend on the fuzzy values occurring in the inputs for those problems in the case of using the Łukasiewicz t-norm.