Approximate children fuzzy automata over the product structure

The general problem of determinization of fuzzy automata over the product structure is unsolvable, which necessitates the use of approximate methods. This paper introduces a new approach to the approximate determinization of fuzzy finite automata by utilizing a transition to a different structure, known as the truncated product structure. This structure is residuated and has a locally finite semiring reduct, which enables efficient computation. The proposed method constructs a so-called Children automaton and employs approximate weak simulations to achieve more effective determinization. In comparison to existing techniques, this approach significantly enhances the performance and precision of the resulting crisp-deterministic fuzzy automata.