Approximate children fuzzy automata over the product structure

Abstract

The problem of determinization of fuzzy automata over the product structure was unsolvable in the general case. Therefore, the approximate determinizations of fuzzy finite automata over the product structure were explored in [14] by using a parametric modification of the product t-norm
called truncated product structure. Although these methods provide minimal crisp-deterministic and fuzzy-deterministic finite automata, they do not always enhance to be highly effective. To address this limitation, we introduce the new approach which is based on the construction of the so-called Children automaton of a fuzzy finite automaton [10] using approximate weak simulations on a fuzzy automaton [15]. The new determinization procedure is also approximate determinization method, which is performed by transferring the fuzzy automaton from the product structure to the truncated product one. The truncated structure is residuated and possesses a locally finite semiring reduct, facilitating the efficient computation of approximate weak simulations. These simulations
enable significant improvements in the approximate determinization process.