Analysis of a Finite-Nonstationary Fuzzy Automaton

The work proposes a solution to the problem of analyzing a finite- nonstationary fuzzy automaton defined over a distributive lattice on a closed interval and maximum and minimum operations, with the notion of fuzzy language represented by this automaton defined for this automaton. The problem is solved by a justified transition to a stationary automaton model, since for stationary fuzzy automata there exist methods, as a result of which it is possible to find a regular expression of the fuzzy language generated by such an automaton. To make the transition, the notion of equivalence of two models in terms of the languages generated is defined. The finite- nonstationary-in-time model is much more complicated than the previously studied stationary and periodically nonstationary models, it meets to a greater extent the paradigm of automatic control of process elements under conditions of parallelism and asynchronous interaction with other processes, or when the information about the functioning of some objects is partially known or not known at all.