Reversion of outputs of fuzzy discrete systems

The problem of reversion of unknown input sequences of fuzzy discrete systems by its observed outputs is investigated. As a mathematical model of fuzzy systems the fuzzy automata (FA) is used. This problem has been considered earlier for deterministic systems. Unambiguous solutions of the problem for such systems have been obtained using the model of finite automata, called the information lossless automata (IL-automata). In the article, for fuzzy discrete systems described by the FA model a similar problem is considered. Due to the specifics of functioning of such systems, unambiguous decoding of messages coming to their inputs is not always possible in principle. For this reason, there are problems of minimization of information lossless (according to various criteria) while solving the address problem. Automata are introduced, which allow solving such problems, called automata with minimized information lossless (FA MIL-automata). Solution of the problem of reversion for FA is a finite set of input words. Each such solution can be estimated according to various criteria — the cardinality of a set of words of the solution, the probability of appearance of these words on the system inputs, the complexity of obtaining different variants of the solutions. In order to minimize information lossless, the article formulates corresponding optimization tasks for FA and specifies possible ways of solving them. Different kinds of FA MIL-automata are considered. The obtained results show that the considered problems of reversion for fuzzy automata inputs are multi-criteria. It is known that solutions of such problems for discrete systems are traditionally evaluated by only one criterion.