Analysis of the Behavior of One Finite Automaton in a Stationary Fuzzy Environment

The behavior of finite automaton with one input and two outputs in a stationary fuzzy environment is considered. The structure of the considered finite automaton is built on the basis of the well-known statistical rule from the theory of repeating events: "either a series of successes of length m, or a series of failures of length l." The fuzzy environment rewards or punishes the automaton for the performed action through some fixed membership functions. It is assumed that the behavior of an automaton in a fuzzy environment is described by a generalized ergodic Markov chain and using the property of such chains it is shown that the automaton in question under certain conditions on a fuzzy punishment function and on the length of a series of successes or failures is trainable.