The Behavior of Some Finite Automata in a Non-stationary Fuzzy Environment

Abstract

The behavior of two types of finite automata in a non-stationary fuzzy environment is considered, which, depending on the states of the automata, encourages or punishes them with some fixed membership functions. It is assumed that the behavior of automata in a fuzzy environment is described by generalized ergodic Markov chains and, using the property of such chains, it is shown that the considered automata, under certain conditions on fuzzy punishment functions, are learners and predominantly perform the action for which the sum of fuzzy functions of belonging to punishment is minimal.