The Behavior of a Finite-State Automaton in a Fuzzy Environment: Theory and Applications

摘要

The behavior of M.L. Tsetlin's automaton with linear tactics in a fuzzy environment is considered. The behavior of such an automaton was previously studied in a random environment, where the classical apparatus of probabilistic Markov chains could be used. This work is based on two results that were previously obtained by the author, namely, a theory that generalizes Markov chains and the axiomatic description of operations with fuzzy evidence. The explicit formulas for describing the behavior of the automaton that were obtained in this paper suggest a deep analogy with the results of M.L. Tsetlin. In particular, it is shown that this automaton in a fuzzy environment also has the property of asymptotic optimality. As an application, we discuss the possibility of using this property to measure membership functions for values that are similar to singletons or point functions. It is concluded that the results that are obtained in this paper make it possible to construct an analogue of the statistics collection procedure for the field of fuzzy systems.