Behavior of finite automata in fuzzy environment: theory and applications

The behavior of Tsetlin’s linear automaton being put in a fuzzy environment is considered. Previously it has been studied in random environments, the latter permitting the use of classic Markov Chains. Our paper relies on the two theoretical results obtained by the present author before, namely the theory of Generalized Markov Chains (Markov–Stefanuk chains) and the axiomatic description of the operations with fuzzy evidences. The explicit expressions obtained in the present paper demonstrate a deep analogy with Tsetlin’s results. Besides, a possibility of the use of asymptotic optimality for measuring the membership functions for singletons are discussed. It is concluded that the results open a possibility to create an analog of the collection of statistics for the area of fuzzy systems.