Asymptotically Optimal Learning in Fuzzy Environments

The paper continues our approach for measuring fuzzy values with a game of learning finite automata that are able to make an optimal choice among several alternatives. In principle, with such a game it is possible to measure any fuzzy values with certain precision. For the mentioned game we used previously a linear tactics automaton as the construction with asymptotically optimal behavior. However, our study showed that its asymptotical optimality is achieved under certain restriction concerning the fuzzy environment. In practice the mentioned automata allow to measure fuzzy value only when it is greater than 0.5. Presently, architecture has been chosen, referred to as trusting automata. The architecture of such an automaton has been proposed many years ago by Prof. V. I. Krinsky. In this paper we proved mathematically that the trusting automata do have the asymptotically optimal property for arbitrary values of memberships in the fuzzy environment. Consequently, the trusting automata may be used to measure arbitrary membership values in the game procedure described above without any restriction. © 2021, Springer Nature Switzerland AG.