Processing of qualitative data

To overcome some problems with deep understanding of fuzzy values, certain learning finite automaton was put into a fuzzy environment. Previously such a device has been studied in the probabilistic environment, where the classic technique of standard Markov chains was applicable. The new study became possible due to several previous results by the present author, namely the axiomatic of fuzzy evidences accumulation and the theory of generalized Markov chains. The mathematical results, obtained in the paper, prove that the learning automaton has the property of asymptotic optimality. This property is proposed to be used for measuring membership. The obtained results might lead to a fuzzy measurement procedure resembling statistics developed in probability area. © Springer International Publishing Switzerland 2016.