Minimization of the number of states of a fuzzy automaton using interval pattern concepts

Relationship between the problem of minimization of the number of states of fuzzy automata and the problem of mining of interval pattern concepts with maximum extent is considered. The clustering method based on interval pattern concept mining combines states of a fuzzy automaton into subsets with similar patterns of confidence of transition into other states, where patterns are considered close to each other if the distance between them is bounded by a predetermined parameter $\sigma$. It is shown that for a certain type of fuzzy transition matrices the behavior of the original fuzzy automaton, as well as the behavior of the minimized one, eventually stabilizes. Moreover, it is proved that the membership value of each word recognized by the fuzzy automaton does not decrease after minimization. This fact allows comparing the fuzzy language recognized by the original automaton and the language recognized by the minimized automaton.