Approximate Bisimulations for Fuzzy Automata Over Complete Heyting Algebras

In this article, we define
$\lambda$
-approximate simulations and bisimulations for fuzzy automata over complete Heyting algebras. The value
$\lambda$
presents the degree of language similarity or equality between observed fuzzy automata. Algorithms for computing the greatest
$\lambda$
-approximate simulations and bisimulations are given. We show that
$\lambda$
-approximate simulations and bisimulations on a fuzzy automaton can be effectively used for factorization of fuzzy automata. We present the algorithm that splits the interval of the degrees of language similarity or equality into subintervals with the same minimal corresponding factor fuzzy automata.