Information retrieval from interval-valued fuzzy automata through K operators

Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s Kα operators allow us to retrieve the information given by the transition functions of the interval-valued automata. Moreover, we analyze the functorial nature of these operators and characterize those Kα operators that provide a fuzzy transformation semigroup from an intervalvalued one.