Morphismes based on compatible tolerances of finite automata

It is suggested a method of a construction with the help of some triple of tolerances defined on the sets of states, input and output symbols of an finite definite automaton an another automaton which is connected with the original automaton by a certain morphism. Considered construction generalizes the known method of finding of the homomorphic images of an automaton with the help of a triple of equivalences, which satisfies to the certain conditions.