Resumen: In a previous paper [10] we explored the no-
tion of coherent fuzzy consequence operator.
It is well-known that the operator induced
by a fuzzy preorder through Zadeh's compo-
sitional rule is always a coherent fuzzy con-
sequence operator. It is also known that
the relation induced by a fuzzy consequence
operator is a fuzzy preorder if such opera-
tor is coherent [7]. Fuzzy closing operators
of mathematical morphology can be consid-
ered as fuzzy consequence operators. In [12]
we showed that they are coherent operators.
The aim of this paper is to analyze the rela-
tions between both classes of operators and
the class of all fuzzy preorders in order to
translate well know properties from Approxi-
mate Reasoning to the one of Image Process-
ing.