On the composition of fuzzy power relations ?
This paper deals with the powering of binary fuzzy relations (i.e. lifting a fuzzy relation R defined on a set X  to the relation R+ R + defined on the set F(X) F ( X ) of all fuzzy subsets of X ). We prove that for any complete residuated lattice L L , the composition of the powers of two L L -relations is always a subset of the power of their composition. Answering to a question posed by Georgescu, we prove that the converse is not always true. We prove that the composition of the powers of two L L -relations is equal to the power of their composition if and only if L L is a Heyting algebra.
fuzzy relation residuated lattice power structure composition of relations