Semi-commutative closure operators. Let us say that the closure operators $f$ and $g$ on a p.o.set $P$ are semi-commutative iff $fg\leq gf$. Fuzzification of the corresponding closure spaces when $P$ is the complete lattice of the subsets of a set $S$. Case where $S$ is a semi-lattice. Case where $S$ is the square of a set $E$.