The choice of the operators min and max and the complementation with 1 respectively to define the intersection, the union and the complement of fuzzy subsets is justified by the fact that these operators preserve almost all the structure of set theory. It has been shown that they are the most satisfactory operators for this preservation.

Other operators are nevertheless possible if we are not as demanding about crisp properties or if there are special reasons to want other behaviour for the operations on fuzzy subsets.