A representation of fuzzy numbers

Each fuzzy number can be written in a unique way as the sum of a symmetric and a skew fuzzy number. These two kinds of fuzzy numbers correspond bijectively to certain functions on the unit interval that are of bounded variation. These bijections give rise to a representation of fuzzy numbers by pairs of functions of bounded variation. As application, mathematical structures on the set of functions of bounded variation are transported to that of fuzzy numbers, making the set of fuzzy numbers into a complete metric space, a commutative semiring, and a commutative residuated lattice.