An implementation of digitised fuzzy numbers on quantum computers is suggested. It is shown that due to the famous quantum parallelism quantum computers can operate "globally" on whole membership functions of fuzzy numbers, not by calculating them "point by point" as classical computers do, which leads to the considerable decrease in the number of operations involved in storing and calculating fuzzy numbers. In particular, we show that the standard quantum adder is perfectly suited to realize Kaufmann-like addition of fuzzy numbers encoded in the form of suitably prepared superpositions of input qubits and that it does it in a single run. Although this computational gain is to some extent lost while reading the output, which has to be done statistically on the enough big sample of single runs of the adder, suitably chosen method of defuzzyfication allows to save a great deal of the original gain.