Modified distance measure between fuzzy sets

Distance measure of fuzzy sets is an important tool to indicate the difference between fuzzy sets. Hatzimichailidis et al proposed a distance measure between fuzzy sets based on D - implication and a matrix norm. Although this distance measure considers the relationship between the elements, the measure is not satisfied the definition of distance measure between fuzzy sets. In this paper, we modify the distance measure between fuzzy sets. The modified distance measure is not only to meet the definition of a distance measure, but also to improve the efficiency of Hatzimichailidis's measure. A series of examples are used to demonstrate this phenomenon.