  The measure of distance between two fuzzy sets is a fundamental tool within
fuzzy set theory, however, distance measures currently within the literature
use a crisp value to represent the distance between fuzzy sets. A real valued
distance measure is developed into a fuzzy distance measure which better
reflects the uncertainty inherent in fuzzy sets and a fuzzy directional
distance measure is presented, which accounts for the direction of change
between fuzzy sets. A multiplicative version is explored as a full maximal
assignment is computationally intractable so an intermediate solution is
offered.
