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The measure of distance between two fuzzy sets is a fundamental tool withinfuzzy set theory. However, current distance measures within the literature donot account for the direction of change between fuzzy sets; a useful concept ina variety of applications, such as Computing With Words. In this paper, wehighlight this utility and introduce a distance measure which takes thedirection between sets into account. We provide details of its application fornormal and non-normal, as well as convex and non-convex fuzzy sets. Wedemonstrate the new distance measure using real data from the MovieLens datasetand establish the benefits of measuring the direction between fuzzy sets.

Measuring the Directional Distance Between Fuzzy Sets