Measuring the Directional Distance Between Fuzzy Sets
This provides a more nuanced tool for fuzzy set theory practitioners, though it appears incremental as it extends existing distance concepts rather than introducing a new paradigm.
The paper addresses the limitation of existing fuzzy set distance measures that ignore directionality, introducing a new directional distance measure applicable to various fuzzy set types. It demonstrates the measure's utility using the MovieLens dataset, showing benefits for applications like Computing With Words.
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory. However, current distance measures within the literature do not account for the direction of change between fuzzy sets; a useful concept in a variety of applications, such as Computing With Words. In this paper, we highlight this utility and introduce a distance measure which takes the direction between sets into account. We provide details of its application for normal and non-normal, as well as convex and non-convex fuzzy sets. We demonstrate the new distance measure using real data from the MovieLens dataset and establish the benefits of measuring the direction between fuzzy sets.