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Measuring the Directional Distance Between Fuzzy Sets

lib:fdca4db1a100668c (v1.0.0)

Authors: Josie McCulloch,Christian Wagner,Uwe Aickelin
ArXiv: 1308.5137
Document:  PDF  DOI 
Abstract URL: http://arxiv.org/abs/1308.5137v1


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.

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