Measuring the directional distance between fuzzy sets

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 p...

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Bibliographic Details
Main Authors: McCulloch, Josie, Wagner, Christian, Aickelin, Uwe
Format: Conference or Workshop Item
Published: 2013
Subjects:
Online Access:https://eprints.nottingham.ac.uk/3340/
Description
Summary: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.