Measuring the directional distance between fuzzy sets

McCulloch, Josie; Wagner, Christian; Aickelin, Uwe

Abstract

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.

Citation

McCulloch, J., Wagner, C., & Aickelin, U. (2013). Measuring the directional distance between fuzzy sets.

• Conference Name: UKCI 2013, the 13th Annual Workshop on Computational Intelligence
• End Date: Sep 11, 2013
• Publication Date: Jan 1, 2013
• Deposit Date: Sep 29, 2014
• Publicly Available Date: Sep 29, 2014
• Peer Reviewed: Peer Reviewed
• Keywords: Fuzzy, Logic
• Public URL: https://nottingham-repository.worktribe.com/output/1004954
• Publisher URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6651285
• Additional Information: Published in: 2013 13th UK Workshop on Computational Intelligence (UKCI): UKCI 2013 / editors: Yaochu Jin, Spencer Angus Thomas. Piscataway, NJ : IEEE, 2013. (ISBN: 9781479915668) pp. 38-45 (doi: 10.1109/UKCI.2013.6651285 ); © IEEE 2013