A bidirectional subsethood based similarity measure for fuzzy sets

Kabir, Shaily; Wagner, Christian; Havens, Timothy C.; Anderson, Derek T.

Abstract

Similarity measures are useful for reasoning about fuzzy sets. Hence, many classical set-theoretic similarity measures have been extended for comparing fuzzy sets. In previous work, a set-theoretic similarity measure considering the bidirectional subsethood for intervals was introduced. The measure addressed specific concerns of many common similarity measures, and it was shown to be bounded above and below by Jaccard and Dice measures respectively. Herein, we extend our prior measure from similarity on intervals to fuzzy sets. Specifically, we propose a vertical-slice extension where two fuzzy sets are compared based on their membership values.We show that the proposed extension maintains all common properties (i.e., reflexivity, symmetry, transitivity, and overlapping) of the original fuzzy similarity measure. We demonstrate and contrast its behaviour along with common fuzzy set-theoretic measures using different types of fuzzy sets (i.e., normal, non-normal, convex, and non-convex) in respect to different discretization levels.

Citation

Kabir, S., Wagner, C., Havens, T. C., & Anderson, D. T. (2018). A bidirectional subsethood based similarity measure for fuzzy sets. In N/A

• Conference Name: IEEE World Congress on Computational Intelligence (WCCI 2018)
• Start Date: Jul 8, 2018
• End Date: Jul 13, 2018
• Acceptance Date: Mar 15, 2018
• Online Publication Date: Jul 13, 2018
• Publication Date: Jul 13, 2018
• Deposit Date: Oct 1, 2018
• Publicly Available Date: Oct 1, 2018
• Book Title: N/A
• Chapter Number: N/A
• ISBN: N/A
• Public URL: https://nottingham-repository.worktribe.com/output/1139971
• Related Public URLs: http://www.ecomp.poli.br/~wcci2018/
• Additional Information: © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
• Contract Date: Oct 1, 2018