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, July). A Bidirectional Subsethood Based Similarity Measure for Fuzzy Sets. Presented at 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Rio de Janeiro

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• Start Date: Jul 8, 2018
• End Date: Jul 13, 2018
• Online Publication Date: Oct 14, 2018
• Deposit Date: Nov 22, 2023
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• Book Title: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-6021-4
• DOI: https://doi.org/10.1109/fuzz-ieee.2018.8491669
• Public URL: https://keele-repository.worktribe.com/output/643478