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A bidirectional subsethood based similarity measure for fuzzy sets

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

A bidirectional subsethood based similarity measure for fuzzy sets Thumbnail


Shaily Kabir

Timothy C. Havens

Derek T. Anderson


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.


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
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Contract Date Oct 1, 2018


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