A bidirectional subsethood based similarity measure for fuzzy sets
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...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2018
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| Online Access: | https://eprints.nottingham.ac.uk/55101/ |
| _version_ | 1848799118168686592 |
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| author | Kabir, Shaily Wagner, Christian Havens, Timothy C. Anderson, Derek T. |
| author_facet | Kabir, Shaily Wagner, Christian Havens, Timothy C. Anderson, Derek T. |
| author_sort | Kabir, Shaily |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:30:35Z |
| format | Conference or Workshop Item |
| id | nottingham-55101 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:30:35Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-551012018-10-10T10:47:13Z https://eprints.nottingham.ac.uk/55101/ A bidirectional subsethood based similarity measure for fuzzy sets Kabir, Shaily Wagner, Christian Havens, Timothy C. Anderson, Derek T. 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. 2018-07-13 Conference or Workshop Item PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/55101/1/A%20Bidirectional%20Subsethood%20Based%20Similarity%20Measure%20for%20Fuzzy%20Sets.pdf Kabir, Shaily, Wagner, Christian, Havens, Timothy C. and Anderson, Derek T. (2018) A bidirectional subsethood based similarity measure for fuzzy sets. In: IEEE World Congress on Computational Intelligence (WCCI 2018), 8-13 July 2018, Rio de Janeiro, Brazil. |
| spellingShingle | Kabir, Shaily Wagner, Christian Havens, Timothy C. Anderson, Derek T. A bidirectional subsethood based similarity measure for fuzzy sets |
| title | A bidirectional subsethood based similarity measure for fuzzy sets |
| title_full | A bidirectional subsethood based similarity measure for fuzzy sets |
| title_fullStr | A bidirectional subsethood based similarity measure for fuzzy sets |
| title_full_unstemmed | A bidirectional subsethood based similarity measure for fuzzy sets |
| title_short | A bidirectional subsethood based similarity measure for fuzzy sets |
| title_sort | bidirectional subsethood based similarity measure for fuzzy sets |
| url | https://eprints.nottingham.ac.uk/55101/ |