Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets
Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we intro...
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Published: |
2013
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/3339/ |
| _version_ | 1848791003984560128 |
|---|---|
| author | McCulloch, Josie Wagner, Christian Aickelin, Uwe |
| author_facet | McCulloch, Josie Wagner, Christian Aickelin, Uwe |
| author_sort | McCulloch, Josie |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Similarity measures provide one of the core tools
that enable reasoning about fuzzy sets. While many types of
similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures
of similarity which preserve all the common properties (i.e.
reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures. |
| first_indexed | 2025-11-14T18:21:36Z |
| format | Conference or Workshop Item |
| id | nottingham-3339 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:21:36Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-33392020-05-04T20:20:35Z https://eprints.nottingham.ac.uk/3339/ Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets McCulloch, Josie Wagner, Christian Aickelin, Uwe Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures. 2013 Conference or Workshop Item PeerReviewed McCulloch, Josie, Wagner, Christian and Aickelin, Uwe (2013) Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets. In: IEEE International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013), 7-10 July 2013, Hyderabad, India. Fuzzy Logic http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6622408 |
| spellingShingle | Fuzzy Logic McCulloch, Josie Wagner, Christian Aickelin, Uwe Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title | Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title_full | Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title_fullStr | Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title_full_unstemmed | Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title_short | Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| title_sort | extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets |
| topic | Fuzzy Logic |
| url | https://eprints.nottingham.ac.uk/3339/ https://eprints.nottingham.ac.uk/3339/ |