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Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

McCulloch, Josie; Wagner, Christian; Aickelin, Uwe

Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets Thumbnail


Authors

Josie McCulloch

Uwe Aickelin



Abstract

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.

Conference Name IEEE International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013)
End Date Jul 10, 2013
Deposit Date Sep 29, 2014
Peer Reviewed Peer Reviewed
Keywords Fuzzy, Logic
Public URL https://nottingham-repository.worktribe.com/output/1004937
Publisher URL http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6622408
Additional Information Published in: IEEE International Conference on Fuzzy Systems (FUZZ) 2013 (ISBN: 9781479900206 ; doi: 10.1109/FUZZ-IEEE.2013.6622408). © IEEE.

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