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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

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.

Citation

McCulloch, J., Wagner, C., & Aickelin, U. Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

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 http://eprints.nottingham.ac.uk/id/eprint/3339
Publisher URL http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6622408
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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