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

McCulloch, Josie; Wagner, Christian; Aickelin, Uwe

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. Presented at IEEE International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013)

• 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.