Measuring the similarity between zSlices general type-2 fuzzy sets with non-normal Secondary membership functions

McCulloch, Josie; Wagner, Christian

Abstract

This paper presents a method of measuring the similarity between general type-2 fuzzy sets that may have non-normal secondary membership functions. Such fuzzy sets are increasingly common in applications such as the modelling of the subjective meaning of linguistic terms by groups of people. By building upon existing similarity measures in the literature, which thus far cannot compare such fuzzy sets, we derive an extended similarity measure which can be applied to both normal and non-normal (in terms of the secondary membership functions) general type-2 fuzzy sets. We provide proofs that the proposed method follows all of the common properties of a similarity measure and demonstrations are given to compare the proposed method with others in the literature.

Citation

McCulloch, J., & Wagner, C. (2016). Measuring the similarity between zSlices general type-2 fuzzy sets with non-normal Secondary membership functions. In 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (461-468). https://doi.org/10.1109/FUZZ-IEEE.2016.7737723

• Conference Name: 2016 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2016
• Conference Location: Vancouver, BC, Canada
• Start Date: Jun 24, 2016
• End Date: Jul 29, 2016
• Acceptance Date: Mar 14, 2016
• Online Publication Date: Nov 10, 2016
• Publication Date: 2016
• Deposit Date: Jun 21, 2016
• Publicly Available Date: Nov 10, 2016
• Peer Reviewed: Peer Reviewed
• Pages: 461-468
• Book Title: 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-0627-4
• DOI: https://doi.org/10.1109/FUZZ-IEEE.2016.7737723
• Keywords: similarity measure, fuzzy sets, general type-2, zSlices, α-planes
• Public URL: https://nottingham-repository.worktribe.com/output/798382
• Publisher URL: https://ieeexplore.ieee.org/document/7737723/