Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets
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.
Keywords
Cite
@article{arxiv.1308.5136,
title = {Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets},
author = {Josie McCulloch and Christian Wagner and Uwe Aickelin},
journal= {arXiv preprint arXiv:1308.5136},
year = {2016}
}
Comments
International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013)